triangularDisp.py

#-*- coding: utf-8 -*-

import copy
import numpy as np
from matplotlib.path import Path

# Translated from Brendan Meade's MATLAB code, citation:
#
# Brendan J. Meade, Algorithms for the calculation of exact 
# displacements, strains, and stresses for Triangular Dislocation 
# Elements in a uniform elastic half space, Computers & 
# Geosciences (2007), doi:10.1016/j.cageo.2006.12.003.

def strain(sx, sy, sz, vertices, ss, ds, ts, nu=0.25):
    """
    Computes the strain tensor at an observation point due to slip on one
    triangular patch at depth.

    Args:
        * sx        : x coordinates of ground points
        * sy        : y coordinates of ground points
        * sz        : z coordinates of ground points
        * ss        : amount of strike-slip
        * ds        : amount of dip-slip
        * ts        : amount of tensile/opening-slip
        * nu        : Poisson's ratio
        
    Returns:
        * Strain    : 3x3xn strain tensor
    """
    
    # Modify input vertices by appending first point to end
    verts = copy.deepcopy(vertices)
    verts.append(verts[0])
    verts = [np.array(p) for p in verts]
    p1, p2, p3 = verts[:3]

    # Compute normal vector
    dx1 = p2 - p1
    dx2 = p3 - p1 
    normVec = np.cross(dx1, dx2)
    normVec /= np.linalg.norm(normVec)
    # Enforce clockwise circulation
    if normVec[2] < 0: 
        normVec *= -1.0
        # Update vertices by swapping 2nd and 3rd vertices
        verts = [p1, p3, p2, p1]
    
    # Compute slip vector in global coordinates
    angle = np.arctan2(normVec[1], normVec[0])
    strikeVec = np.array([-np.sin(angle), np.cos(angle), 0.0])
    dipVec = np.cross(normVec, strikeVec)
    # Change sign of slip components to be consistent with Okada (BVR)
    slipComp = np.array([-ss, -ds, -ts])
    slipVec = np.dot(np.column_stack((strikeVec, dipVec, normVec)), slipComp)

    # Allocate solution array
    Strain = np.zeros((3,3,len(sx)))
    
    # Some number 
    halfPi = 0.5 * np.pi

    # Loop over legs of triangle
    for iTri in range(3):
    
        # Get the vertices of the leg
        p1, p2 = verts[iTri], verts[iTri+1]
        x1, y1, z1 = p1
        x2, y2, z2 = p2
    
        # Calculate strike and dip of current leg
        dx, dy = x2 - x1, y2 - y1
        strike = np.arctan2(dy, dx)
        segMapLength = np.sqrt(dx**2 + dy**2)
        rx, ry = RotateXyVec(dx, dy, -strike)
        dip = np.arctan2(z2 - z1, rx)
    
        if dip >= 0.0:
            beta = halfPi - dip
            if beta > halfPi:
                beta = halfPi - beta
        else:
            beta = -1.0 * (halfPi + dip)
            if beta < -halfPi:
                beta = halfPi - abs(beta)

        ssVec = np.array([np.cos(strike), np.sin(strike), 0.0])
        tsVec = np.array([-np.sin(strike), np.cos(strike), 0.0])
        dsVec = np.cross(ssVec, tsVec)
        lss = np.dot(slipVec, ssVec)
        lts = np.dot(slipVec, tsVec)
        lds = np.dot(slipVec, dsVec)
        
        if (abs(beta) > 1.0e-6) and (abs(beta - np.pi) > 1.0e-6):
            
            # First dislocation
            sx1, sy1 = RotateXyVec(sx - x1, sy - y1, -strike)
            a11, a22, a33, a12, a13, a23 = advs(sx1, sy1, sz - z1, z1, beta, nu, lss, lts, lds)
            
            # Second dislocation 
            sx2, sy2 = RotateXyVec(sx - x2, sy - y2, -strike)
            b11, b22, b33, b12, b13, b23 = advs(sx2, sy2, sz - z2, z2, beta, nu, lss, lts, lds)
            
            # Rotate tensors to correct for strike
            bxx = a11-b11
            byy = a22-b22
            bzz = a33-b33
            bxy = a12-b12
            bxz = a13-b13
            byz = a23-b23
      
            e11n = (np.cos(strike)*bxx-np.sin(strike)*bxy)*np.cos(strike)-(np.cos(strike)*bxy-np.sin(strike)*byy)*np.sin(strike)
            e12n = (np.cos(strike)*bxx-np.sin(strike)*bxy)*np.sin(strike)+(np.cos(strike)*bxy-np.sin(strike)*byy)*np.cos(strike)
            e13n = -1.0*(np.cos(strike)*bxz-np.sin(strike)*byz)
            e22n = (np.sin(strike)*bxx+np.cos(strike)*bxy)*np.sin(strike)+(np.sin(strike)*bxy+np.cos(strike)*byy)*np.cos(strike)
            e23n = -1.0*(np.sin(strike)*bxz+np.cos(strike)*byz)
            e33n = bzz
            
            # Add strains to the strain tensor
            Strain[0,0,:] += e11n
            Strain[1,1,:] += e22n
            Strain[2,2,:] += e33n
            Strain[0,1,:] += e12n
            Strain[1,0,:] += e12n
            Strain[0,2,:] += e13n
            Strain[2,0,:] += e13n
            Strain[1,2,:] += e23n
            Strain[2,1,:] += e23n
        
    # All done
    return Strain
    
def displacement(sx, sy, sz, vertices, ss, ds, ts, nu=0.25):
    """
    Computes the displacement vector at an observation point due to slip on one
    triangular patch at depth.

    Args:
        * sx        : x coordinates of ground points
        * sy        : y coordinates of ground points
        * sz        : z coordinates of ground points
        * vertices  : list of 3-component vertices of the triangle
        * ss        : amount of strike-slip
        * ds        : amount of dip-slip
        * ts        : amount of tensile/opening-slip
        * nu        : Poisson's ratio
    
    Returns:
        * ux        : x component of displacement
        * uy        : y component of displacement
        * uz        : z component of displacement
    """

    # Modify input vertices by appending first point to end
    verts = copy.deepcopy(vertices)
    verts.append(verts[0])
    verts = [np.array(p) for p in verts]
    p1, p2, p3 = verts[:3]

    # Compute normal vector
    dx1 = p2 - p1
    dx2 = p3 - p1 
    normVec = np.cross(dx1, dx2)
    normVec /= np.linalg.norm(normVec)
    # Enforce clockwise circulation
    if normVec[2] < 0: 
        normVec *= -1.0
        # Update vertices by swapping 2nd and 3rd vertices
        verts = [p1, p3, p2, p1]
    
    # Compute slip vector in global coordinates
    angle = np.arctan2(normVec[1], normVec[0])
    strikeVec = np.array([-np.sin(angle), np.cos(angle), 0.0])
    dipVec = np.cross(normVec, strikeVec)
    # Change sign of slip components to be consistent with Okada (BVR)
    slipComp = np.array([-ss, -ds, -ts])
    slipVec = np.dot(np.column_stack((strikeVec, dipVec, normVec)), slipComp)

    # Allocate solution vectors
    ux = np.zeros_like(sx)
    uy = np.zeros_like(sx)
    uz = np.zeros_like(sx)
    
    # Loop over legs of triangle
    halfPi = 0.5 * np.pi
    for iTri in range(3):
    
        # Get the vertices of the leg
        p1, p2 = verts[iTri], verts[iTri+1]
        x1, y1, z1 = p1
        x2, y2, z2 = p2
    
        # Calculate strike and dip of current leg
        dx, dy = x2 - x1, y2 - y1
        strike = np.arctan2(dy, dx)
        segMapLength = np.sqrt(dx**2 + dy**2)
        rx, ry = RotateXyVec(dx, dy, -strike)
        dip = np.arctan2(z2 - z1, rx)
    
        if dip >= 0.0:
            beta = halfPi - dip
            if beta > halfPi:
                beta = halfPi - beta
        else:
            beta = -1.0 * (halfPi + dip)
            if beta < -halfPi:
                beta = halfPi - abs(beta)

        ssVec = np.array([np.cos(strike), np.sin(strike), 0.0])
        tsVec = np.array([-np.sin(strike), np.cos(strike), 0.0])
        dsVec = np.cross(ssVec, tsVec)
        lss = np.dot(slipVec, ssVec)
        lts = np.dot(slipVec, tsVec)
        lds = np.dot(slipVec, dsVec)
    
        if (abs(beta) > 1.0e-6) and (abs(beta - np.pi) > 1.0e-6):
            # First angular dislocation
            sx1, sy1 = RotateXyVec(sx - x1, sy - y1, -strike)
            ux1, uy1, uz1 = adv(sx1, sy1, sz - z1, z1, beta, nu, lss, lts, lds)

            # Second angular dislocation
            sx2, sy2 = RotateXyVec(sx - x2, sy - y2, -strike)
            ux2, uy2, uz2 = adv(sx2, sy2, sz - z2, z2, beta, nu, lss, lts, lds)
    
            # Rotate vectors to correct for strike
            uxn, uyn = RotateXyVec(ux1 - ux2, uy1 - uy2, strike)
            uzn = uz1 - uz2
         
            # Add the displacements from current leg
            ux += uxn
            uy += uyn
            uz += uzn

    # Identify indices for stations under current triangle
    p1, p2, p3 = verts[:3]
    path = Path([p1[:2], p2[:2], p3[:2], p1[:2]])
    inPolyIdx = path.contains_points(np.column_stack((sx, sy))).nonzero()[0]
    underIdx = []
    for iIdx in inPolyIdx:
        d = LinePlaneIntersect(sx[iIdx], sy[iIdx], sz[iIdx], p1, p2, p3)
        if d[2] - sz[iIdx] < 0.0:
            underIdx.append(iIdx)
    
    # Apply static offset to the points that lie underneath the current triangle
    ux[underIdx] -= slipVec[0]
    uy[underIdx] -= slipVec[1]
    uz[underIdx] -= slipVec[2]

    # Make sure to change sign on the vertical displacements!
    return ux, uy, -uz

def LinePlaneIntersect(sx, sy, sz, p1, p2, p3):
    """
    Calculate the intersection of a line and a plane using a parametric
    representation of the plane.  This is hardcoded for a vertical line.

    Args:
        * sx        : x coordinates of ground points
        * sy        : y coordinates of ground points
        * sz        : z coordinates of ground points
        * p1        : xyz tuple or list of first triangle vertex
        * p2        : xyz tuple or list of second triangle vertex
        * p3        : xyz tuple or list of third triangle vertex
    """
    # Extract the separate x,y,z values
    x1, y1, z1 = p1
    x2, y2, z2 = p2
    x3, y3, z3 = p3

    numerator = np.array([[1.0, 1.0, 1.0, 1.0],
                          [x1, x2, x3, sx],
                          [y1, y2, y3, sy],
                          [z1, z2, z3, sz]])
    numerator = np.linalg.det(numerator)
    denominator = np.array([[1.0, 1.0, 1.0, 0.0], 
                            [x1, x2, x3, 0.0],
                            [y1, y2, y3, 0.0], 
                            [z1, z2, z3, -sz]])
    denominator = np.linalg.det(denominator)
    if denominator == 0:
        denominator = 1.0e-15
    # Parameteric curve parameter
    t = numerator / denominator
    d = np.array([sx, sy, sz]) - np.array([0.0, 0.0, -sz]) * t

    return d

def RotateXyVec(x, y, alpha):
    """
    Rotate components by an angle alpha.
    """
    sina, cosa = np.sin(alpha), np.cos(alpha)
    xp = x * cosa - y * sina + np.spacing(1)
    yp = x * sina + y * cosa + np.spacing(1)
    return xp, yp

def adv(y1, y2, y3, a, beta, nu, B1, B2, B3):
    """    
    These are the displacements in a uniform elastic half space due to slip
    on an angular dislocation (Comninou and Dunders, 1975).  Some of the
    equations for the B2 and B3 cases have been corrected following Thomas
    1993.  The equations are coded in way such that they roughly correspond
    to each line in original text.  Exceptions have been made where it made 
    more sense because of grouping symbols.
    """

    sinbeta = np.sin(beta)
    cosbeta = np.cos(beta)
    cotbeta = 1.0 / np.tan(beta)
    z1 = y1 * cosbeta - y3 * sinbeta
    z3 = y1 * sinbeta + y3 * cosbeta
    R2 = y1 * y1 + y2 * y2 + y3 * y3
    R = np.sqrt(R2)
    y3bar = y3 + 2.0 * a
    z1bar =  y1 * cosbeta + y3bar * sinbeta
    z3bar = -y1 * sinbeta + y3bar * cosbeta
    R2bar = y1 * y1 + y2 * y2 + y3bar * y3bar
    Rbar = np.sqrt(R2bar)
    F = (-np.arctan2(y2, y1) + np.arctan2(y2, z1) 
        + np.arctan2(y2*R*sinbeta, y1*z1 + y2*y2*cosbeta))
    Fbar = (-np.arctan2(y2, y1) + np.arctan2(y2, z1bar) 
           + np.arctan2(y2*Rbar*sinbeta, y1*z1bar + y2*y2*cosbeta))
    Rbar3 = Rbar**3
    cotbeta2 = cotbeta**2
    Rby3bar = Rbar + y3bar
    Rbz3bar = Rbar + z3bar

    # Cache Poisson's ratio terms
    nu1 = 1.0 - nu
    nu2 = 1.0 - 2.0 * nu
    
    # Case I: Burgers vector (B1,0,0)
    v1InfB1 = (2.0 * nu1 * (F + Fbar) - y1 * y2 * (1.0 / (R * (R - y3))
             + 1.0 / (Rbar * (Rby3bar))) - y2 * cosbeta * ((R * sinbeta - y1) 
             / (R * (R-z3)) + (Rbar * sinbeta - y1) / (Rbar * (Rbz3bar))))
    v2InfB1 = (nu2 * (np.log(R - y3) + np.log(Rby3bar) 
              - cosbeta * (np.log(R - z3) + np.log(Rbz3bar))) 
              - y2 * y2 * (1.0 / (R * (R - y3)) + 1.0 / (Rbar * (Rby3bar)) 
              - cosbeta * (1.0 / (R * (R - z3)) + 1.0 / (Rbar * (Rbz3bar)))))
    v3InfB1 = (y2 * (1.0 / R - 1.0 / Rbar - cosbeta * ((R * cosbeta - y3) / (R * (R - z3)) 
            - (Rbar * cosbeta + y3bar) / (Rbar * (Rbz3bar)))))
    denom = 1.0 / (8.0 * np.pi * nu1)
    v1InfB1 *= denom
    v2InfB1 *= denom
    v3InfB1 *= denom
    
    v1CB1 = (-2.0 * nu1 * nu2 * Fbar * (cotbeta2) 
           + nu2 * y2 / (Rby3bar) * ((1.0 - 2.0 * nu - a / Rbar) * cotbeta 
           - y1 / (Rby3bar) * (nu + a / Rbar)) + nu2 * y2 * cosbeta * cotbeta 
           / (Rbz3bar) * (cosbeta + a / Rbar) + a * y2 * (y3bar - a) * cotbeta 
           / Rbar3 + y2 * (y3bar - a) / (Rbar * (Rby3bar)) * (-(1.0 - 2.0*nu)
           * cotbeta + y1 / (Rby3bar) * (2.0 * nu + a / Rbar) + a * y1 / (Rbar * Rbar)) 
           + y2 * (y3bar - a) / (Rbar * (Rbz3bar)) * (cosbeta / (Rbz3bar) 
           * ((Rbar * cosbeta + y3bar) * (nu2 * cosbeta - a / Rbar) * cotbeta 
           + 2.0 * nu1 * (Rbar * sinbeta - y1) * cosbeta) - a * y3bar *cosbeta *cotbeta 
           / (Rbar * Rbar)))

    v2CB1 = (nu2 * ((2.0 * nu1 * (cotbeta2) - nu) 
           * np.log(Rby3bar) - (2.0 * nu1 * (cotbeta2) + 1.0 - 2.0 * nu) 
           * cosbeta * np.log(Rbz3bar)) - nu2 / (Rby3bar) * (y1 * cotbeta
           * (1.0 - 2.0 * nu - a / Rbar) + nu * y3bar - a + (y2 * y2) / (Rby3bar) 
           * (nu + a / Rbar)) - nu2 * z1bar * cotbeta / (Rbz3bar) * (cosbeta + a / Rbar) 
           - a * y1 * (y3bar - a) * cotbeta / Rbar3 + (y3bar - a) / (Rby3bar)
           * (-2.0 * nu + 1.0 / Rbar * (nu2 * y1 * cotbeta - a) + (y2 * y2) 
           / (Rbar * (Rby3bar)) * (2.0 * nu + a / Rbar) + a * (y2 * y2) 
           / Rbar3) + (y3bar - a) / (Rbz3bar) * ((cosbeta * cosbeta) - 1.0 
           / Rbar * (nu2 * z1bar * cotbeta + a * cosbeta) + a * y3bar * z1bar 
           * cotbeta / Rbar3 - 1.0 / (Rbar * (Rbz3bar)) * ((y2 * y2) 
           * (cosbeta * cosbeta) - a * z1bar * cotbeta / Rbar * (Rbar * cosbeta + y3bar))))
    
    v3CB1 = (2.0 * nu1 * ((nu2 * Fbar * cotbeta) + (y2 / (Rby3bar) 
          * (2.0 * nu + a / Rbar)) - (y2 * cosbeta / (Rbz3bar) * (cosbeta + a / Rbar))) 
          + y2 * (y3bar - a) / Rbar * (2 * nu / (Rby3bar) + a / (Rbar * Rbar)) + y2 
          * (y3bar - a) * cosbeta / (Rbar * (Rbz3bar)) * (1.0 -2.0 * nu - (Rbar * cosbeta
          + y3bar) / (Rbz3bar) * (cosbeta + a / Rbar) - a * y3bar / (Rbar * Rbar)))
   
    denom = 1.0 / (4.0 * np.pi * nu1) 
    v1CB1 *= denom 
    v2CB1 *= denom 
    v3CB1 *= denom 
    
    v1B1 = v1InfB1 + v1CB1
    v2B1 = v2InfB1 + v2CB1
    v3B1 = v3InfB1 + v3CB1

    # Case II: Burgers vector (0,B2,0)
    v1InfB2 = (-nu2 * (np.log(R - y3) + np.log(Rby3bar) - cosbeta 
            * (np.log(R - z3) + np.log(Rbz3bar))) + y1 * y1 * (1.0 / (R * (R - y3)) + 1.0 
            / (Rbar * (Rby3bar))) + z1 * (R * sinbeta - y1) / (R * (R - z3)) + z1bar 
            * (Rbar * sinbeta - y1) / (Rbar * (Rbz3bar)))
    v2InfB2 = (2.0 * nu1 * (F + Fbar) + y1 * y2 * (1.0 / (R * (R - y3)) + 1.0 / (Rbar 
            * (Rby3bar))) - y2 * (z1 / (R * (R - z3)) + z1bar / (Rbar * (Rbz3bar))))
    v3InfB2 = (-nu2 * sinbeta * (np.log(R - z3) - np.log(Rbz3bar)) - y1 
            * (1.0 / R - 1.0 / Rbar) + z1 * (R * cosbeta - y3) / (R * (R - z3)) - z1bar 
            * (Rbar * cosbeta + y3bar) / (Rbar * (Rbz3bar)))
    denom = 1.0 / (8.0 * np.pi * nu1)
    v1InfB2 *= denom
    v2InfB2 *= denom
    v3InfB2 *= denom
    
    v1CB2 = (nu2 * ((2.0 * nu1 * (cotbeta2) + nu) 
          * np.log(Rby3bar) - (2.0 * nu1 * (cotbeta2) + 1.0) * cosbeta
          * np.log(Rbz3bar)) + nu2 / (Rby3bar) * (-nu2 
          * y1 * cotbeta + nu * y3bar - a + a * y1 * cotbeta / Rbar + (y1 * y1) / (Rbar 
          + y3bar) * (nu + a / Rbar)) - nu2 * cotbeta / (Rbz3bar) * (z1bar * cosbeta 
          - a * (Rbar * sinbeta - y1) / (Rbar * cosbeta)) - a * y1 * (y3bar - a) * cotbeta 
          / Rbar3 + (y3bar - a) / (Rby3bar) * (2.0 * nu + 1.0 / Rbar 
          * (nu2 * y1 * cotbeta + a) - (y1 * y1) / (Rbar * (Rby3bar)) 
          * (2.0 * nu + a / Rbar) - a * (y1 * y1) / Rbar3) + (y3bar - a) * cotbeta
          / (Rbz3bar) * (-cosbeta * sinbeta + a * y1 * y3bar / (Rbar3 * cosbeta) 
          + (Rbar * sinbeta - y1) / Rbar * (2.0 * nu1 * cosbeta - (Rbar * cosbeta + y3bar) 
          / (Rbar+z3bar) * (1.0 + a / (Rbar * cosbeta)))))

    v2CB2 = (2.0 * nu1 * nu2 * Fbar * cotbeta2 + (1.0 - 2 * nu) 
          * y2 / (Rby3bar) * (-(1.0 - 2.0 * nu - a / Rbar) * cotbeta + y1 / (Rby3bar)
          * (nu + a / Rbar)) - nu2 * y2 * cotbeta / (Rbz3bar) * (1.0 + a 
          / (Rbar * cosbeta)) - a * y2 * (y3bar - a) * cotbeta / Rbar3 + y2 
          * (y3bar - a) / (Rbar * (Rby3bar)) * (nu2 * cotbeta - 2.0 * nu * y1 
          / (Rby3bar) - a * y1 / Rbar * (1.0 / Rbar + 1.0 / (Rby3bar))) + y2 
          * (y3bar - a) * cotbeta / (Rbar * (Rbz3bar)) * (-2.0 * nu1 * cosbeta 
          + (Rbar * cosbeta + y3bar) / (Rbz3bar) * (1.0 + a / (Rbar * cosbeta)) + a 
          * y3bar / ((Rbar * Rbar) * cosbeta)))

    v3CB2 = (-2.0 * nu1 * nu2 * cotbeta * (np.log(Rby3bar) - cosbeta
          * np.log(Rbz3bar)) - 2.0 * nu1 * y1 / (Rby3bar) * (2.0 * nu + a / Rbar) 
          + 2.0 * nu1 * z1bar / (Rbz3bar) * (cosbeta + a / Rbar) + (y3bar - a) / Rbar
          * (nu2 * cotbeta - 2.0 * nu * y1 / (Rby3bar) - a * y1 / (Rbar * Rbar)) 
          - (y3bar - a) / (Rbz3bar) * (cosbeta * sinbeta + (Rbar * cosbeta + y3bar) 
          * cotbeta / Rbar * (2.0 * nu1 * cosbeta - (Rbar * cosbeta + y3bar) / (Rbz3bar)) 
          + a / Rbar * (sinbeta - y3bar * z1bar / (Rbar * Rbar) - z1bar * (Rbar * cosbeta 
          + y3bar) / (Rbar * (Rbz3bar)))))

    denom = 1.0 / (4.0 * np.pi * nu1)
    v1CB2 *= denom
    v2CB2 *= denom
    v3CB2 *= denom
    v1B2 = v1InfB2 + v1CB2
    v2B2 = v2InfB2 + v2CB2
    v3B2 = v3InfB2 + v3CB2

    # Case III: Burgers vector (0,0,B3)
    v1InfB3 = (y2 * sinbeta * ((R * sinbeta - y1) / (R * (R - z3)) + (Rbar * sinbeta - y1) 
            / (Rbar * (Rbz3bar))))
    v2InfB3 = (nu2 * sinbeta * (np.log(R - z3) + np.log(Rbz3bar)) - (y2 * y2) 
            * sinbeta * (1.0 / (R * (R - z3)) + 1.0 / (Rbar * (Rbz3bar))))
    v3InfB3 = (2.0 * nu1 * (F - Fbar) + y2 * sinbeta * ((R * cosbeta - y3) / (R 
            * (R - z3)) - (Rbar * cosbeta + y3bar) / (Rbar * (Rbz3bar))))
    denom = 1.0 / (8.0 * np.pi * nu1)
    v1InfB3 *= denom
    v2InfB3 *= denom
    v3InfB3 *= denom
    
    v1CB3 = (nu2 * (y2 / (Rby3bar) * (1.0 + a / Rbar) - y2 * cosbeta / (Rbar
          + z3bar) * (cosbeta + a / Rbar)) - y2 * (y3bar - a) / Rbar * (a / (Rbar * Rbar) 
          + 1.0 / (Rby3bar)) + y2 * (y3bar - a) * cosbeta / (Rbar * (Rbz3bar)) 
          * ((Rbar * cosbeta + y3bar) / (Rbz3bar) * (cosbeta + a / Rbar) + a * y3bar 
          / (Rbar * Rbar)))

    v2CB3 = (nu2 * (-sinbeta * np.log(Rbz3bar) - y1 / (Rby3bar) * (1.0 
          + a / Rbar) + z1bar / (Rbz3bar) * (cosbeta + a / Rbar)) + y1 * (y3bar - a) 
          / Rbar * (a / (Rbar * Rbar) + 1.0 / (Rby3bar)) - (y3bar - a) / (Rbz3bar) 
          * (sinbeta * (cosbeta - a / Rbar) + z1bar / Rbar * (1 + a * y3bar / (Rbar * Rbar)) 
          - 1.0 / (Rbar * (Rbz3bar)) * ((y2 * y2) * cosbeta * sinbeta - a * z1bar / Rbar 
          * (Rbar * cosbeta + y3bar))))

    v3CB3 = (2.0 * nu1 * Fbar + 2.0 * nu1 * (y2 * sinbeta / (Rbz3bar) 
          * (cosbeta + a / Rbar)) + y2 * (y3bar - a) * sinbeta / (Rbar * (Rbz3bar)) 
          * (1.0 + (Rbar * cosbeta + y3bar) / (Rbz3bar) * (cosbeta + a / Rbar) + a 
          * y3bar / (Rbar * Rbar)))

    denom = 1.0 / (4.0 * np.pi * nu1)
    v1CB3 *= denom
    v2CB3 *= denom
    v3CB3 *= denom
    
    v1B3 = v1InfB3 + v1CB3
    v2B3 = v2InfB3 + v2CB3
    v3B3 = v3InfB3 + v3CB3

    # Sum the for each slip component
    v1 = B1 * v1B1 + B2 * v1B2 + B3 * v1B3
    v2 = B1 * v2B1 + B2 * v2B2 + B3 * v2B3
    v3 = B1 * v3B1 + B2 * v3B2 + B3 * v3B3

    return v1, v2, v3

def advs(y1, y2, y3, a, b, nu, B1, B2, B3):
    '''
    These are the strains in a uniform elastic half space due to slip
    on an angular dislocation.  They were calculated by symbolically
    differentiating the expressions for the displacements (Comninou and
    Dunders, 1975, with typos noted by Thomas 1993) then combining the
    elements of the displacement gradient tensor to form the strain tensor.
    '''
    # Needed to make my life simpler (I have copy pasted and replaced the simple stuff using vim but cot does not exist in Python)
    cot = lambda x: 1./np.tan(x)
    
    # Precompute repeated terms
    y1_cos_b = y1 * np.cos(b)
    y3_sin_b = y3 * np.sin(b)
    # y1_cos_b_y3_sin_b = y1_cos_b - y3_sin_b
    # y1_cos_b_y3_2a_sin_b = y1_cos_b + (y3 + 2 * a) * np.sin(b)
    # R1 = np.sqrt(y1**2 + y2**2 + y3**2)
    # R2 = np.sqrt(y1**2 + y2**2 + (y3 + 2 * a)**2)
    
    # # Simplify e11 calculation
    # term1 = y2 / y1**2 / (1 + y2**2 / y1**2)
    # term2 = y2 / (y1_cos_b_y3_sin_b)**2 * np.cos(b) / (1 + y2**2 / (y1_cos_b_y3_sin_b)**2)
    # term3 = y2 / R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y2**2 * np.cos(b)) * y1
    # term4 = y2 * R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y2**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) - y3 * np.sin(b))
    # term5 = y2 / (y1_cos_b_y3_2a_sin_b)**2 * np.cos(b) / (1 + y2**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term6 = y2 / R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y2**2 * np.cos(b)) * y1
    # term7 = y2 * R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y2**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) + (y3 + 2 * a) * np.sin(b))
    # e11 = B1 * (1 / 8 * ((2 - 2 * nu) * (2 * term1 - term2 + term3 - term4 - term5 + term6 - term7)) / np.pi / (1 - nu))
    
    # # Simplify e22 calculation
    # term8 = y1 / y2**2 / (1 + y1**2 / y2**2)
    # term9 = y1 / (y1_cos_b_y3_sin_b)**2 * np.sin(b) / (1 + y1**2 / (y1_cos_b_y3_sin_b)**2)
    # term10 = y1 / R1 * np.cos(b) / (y2 * y1_cos_b_y3_sin_b + y1**2 * np.sin(b)) * y2
    # term11 = y1 * R1 * np.cos(b) / (y2 * y1_cos_b_y3_sin_b + y1**2 * np.sin(b))**2 * (2 * y2 * np.sin(b) - y3 * np.cos(b))
    # term12 = y1 / (y1_cos_b_y3_2a_sin_b)**2 * np.sin(b) / (1 + y1**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term13 = y1 / R2 * np.cos(b) / (y2 * y1_cos_b_y3_2a_sin_b + y1**2 * np.sin(b)) * y2
    # term14 = y1 * R2 * np.cos(b) / (y2 * y1_cos_b_y3_2a_sin_b + y1**2 * np.sin(b))**2 * (2 * y2 * np.sin(b) + (y3 + 2 * a) * np.cos(b))
    # e22 = B2 * (1 / 8 * ((2 - 2 * nu) * (2 * term8 - term9 + term10 - term11 - term12 + term13 - term14)) / np.pi / (1 - nu))
    
    # # Simplify e33 calculation
    # term15 = y3 / y1**2 / (1 + y3**2 / y1**2)
    # term16 = y3 / (y1_cos_b_y3_sin_b)**2 * np.cos(b) / (1 + y3**2 / (y1_cos_b_y3_sin_b)**2)
    # term17 = y3 / R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b)) * y1
    # term18 = y3 * R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) - y3 * np.sin(b))
    # term19 = y3 / (y1_cos_b_y3_2a_sin_b)**2 * np.cos(b) / (1 + y3**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term20 = y3 / R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b)) * y1
    # term21 = y3 * R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) + (y3 + 2 * a) * np.sin(b))
    # e33 = B3 * (1 / 8 * ((2 - 2 * nu) * (2 * term15 - term16 + term17 - term18 - term19 + term20 - term21)) / np.pi / (1 - nu))
    
    # # Simplify e12 calculation
    # term22 = y1 * y2 / (y1**2 + y2**2)
    # term23 = y1 * y2 / (y1_cos_b_y3_sin_b)**2 * np.cos(b) / (1 + y1**2 / (y1_cos_b_y3_sin_b)**2)
    # term24 = y1 * y2 / R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y2**2 * np.cos(b))
    # term25 = y1 * y2 * R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y2**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) - y3 * np.sin(b))
    # term26 = y1 * y2 / (y1_cos_b_y3_2a_sin_b)**2 * np.cos(b) / (1 + y1**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term27 = y1 * y2 / R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y2**2 * np.cos(b))
    # term28 = y1 * y2 * R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y2**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) + (y3 + 2 * a) * np.sin(b))
    # e12 = B1 * (1 / 8 * ((2 - 2 * nu) * (2 * term22 - term23 + term24 - term25 - term26 + term27 - term28)) / np.pi / (1 - nu))
    
    # # Simplify e13 calculation
    # term29 = y1 * y3 / (y1**2 + y3**2)
    # term30 = y1 * y3 / (y1_cos_b_y3_sin_b)**2 * np.cos(b) / (1 + y1**2 / (y1_cos_b_y3_sin_b)**2)
    # term31 = y1 * y3 / R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b))
    # term32 = y1 * y3 * R1 * np.sin(b) / (y1 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) - y3 * np.sin(b))
    # term33 = y1 * y3 / (y1_cos_b_y3_2a_sin_b)**2 * np.cos(b) / (1 + y1**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term34 = y1 * y3 / R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b))
    # term35 = y1 * y3 * R2 * np.sin(b) / (y1 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b))**2 * (2 * y1 * np.cos(b) + (y3 + 2 * a) * np.sin(b))
    # e13 = B1 * (1 / 8 * ((2 - 2 * nu) * (2 * term29 - term30 + term31 - term32 - term33 + term34 - term35)) / np.pi / (1 - nu))
    
    # # Simplify e23 calculation
    # term36 = y2 * y3 / (y2**2 + y3**2)
    # term37 = y2 * y3 / (y1_cos_b_y3_sin_b)**2 * np.cos(b) / (1 + y2**2 / (y1_cos_b_y3_sin_b)**2)
    # term38 = y2 * y3 / R1 * np.sin(b) / (y2 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b))
    # term39 = y2 * y3 * R1 * np.sin(b) / (y2 * y1_cos_b_y3_sin_b + y3**2 * np.cos(b))**2 * (2 * y2 * np.cos(b) - y3 * np.sin(b))
    # term40 = y2 * y3 / (y1_cos_b_y3_2a_sin_b)**2 * np.cos(b) / (1 + y2**2 / (y1_cos_b_y3_2a_sin_b)**2)
    # term41 = y2 * y3 / R2 * np.sin(b) / (y2 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b))
    # term42 = y2 * y3 * R2 * np.sin(b) / (y2 * y1_cos_b_y3_2a_sin_b + y3**2 * np.cos(b))**2 * (2 * y2 * np.cos(b) + (y3 + 2 * a) * np.sin(b))
    # e23 = B2 * (1 / 8 * ((2 - 2 * nu) * (2 * term36 - term37 + term38 - term39 - term40 + term41 - term42)) / np.pi / (1 - nu))

    e11 = B1*(1/8*((2-2*nu)*(2*y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b-y3_sin_b)**2*np.cos(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*(2*y1_cos_b-y3_sin_b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))-y2*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y1-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y1-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y1)-y2*np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))))/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*(y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2-(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1*cot(b)-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))-(1-2*nu)*y2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(1-2*nu)*y2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-3*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))*y1+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+a/(y1**2+y2**2+(y3+2*a)**2)-2*a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**2)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1*cot(b)+(2-2*nu)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)*np.cos(b))+2*a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**2*y1))/np.pi/(1-nu))+B2*(1/8*((-1+2*nu)*(1/(y1**2+y2**2+y3**2)**(1/2)*y1/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))+2*y1*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+y1**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y1-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y1-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y1)+np.cos(b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(y1_cos_b-y3_sin_b)*(1/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))+np.cos(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+(y1_cos_b+(y3+2*a)*np.sin(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2+nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1)*np.cos(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*y1*cot(b)+nu*(y3+2*a)-a+a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+a*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-a*y1**2*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+2*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y1**3/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1**3/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))+(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((y1_cos_b+(y3+2*a)*np.sin(b))*np.cos(b)-a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)**2-a*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)+a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y1)-a*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+3*a*y1**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)+a)-y1**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)+a)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1-2*nu)*cot(b)-2*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y1**3/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y1**3/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y1**3/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a-2*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1+3*a*y1**3/(y1**2+y2**2+(y3+2*a)**2)**(5/2))-(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(-np.cos(b)*np.sin(b)+a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)-3*a*y1**2*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)/np.cos(b)+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))*y1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y1)))/np.pi/(1-nu))+B3*(1/8*y2*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y1-1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))/np.pi/(1-nu)+1/4*((1-2*nu)*(-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y1-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1)-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*y1-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y1))/np.pi/(1-nu))    
    e22 = B1*(1/8*((1-2*nu)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))-2*y2*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))-y2**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y2-np.cos(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2)))/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2-nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1-2*nu)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(y1*cot(b)*(1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+nu*(y3+2*a)-a+y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2+2*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**3/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y2**3/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))+(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2+3*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(-2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)-a)+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)-a)*y2+2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**3/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**3/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**3/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a+2*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-3*a*y2**3/(y1**2+y2**2+(y3+2*a)**2)**(5/2))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)**2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))+a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))*y2-3*a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y2+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y2+1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y2*np.cos(b)**2+a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*y2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2)))/np.pi/(1-nu))+B2*(1/8*((2-2*nu)*(-2/y1/(1+y2**2/y1**2)+1/(y1_cos_b-y3_sin_b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+y1*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y2)-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-y2*(-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2))/np.pi/(1-nu)+1/4*((2-2*nu)*(1-2*nu)*(-1/y1/(1+y2**2/y1**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))-(1-2*nu)*y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)-(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+(1-2*nu)*y2**2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+(1-2*nu)*y2**2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)-a*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+3*a*y2**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+a*y1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*y2-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2))+(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))-y2**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))-y2**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))+y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y2-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2/np.cos(b)*y2))/np.pi/(1-nu))+B3*(1/8*((1-2*nu)*np.sin(b)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-2*y2*np.sin(b)*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y2**2*np.sin(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2))/np.pi/(1-nu)+1/4*((1-2*nu)*(-np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*y1+y1*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y2-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.sin(b)*(np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.sin(b)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*y2-2*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*a*(y3+2*a)*y2+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y2+1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y2*np.cos(b)*np.sin(b)+a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*y2-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2)))/np.pi/(1-nu))
    e33 = B1*(1/8*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)*y3+1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*np.cos(b)*y3-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*((1-2*nu)*(-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))+y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+a/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+a/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-a/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a))+y2*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-a/(y1**2+y2**2+(y3+2*a)**2)+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)))/np.pi/(1-nu))+B2*(1/8*((-1+2*nu)*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y1*(-1/(y1**2+y2**2+y3**2)**(3/2)*y3+1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))-np.sin(b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(y1_cos_b-y3_sin_b)*(1/(y1**2+y2**2+y3**2)**(1/2)*np.cos(b)*y3-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))-np.sin(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+1/2*(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*cot(b)*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+(2-2*nu)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+1/2*(2-2*nu)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+(2-2*nu)*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2))-1/2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+a*y1/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a))-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)*np.sin(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)*np.sin(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*(2*y3+4*a)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))-1/2*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*(2*y3+4*a)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y3+2*a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)+(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)-np.sin(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+1/2*(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))))/np.pi/(1-nu))+B3*(1/8*((2-2*nu)*(y2/(y1_cos_b-y3_sin_b)**2*np.sin(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y3+y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)+y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)-(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+y2*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*np.cos(b)*y3-1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*(-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))-(2-2*nu)*y2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*(2-2*nu)*y2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+y2*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)-y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+a/(y1**2+y2**2+(y3+2*a)**2)-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)))/np.pi/(1-nu))
    e12 = 1/2*B1*(1/8*((2-2*nu)*(-2/y1/(1+y2**2/y1**2)+1/(y1_cos_b-y3_sin_b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))-y1*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y2)-np.cos(b)*(((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y2*np.cos(b)*(1/(y1**2+y2**2+y3**2)*np.sin(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2+1/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2))/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*(-1/y1/(1+y2**2/y1**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))-(1-2*nu)*y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)+(1-2*nu)*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(1-2*nu)*y2**2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-(1-2*nu)*y2**2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+a*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-3*a*y2**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-2*a*y1/(y1**2+y2**2+(y3+2*a)**2)**2*y2)+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2*cot(b)+(2-2*nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*y2*np.cos(b))+2*a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**2*y2))/np.pi/(1-nu))+1/2*B2*(1/8*((-1+2*nu)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))+y1**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y2-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y2-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y2)+(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)*np.sin(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2)/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2+nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*y1*cot(b)+nu*(y3+2*a)-a+a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2)+(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((y1_cos_b+(y3+2*a)*np.sin(b))*np.cos(b)-a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-a/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*y2/np.cos(b)+a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y2)+3*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)+a)-y1**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)+a)*y2+y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*y2+y1**2/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*y2+y1**2/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a*y2+3*a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y2)-(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(-np.cos(b)*np.sin(b)+a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-3*a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)/np.cos(b)*y2+1/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*y2*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y2)))/np.pi/(1-nu))+1/2*B3*(1/8*np.sin(b)*(((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))/np.pi/(1-nu)+1/8*y2*np.sin(b)*(1/(y1**2+y2**2+y3**2)*np.sin(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2+1/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2)/np.pi/(1-nu)+1/4*((1-2*nu)*(1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y2**2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y2**2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))-(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y2-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2)+(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y2))/np.pi/(1-nu))+1/2*B1*(1/8*((1-2*nu)*(1/(y1**2+y2**2+y3**2)**(1/2)*y1/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))-y2**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y1-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y1-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y1-np.cos(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))))/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2-nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1-2*nu)*np.cos(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(y1*cot(b)*(1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+nu*(y3+2*a)-a+y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+a*y1**2*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)-(1-2*nu)*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-a*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+3*a*y1**2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(-2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)-a)+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)-a)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1-2*nu)*cot(b)-y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*y1-y2**2/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*y1-y2**2/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a*y1-3*a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1)-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)**2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))+a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1-2*nu)*np.cos(b)*cot(b)+a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-3*a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-a*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)+a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*y1-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1)))/np.pi/(1-nu))+1/2*B2*(1/8*((2-2*nu)*(2*y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b-y3_sin_b)**2*np.cos(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*(2*y1_cos_b-y3_sin_b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+y2*(1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y1-1/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*y1-1/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*y1)-y2*(np.cos(b)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))+np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*(1-2*nu)*(y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2-(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1*cot(b)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))+(1-2*nu)*y2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+(1-2*nu)*y2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y1+3*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))*y1-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))*y1+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+2*nu*y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1))-y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))*y1-y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y1-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2/np.cos(b)*y1))/np.pi/(1-nu))+1/2*B3*(1/8*((1-2*nu)*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y2**2*np.sin(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))))/np.pi/(1-nu)+1/4*((1-2*nu)*(-np.sin(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-y1**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+y1*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y1-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.sin(b)*(np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.sin(b)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1+np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*y1-2*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*a*(y3+2*a)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-a*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)+a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*y1-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1)))/np.pi/(1-nu))
    e13 = 1/2*B1*(1/8*((2-2*nu)*(y2/(y1_cos_b-y3_sin_b)**2*np.sin(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y3+y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))-y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1))-y2*np.cos(b)*(1/(y1**2+y2**2+y3**2)*np.sin(b)*y3/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))+1/2/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*(2*y3+4*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))))/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*(-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2-(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(1/2*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+1/2*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))-(1-2*nu)*y2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*(1-2*nu)*y2*np.cos(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2*cot(b)-3/2*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a)+y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y1/(y1**2+y2**2+(y3+2*a)**2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a))+y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))-a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+(2-2*nu)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)*np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)*((1-2*nu)*np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)*cot(b)+1/2*(2-2*nu)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)*(2*y3+4*a)*np.cos(b))-a*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)+a*(y3+2*a)*np.cos(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)))/np.pi/(1-nu))+1/2*B2*(1/8*((-1+2*nu)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)/((y1**2+y2**2+y3**2)**(1/2)-y3)+(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))+y1**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1))-np.sin(b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)*np.sin(b)*y3/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))+np.sin(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+1/2*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*(2*y3+4*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-1/2*(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2+nu)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1)*np.cos(b)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu)*y1*cot(b)+nu*(y3+2*a)-a+a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu-1/2*a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))+(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((y1_cos_b+(y3+2*a)*np.sin(b))*np.cos(b)-a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-(1-2*nu)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)*np.sin(b)-1/2*a/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*(2*y3+4*a)/np.cos(b)+1/2*a*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*(2*y3+4*a))-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1*cot(b)+3/2*a*y1*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)+a)-y1**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)+a)-y1**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)+a)*(2*y3+4*a)+1/2*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(2*y3+4*a)+y1**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+1/2*y1**2/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a*(2*y3+4*a)+3/2*a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a))+cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-np.cos(b)*np.sin(b)+a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))))-(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(-np.cos(b)*np.sin(b)+a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+(y3+a)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*y1-3/2*a*y1*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)/np.cos(b)*(2*y3+4*a)+1/2/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*(2*y3+4*a)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b)))*(2*y3+4*a)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*(2*y3+4*a))))/np.pi/(1-nu))+1/2*B3*(1/8*y2*np.sin(b)*(1/(y1**2+y2**2+y3**2)*np.sin(b)*y3/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))+1/2/(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)*(2*y3+4*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)-y1)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))/np.pi/(1-nu)+1/4*((1-2*nu)*(-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))-y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))+1/2*y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*(2*y3+4*a)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-a/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1))+y2*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/2*y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+a/(y1**2+y2**2+(y3+2*a)**2)-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)))/np.pi/(1-nu))+1/2*B1*(1/8*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-np.cos(b)*(1/(y1**2+y2**2+y3**2)*np.cos(b)*y1/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*((1-2*nu)*(y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+a/(y1**2+y2**2+(y3+2*a)**2))*y1+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y1)-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*y1-y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1+2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y1))/np.pi/(1-nu))+1/2*B2*(1/8*((-1+2*nu)*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-1/(y1**2+y2**2+y3**2)**(1/2)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*(-1/(y1**2+y2**2+y3**2)**(3/2)*y1+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1)+np.cos(b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)*np.cos(b)*y1/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))-np.cos(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*cot(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-(2-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(2-2*nu)*y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+(2-2*nu)*y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+(2-2*nu)*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2))*y1+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+2*nu*y1**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-a/(y1**2+y2**2+(y3+2*a)**2)+2*a*y1**2/(y1**2+y2**2+(y3+2*a)**2)**2)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)*np.sin(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1*cot(b)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*y1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*y1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-(y3+2*a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)+2*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**2*y1-np.cos(b)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b)))))/np.pi/(1-nu))+1/2*B3*(1/8*((2-2*nu)*(-y2/(y1_cos_b-y3_sin_b)**2*np.cos(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*(2*y1_cos_b-y3_sin_b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)+y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)-(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+y2*np.sin(b)*(1/(y1**2+y2**2+y3**2)*np.cos(b)*y1/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y1-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y1-np.sin(b))-1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*(y2/y1**2/(1+y2**2/y1**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.cos(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*y1-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*(2*y1_cos_b+(y3+2*a)*np.sin(b)))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))-(2-2*nu)*y2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-(2-2*nu)*y2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*y1-y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))+y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y1-np.sin(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y1))/np.pi/(1-nu))
    e23 = 1/2*B1*(1/8*((1-2*nu)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)/((y1**2+y2**2+y3**2)**(1/2)-y3)+(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))-y2**2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-np.cos(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b)))))/np.pi/(1-nu)+1/4*((1-2*nu)*(((2-2*nu)*cot(b)**2-nu)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-((2-2*nu)*cot(b)**2+1-2*nu)*np.cos(b)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(y1*cot(b)*(1-2*nu-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+nu*(y3+2*a)-a+y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-(1-2*nu)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(1/2*a*y1*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+nu-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))-(1-2*nu)*np.sin(b)*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*(1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y1*cot(b)+3/2*a*y1*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)-a)+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(-2*nu+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*y1*cot(b)-a)+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*y1*cot(b)-a)*(2*y3+4*a)-1/2*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(2*y3+4*a)-y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y2**2/(y1**2+y2**2+(y3+2*a)**2)**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a*(2*y3+4*a)-3/2*a*y2**2/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a))+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)**2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))+a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)**2-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))+a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)+a*np.cos(b))*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1-2*nu)*np.sin(b)*cot(b)+a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+a*(y3+2*a)*np.sin(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-3/2*a*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a)+1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(2*y3+4*a)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)**2-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-a*np.sin(b)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)+1/2*a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*(2*y3+4*a)-a*(y1_cos_b+(y3+2*a)*np.sin(b))*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1))))/np.pi/(1-nu))+1/2*B2*(1/8*((2-2*nu)*(y2/(y1_cos_b-y3_sin_b)**2*np.sin(b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+(y2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))*y3+y2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+y1*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y3)**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-1)-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1))-y2*(-np.sin(b)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))+np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))-1/2*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))))/np.pi/(1-nu)+1/4*((2-2*nu)*(1-2*nu)*(-y2/(y1_cos_b+(y3+2*a)*np.sin(b))**2*np.sin(b)/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+(1/2*y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))*(2*y3+4*a)-y2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*y1)/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)**2-(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((-1+2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*cot(b)+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+(1-2*nu)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(-1/2*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)*cot(b)-y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)-1/2*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))+(1-2*nu)*y2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+1/2*(1-2*nu)*y2*cot(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*(2*y3+4*a)-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2*cot(b)+3/2*a*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(5/2)*(2*y3+4*a)+y2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))-1/2*y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))*(2*y3+4*a)-y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+1/2*a*y1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*(2*y3+4*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)))+y2*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))-1/2*y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))*(2*y3+4*a)-y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*((-2+2*nu)*np.cos(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))+y2*(y3+a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*((1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/np.cos(b))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/np.cos(b)*(2*y3+4*a)+a/(y1**2+y2**2+(y3+2*a)**2)/np.cos(b)-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2/np.cos(b)*(2*y3+4*a)))/np.pi/(1-nu))+1/2*B3*(1/8*((1-2*nu)*np.sin(b)*((1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))+(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y2**2*np.sin(b)*(-1/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y3-1/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*(1/(y1**2+y2**2+y3**2)**(1/2)*y3-np.cos(b))-1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(2*y3+4*a)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))))/np.pi/(1-nu)+1/4*((1-2*nu)*(-np.sin(b)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1)+1/2*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/2*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a))+y1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))-1/2*y1*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(a/(y1**2+y2**2+(y3+2*a)**2)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a))*(2*y3+4*a)+y1*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-a/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a)-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+1))-1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.sin(b)*(np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.sin(b)*(np.cos(b)-a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/2*np.sin(b)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*y3+4*a)+np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-1/2*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(1+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))*(2*y3+4*a)+(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(a/(y1**2+y2**2+(y3+2*a)**2)-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*(2*y3+4*a))+1/2/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(2*y3+4*a)+1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(y2**2*np.cos(b)*np.sin(b)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a))*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*y3+4*a)+np.cos(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-a*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)+1/2*a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*(2*y3+4*a)-a*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(1/2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*(2*y3+4*a)+1))))/np.pi/(1-nu))+1/2*B1*(1/8*(1/(y1**2+y2**2+y3**2)**(1/2)-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-np.cos(b)*(((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))/np.pi/(1-nu)+1/8*y2*(-1/(y1**2+y2**2+y3**2)**(3/2)*y2+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-np.cos(b)*(1/(y1**2+y2**2+y3**2)*np.cos(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2))/np.pi/(1-nu)+1/4*((2-2*nu)*((1-2*nu)*(-1/y1/(1+y2**2/y1**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))*cot(b)+1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-y2**2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)-np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+y2**2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)+y2**2*np.cos(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2))+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+a/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)+a/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-2*nu/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-2*a/(y1**2+y2**2+(y3+2*a)**2)**2*y2)+(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1-2*nu-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)*np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2+2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y2))/np.pi/(1-nu))+1/2*B2*(1/8*((-1+2*nu)*np.sin(b)*(1/(y1**2+y2**2+y3**2)**(1/2)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-y1*(-1/(y1**2+y2**2+y3**2)**(3/2)*y2+1/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2)+(y1_cos_b-y3_sin_b)/(y1**2+y2**2+y3**2)*np.cos(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-(y1_cos_b-y3_sin_b)*((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2)/np.pi/(1-nu)+1/4*((-2+2*nu)*(1-2*nu)*cot(b)*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+(2-2*nu)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2*(2*nu+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+(2-2*nu)*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(2-2*nu)*(y1_cos_b+(y3+2*a)*np.sin(b))/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((1-2*nu)*cot(b)-2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)-a*y1/(y1**2+y2**2+(y3+2*a)**2))*y2+(y3+a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*nu*y1/((y1**2+y2**2+(y3+2*a)**2)**(1/2)+y3+2*a)**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2+2*a*y1/(y1**2+y2**2+(y3+2*a)**2)**2*y2)+(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)*np.sin(b)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-(y3+a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2*cot(b)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*((2-2*nu)*np.cos(b)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)*cot(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(-np.cos(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2)-a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*(np.sin(b)-(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)-(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))*y2+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*(2*(y3+2*a)*(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)**2*y2-(y1_cos_b+(y3+2*a)*np.sin(b))/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2+(y1_cos_b+(y3+2*a)*np.sin(b))*((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2)))/np.pi/(1-nu))+1/2*B3*(1/8*((2-2*nu)*(1/(y1_cos_b-y3_sin_b)/(1+y2**2/(y1_cos_b-y3_sin_b)**2)+((y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+y3**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+y3**2)*np.sin(b)**2/(y1*(y1_cos_b-y3_sin_b)+y2**2*np.cos(b))**2)-1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+np.sin(b)*(((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(1/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b)))+y2*np.sin(b)*(1/(y1**2+y2**2+y3**2)*np.cos(b)*y2/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)**(3/2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))*y2-((y1**2+y2**2+y3**2)**(1/2)*np.cos(b)-y3)/(y1**2+y2**2+y3**2)/((y1**2+y2**2+y3**2)**(1/2)-y1*np.sin(b)-y3*np.cos(b))**2*y2-1/(y1**2+y2**2+(y3+2*a)**2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*y2+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*y2))/np.pi/(1-nu)+1/4*((2-2*nu)*(-1/y1/(1+y2**2/y1**2)+1/(y1_cos_b+(y3+2*a)*np.sin(b))/(1+y2**2/(y1_cos_b+(y3+2*a)*np.sin(b))**2)+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))+y2**2/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))-2*y2**2*(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.sin(b)/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2*np.cos(b))/(1+y2**2*(y1**2+y2**2+(y3+2*a)**2)*np.sin(b)**2/(y1*(y1_cos_b+(y3+2*a)*np.sin(b))+y2**2*np.cos(b))**2))+(2-2*nu)*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-(2-2*nu)*y2**2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)-(2-2*nu)*y2**2*np.sin(b)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)+(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(3/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))-y2**2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(1+((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))+a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2))+y2*(y3+a)*np.sin(b)/(y1**2+y2**2+(y3+2*a)**2)**(1/2)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(1/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)*y2/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))**2*(np.cos(b)+a/(y1**2+y2**2+(y3+2*a)**2)**(1/2))/(y1**2+y2**2+(y3+2*a)**2)**(1/2)*y2-((y1**2+y2**2+(y3+2*a)**2)**(1/2)*np.cos(b)+y3+2*a)/((y1**2+y2**2+(y3+2*a)**2)**(1/2)-y1*np.sin(b)+(y3+2*a)*np.cos(b))*a/(y1**2+y2**2+(y3+2*a)**2)**(3/2)*y2-2*a*(y3+2*a)/(y1**2+y2**2+(y3+2*a)**2)**2*y2))/np.pi/(1-nu))

    return e11, e22, e33, e12, e13, e23

#EOF