06_bead_optimization_plate (#73)

* Adding bead optimization example

* objective graph

* adding image table

* Update README.md

step size 0.3 --> 0.15

* Comparison with manual solution

* minor fixes

* table fixes

* Table fixes

* Update README.md

reordering

* Update links for bead example in toplevel Readme files

Co-authored-by: Rahul Kikkeri Nagaraja <[email protected]>
Co-authored-by: Armin Geiser <[email protected]>

README.md

@@ -144,3 +144,4 @@ Unit tests should *not* be uploaded to this repository. Please put them in the `
 - [Multi Constraint Optimization 3D Hook](shape_optimization/10_Multi_Constraint_Optimization_3D_Hook)
 - [Smooth Surface Wrapping - Stanford Bunny](shape_optimization/11_Shape_Update_Optimization_Stanford_Bunny)
 - [Strain Energy Minimization - 3D Shell](shape_optimization/02_Strain_Energy_Minimization_3D_Shell)
+- [Bead Optimization Plate](shape_optimization/06_bead_optimization_plate)

shape_optimization/06_bead_optimization_plate/README.md

@@ -0,0 +1,49 @@
+# Bead Optimization of a Plate
+
+A bead optimization problem to minimize the strain energy of a square plate - supported at the corners and subject to a single force in the center.
+
+> **Author**: Armin Geiser
+>
+> **Kratos version**: 9.0
+
+## Optimization Problem
+
+### Objective
+- Minimize strain energy
+
+  <p align="center">
+    <img src="images/beadOpt_SetupwithBC.png">
+  </p>
+
+## Optimization settings
+- Algorithm type : `bead_optimization`
+- Number of steps : `300`
+- Step size : `0.25`
+- Filter radius : `0.075`
+- Mesh motion : `False`
+
+## Results
+
+### Shape Evolution
+The below images shows the shape evolution of the bead pattern on a plate during the optimization iterations. 
+
+<p align="center">
+    <img src="images/beadOpt_result.gif" width="800">
+</p>
+
+### Comparison with manual solutions
+
+In the table below, a comparison with manual solutions shows that the bead pattern obtained from the optimized solutions perform better. The last row shows the value of the objective function (here strain energy) for each of the bead patterns.
+
+|             Manual Solution 1              |             Manual Solution 2              |             Manual Solution 3              |             Manual Solution 4              |             Manual Solution 5              |          Optimized Solution           |
+| :----------------------------------------: | :----------------------------------------: | :----------------------------------------: | :----------------------------------------: | :----------------------------------------: | :-----------------------------------: |
+| <img src="images/beadOpt_Manual_1_2D.png"> | <img src="images/beadOpt_Manual_2_2D.png"> | <img src="images/beadOpt_Manual_3_2D.png"> | <img src="images/beadOpt_Manual_4_2D.png"> | <img src="images/beadOpt_Manual_5_2D.png"> | <img src="images/beadOpt_Opt_2D.png"> |
+| <img src="images/beadOpt_Manual_1_3D.png"> | <img src="images/beadOpt_Manual_2_3D.png"> | <img src="images/beadOpt_Manual_3_3D.png"> | <img src="images/beadOpt_Manual_4_3D.png"> | <img src="images/beadOpt_Manual_5_3D.png"> | <img src="images/beadOpt_Opt_3D.png"> |
+|                  2.46e-3                   |                  1.56e-3                   |                  1.17e-3                   |                  1.06e-3                   |                  7.86e-4                   |                4.23e-4                |
+
+### Convergence
+The below plots shows the evolution of the objective function over the bead optimization iterations.
+
+<p align="center">
+    <img src="images/beadOpt_plot.svg" height="650">
+</p>

shape_optimization/06_bead_optimization_plate/analysis_parameters.json

@@ -1,108 +1,160 @@
 {
-  "problem_data"             : {
-      "problem_name"    : "Plate",
-      "parallel_type"   : "OpenMP",
-      "start_time"      : 0.0,
-      "end_time"        : 1.0,
-      "echo_level"      : 0
-  },
-  "solver_settings"          : {
-      "solver_type"     : "static",
-      "echo_level"      : 0,
-      "analysis_type"   : "linear",
-      "model_part_name" : "plate",
-      "domain_size"     : 3,
-      "time_stepping" : {
-          "time_step"       : 1.0
-      },
-      "model_import_settings"              : {
-          "input_type"     : "use_input_model_part",
-          "input_filename" : "plate"
-      },
-          "material_import_settings" :{
-          "materials_filename": "2D_material.json"
-      },
-      "line_search"                        : false,
-      "convergence_criterion"              : "residual_criterion",
-      "displacement_relative_tolerance"    : 0.0001,
-      "displacement_absolute_tolerance"    : 1e-9,
-      "residual_relative_tolerance"        : 0.0001,
-      "residual_absolute_tolerance"        : 1e-9,
-      "max_iteration"                      : 10,
-      "linear_solver_settings"             : {
-          "solver_type" : "ExternalSolversApplication.super_lu",
-          "scaling"     : false,
-          "verbosity"   : 0
-      },
-      "rotation_dofs"                      : true
-  },
-  "processes": {
-    "constraints_process_list" : [{
-        "python_module" : "assign_vector_variable_process",
-        "kratos_module" : "KratosMultiphysics",
-        "help"          : "This process fixes the selected components of a given vector variable",
-        "process_name"  : "AssignVectorVariableProcess",
-        "Parameters"    : {
-            "mesh_id"         : 0,
-            "model_part_name" : "plate.corner_points",
-            "variable_name"   : "DISPLACEMENT",
-            "value"           : [0.0,0.0,0.0]
-        }
+    "problem_data": {
+        "problem_name": "Plate",
+        "parallel_type": "OpenMP",
+        "start_time": 0.0,
+        "end_time": 1.0,
+        "echo_level": 0
     },
-    {
-        "python_module" : "assign_vector_variable_process",
-        "kratos_module" : "KratosMultiphysics",
-        "help"          : "This process fixes the selected components of a given vector variable",
-        "process_name"  : "AssignVectorVariableProcess",
-        "Parameters"    : {
-            "mesh_id"         : 0,
-            "model_part_name" : "plate.corner_points",
-            "variable_name"   : "ROTATION",
-            "value"           : [0.0,0.0,0.0]
-        }
-    }],
-    "loads_process_list"       : [{
-        "python_module" : "assign_vector_by_direction_process",
-        "kratos_module" : "KratosMultiphysics",
-        "process_name"  : "AssignVectorByDirectionProcess",
-        "Parameters"    : {
-            "mesh_id"         : 0,
-            "model_part_name" : "plate.load_point",
-            "variable_name"   : "POINT_LOAD",
-            "modulus"         : 100.0,
-            "constrained"     : false,
-            "direction"       : [0.0,0.0,-1.0]
-        }
-    }]
-  },
-  "output_processes" : {
-    "gid_output" : [{
-        "python_module" : "gid_output_process",
-        "kratos_module" : "KratosMultiphysics",
-        "process_name"  : "GiDOutputProcess",
-        "help"          : "This process writes postprocessing files for GiD",
-        "Parameters"    : {
-            "model_part_name"        : "plate",
-            "output_name"            : "plate",
-            "postprocess_parameters" : {
-                "result_file_configuration" : {
-                    "gidpost_flags"       : {
-                        "GiDPostMode"           : "GiD_PostBinary",
-                        "WriteDeformedMeshFlag" : "WriteDeformed",
-                        "WriteConditionsFlag"   : "WriteConditions",
-                        "MultiFileFlag"         : "SingleFile"
-                    },
-                    "file_label"          : "step",
-                    "output_control_type" : "step",
-                    "output_frequency"    : 1,
-                    "body_output"         : true,
-                    "node_output"         : false,
-                    "skin_output"         : false,
-                    "nodal_results"       : ["DISPLACEMENT","REACTION","POINT_LOAD","ROTATION"]
-                },
-                "point_data_configuration"  : []
+    "solver_settings": {
+        "solver_type": "static",
+        "echo_level": 0,
+        "analysis_type": "linear",
+        "model_part_name": "plate",
+        "domain_size": 3,
+        "time_stepping": {
+            "time_step": 1.0
+        },
+        "model_import_settings": {
+            "input_type": "use_input_model_part",
+            "input_filename": "plate"
+        },
+        "material_import_settings": {
+            "materials_filename": "2D_material.json"
+        },
+        "line_search": false,
+        "convergence_criterion": "residual_criterion",
+        "displacement_relative_tolerance": 0.0001,
+        "displacement_absolute_tolerance": 1e-9,
+        "residual_relative_tolerance": 0.0001,
+        "residual_absolute_tolerance": 1e-9,
+        "max_iteration": 10,
+        "linear_solver_settings": {
+            "solver_type": "EigenSolversApplication.sparse_lu",
+            "scaling": false,
+            "verbosity": 0
+        },
+        "rotation_dofs": true
+    },
+    "processes": {
+        "constraints_process_list": [
+            {
+                "python_module": "assign_vector_variable_process",
+                "kratos_module": "KratosMultiphysics",
+                "help": "This process fixes the selected components of a given vector variable",
+                "process_name": "AssignVectorVariableProcess",
+                "Parameters": {
+                    "mesh_id": 0,
+                    "model_part_name": "plate.corner_points",
+                    "variable_name": "DISPLACEMENT",
+                    "value": [
+                        0.0,
+                        0.0,
+                        0.0
+                    ]
+                }
+            },
+            {
+                "python_module": "assign_vector_variable_process",
+                "kratos_module": "KratosMultiphysics",
+                "help": "This process fixes the selected components of a given vector variable",
+                "process_name": "AssignVectorVariableProcess",
+                "Parameters": {
+                    "mesh_id": 0,
+                    "model_part_name": "plate.corner_points",
+                    "variable_name": "ROTATION",
+                    "value": [
+                        0.0,
+                        0.0,
+                        0.0
+                    ]
+                }
+            }
+        ],
+        "loads_process_list": [
+            {
+                "python_module": "assign_vector_by_direction_process",
+                "kratos_module": "KratosMultiphysics",
+                "process_name": "AssignVectorByDirectionProcess",
+                "Parameters": {
+                    "mesh_id": 0,
+                    "model_part_name": "plate.load_point",
+                    "variable_name": "POINT_LOAD",
+                    "modulus": 100.0,
+                    "constrained": false,
+                    "direction": [
+                        0.0,
+                        0.0,
+                        -1.0
+                    ]
+                }
+            }
+        ]
+    },
+    "output_processes": {
+        "gid_output": [
+            {
+                "python_module": "gid_output_process",
+                "kratos_module": "KratosMultiphysics",
+                "process_name": "GiDOutputProcess",
+                "help": "This process writes postprocessing files for GiD",
+                "Parameters": {
+                    "model_part_name": "plate",
+                    "output_name": "plate",
+                    "postprocess_parameters": {
+                        "result_file_configuration": {
+                            "gidpost_flags": {
+                                "GiDPostMode": "GiD_PostBinary",
+                                "WriteDeformedMeshFlag": "WriteDeformed",
+                                "WriteConditionsFlag": "WriteConditions",
+                                "MultiFileFlag": "SingleFile"
+                            },
+                            "file_label": "step",
+                            "output_control_type": "step",
+                            "output_frequency": 1,
+                            "body_output": true,
+                            "node_output": false,
+                            "skin_output": false,
+                            "nodal_results": [
+                                "DISPLACEMENT",
+                                "REACTION",
+                                "POINT_LOAD",
+                                "ROTATION"
+                            ]
+                        },
+                        "point_data_configuration": []
+                    }
+                }
+            }
+        ],
+        "vtk_output": [
+            {
+                "python_module": "vtk_output_process",
+                "kratos_module": "KratosMultiphysics",
+                "process_name": "VTKOutputProcess",
+                "help": "This process writes postprocessing files for VTK",
+                "Parameters": {
+                    "model_part_name": "plate",
+                    "file_format": "binary",
+                    "output_precision": 7,
+                    "output_control_type": "step",
+                    "output_interval": 1.0,
+                    "output_sub_model_parts": false,
+                    "folder_name": "analysis_Results",
+                    "save_output_files_in_folder": true,
+                    "nodal_solution_step_data_variables": [
+                        "DISPLACEMENT",
+                        "REACTION",
+                        "ROTATION",
+                        "POINT_LOAD"
+                    ],
+                    "nodal_data_value_variables": [],
+                    "element_data_value_variables": [],
+                    "condition_data_value_variables": [],
+                    "gauss_point_variables_extrapolated_to_nodes": [],
+                    "gauss_point_variables_in_elements": []
+                }
             }
-        }
-    }]
-  }
-}
+        ]
+    }
+}