-
Notifications
You must be signed in to change notification settings - Fork 1
/
manuscript_Stragiotti.toc
157 lines (157 loc) · 14.1 KB
/
manuscript_Stragiotti.toc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
\@ifundefined {etoctocstyle}{\let \etoc@startlocaltoc \@gobble \let \etoc@settocdepth \@gobble \let \etoc@depthtag \@gobble \let \etoc@setlocaltop \@gobble }{}
\babel@toc {english}{}\relax
\contentsline {chapter}{Abstract}{iii}{section*.2}%
\contentsline {chapter}{Acknowledgement}{v}{section*.4}%
\contentsline {chapter}{\nonumberline Contents}{vii}{chapter*.5}%
\contentsline {chapter}{\nonumberline List of Figures}{xi}{chapter*.6}%
\contentsline {chapter}{\nonumberline List of Tables}{xviii}{chapter*.7}%
\contentsline {chapter}{List of Abbreviations}{xx}{section*.8}%
\contentsline {chapter}{Introduction}{1}{section*.11}%
\contentsline {chapter}{\numberline {1}Literature review}{5}{chapter.1}%
\etoc@startlocaltoc {2}
\etoc@startlocaltoc {3}
\contentsline {section}{\numberline {1.1}Generalities of structural optimization}{5}{section.1.1}%
\contentsline {mtocsection}{\numberline {1.1}Generalities of structural optimization}{5}{section.1.1}%
\contentsline {paragraph}{\nonumberline Objective Function}{6}{paragraph*.20}%
\contentsline {paragraph}{\nonumberline Design Variables}{6}{paragraph*.22}%
\contentsline {paragraph}{\nonumberline Constraints}{6}{paragraph*.24}%
\contentsline {subsection}{\numberline {1.1.1}Optimizers}{7}{subsection.1.1.1}%
\contentsline {section}{\numberline {1.2}Ultra-lightweight structures optimization approaches}{9}{section.1.2}%
\contentsline {mtocsection}{\numberline {1.2}Ultra-lightweight structures optimization approaches}{9}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}Density-based topology optimization}{10}{subsection.1.2.1}%
\contentsline {paragraph}{\nonumberline Compliance minimization formulation}{11}{paragraph*.27}%
\contentsline {paragraph}{\nonumberline Spatial filtering and projection}{12}{paragraph*.30}%
\contentsline {subsection}{\numberline {1.2.2}Feature-mapping topology optimization}{14}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {1.2.3}Truss Topology Optimization (TTO)}{14}{subsection.1.2.3}%
\contentsline {paragraph}{\nonumberline Classical Michell structures}{15}{paragraph*.35}%
\contentsline {paragraph}{\nonumberline Plastic material formulation}{16}{paragraph*.37}%
\contentsline {paragraph}{\nonumberline The ground structure approach}{16}{paragraph*.39}%
\contentsline {paragraph}{\nonumberline Optimization formulation}{17}{paragraph*.42}%
\contentsline {section}{\numberline {1.3}Lattice structures and materials}{18}{section.1.3}%
\contentsline {mtocsection}{\numberline {1.3}Lattice structures and materials}{18}{section.1.3}%
\contentsline {subsection}{\numberline {1.3.1}Modular structures and cellular materials optimization}{22}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {1.3.2}Multi-scale structures optimization}{23}{subsection.1.3.2}%
\contentsline {subsection}{\numberline {1.3.3}Full-scale structures optimization}{25}{subsection.1.3.3}%
\contentsline {section}{\numberline {1.4}Conclusion}{26}{section.1.4}%
\contentsline {mtocsection}{\numberline {1.4}Conclusion}{26}{section.1.4}%
\contentsline {chapter}{\numberline {2}Evaluating discretization approaches for ultralight structure optimization}{27}{chapter.2}%
\etoc@startlocaltoc {4}
\etoc@startlocaltoc {5}
\contentsline {section}{\numberline {2.1}The formulation of a shared problem: volume minimization with stress constraints}{27}{section.2.1}%
\contentsline {mtocsection}{\numberline {2.1}The formulation of a shared problem: volume minimization with stress constraints}{27}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}Density-based topology optimization minimum volume formulation}{27}{subsection.2.1.1}%
\contentsline {paragraph}{\nonumberline Objective and constraint functions}{28}{paragraph*.54}%
\contentsline {paragraph}{\nonumberline Von Mises stress evaluation}{28}{paragraph*.56}%
\contentsline {paragraph}{\nonumberline Microscopic and macroscopic stress}{29}{paragraph*.59}%
\contentsline {paragraph}{\nonumberline Constraints aggregation and relaxation}{30}{paragraph*.61}%
\contentsline {paragraph}{\nonumberline Minimum volume formulation}{31}{paragraph*.63}%
\contentsline {paragraph}{\nonumberline Sensitivity analysis of the objective function}{31}{paragraph*.65}%
\contentsline {paragraph}{\nonumberline Sensitivity analysis of the constraint function}{32}{paragraph*.67}%
\contentsline {subsection}{\numberline {2.1.2}\acrfull {tto} minimum volume formulation}{34}{subsection.2.1.2}%
\contentsline {paragraph}{\nonumberline Objective and constraint functions}{34}{paragraph*.69}%
\contentsline {paragraph}{\nonumberline Minimum volume formulation}{35}{paragraph*.71}%
\contentsline {section}{\numberline {2.2}Comparison between density-based topology optimization and TTO}{36}{section.2.2}%
\contentsline {mtocsection}{\numberline {2.2}Comparison between density-based topology optimization and TTO}{36}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}Definition of a test case for the comparison}{36}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}Numerical application}{37}{subsection.2.2.2}%
\contentsline {paragraph}{\nonumberline density-based topology optimization results}{38}{figure.caption.76}%
\contentsline {paragraph}{\nonumberline TTO optimization results}{41}{paragraph*.82}%
\contentsline {subsection}{\numberline {2.2.3}Discussion}{44}{subsection.2.2.3}%
\contentsline {section}{\numberline {2.3}Conclusion}{47}{section.2.3}%
\contentsline {mtocsection}{\numberline {2.3}Conclusion}{47}{section.2.3}%
\contentsline {chapter}{\numberline {3}Enriching the classic TTO formulation with advanced mechanical constraints}{49}{chapter.3}%
\etoc@startlocaltoc {6}
\etoc@startlocaltoc {7}
\contentsline {section}{\numberline {3.1}Advanced mechanical constraints}{49}{section.3.1}%
\contentsline {mtocsection}{\numberline {3.1}Advanced mechanical constraints}{49}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}Minimum slenderness constraints}{50}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {3.1.2}Local and topological buckling constraints}{51}{subsection.3.1.2}%
\contentsline {subsection}{\numberline {3.1.3}Kinematic compatibility constraints}{53}{subsection.3.1.3}%
\contentsline {section}{\numberline {3.2}Optimization formulation and solving strategy}{54}{section.3.2}%
\contentsline {mtocsection}{\numberline {3.2}Optimization formulation and solving strategy}{54}{section.3.2}%
\contentsline {subsection}{\numberline {3.2.1}Formulation of a two-step optimization strategy}{55}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {3.2.2}First step: SLP optimization}{55}{subsection.3.2.2}%
\contentsline {subsection}{\numberline {3.2.3}Handling local minima: reinitialization strategy}{57}{subsection.3.2.3}%
\contentsline {subsection}{\numberline {3.2.4}Second step: NLP optimization}{59}{subsection.3.2.4}%
\contentsline {section}{\numberline {3.3}Numerical optimization of monolithic structures}{60}{section.3.3}%
\contentsline {mtocsection}{\numberline {3.3}Numerical optimization of monolithic structures}{60}{section.3.3}%
\contentsline {subsection}{\numberline {3.3.1}L-shaped beam}{62}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {3.3.2}Ten-bar truss}{63}{subsection.3.3.2}%
\contentsline {subsection}{\numberline {3.3.3}2D cantilever beam}{66}{subsection.3.3.3}%
\contentsline {subsection}{\numberline {3.3.4}Simply supported 3D beam}{69}{subsection.3.3.4}%
\contentsline {subsection}{\numberline {3.3.5}Ten-bar truss with multiple load cases}{71}{subsection.3.3.5}%
\contentsline {section}{\numberline {3.4}Conclusion}{74}{section.3.4}%
\contentsline {mtocsection}{\numberline {3.4}Conclusion}{74}{section.3.4}%
\contentsline {chapter}{\numberline {4}Optimizing modular lattice structures}{75}{chapter.4}%
\etoc@startlocaltoc {8}
\etoc@startlocaltoc {9}
\contentsline {section}{\numberline {4.1}Formulation of a modular structure optimization algorithm}{75}{section.4.1}%
\contentsline {mtocsection}{\numberline {4.1}Formulation of a modular structure optimization algorithm}{75}{section.4.1}%
\contentsline {subsection}{\numberline {4.1.1}Variable linking}{76}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {4.1.2}Topological buckling of modular structures}{77}{subsection.4.1.2}%
\contentsline {subsection}{\numberline {4.1.3}Modular optimization formulation}{78}{subsection.4.1.3}%
\contentsline {subsection}{\numberline {4.1.4}Sensitivity analysis}{79}{subsection.4.1.4}%
\contentsline {section}{\numberline {4.2}Optimization of modular structures using the variable linking approach}{80}{section.4.2}%
\contentsline {mtocsection}{\numberline {4.2}Optimization of modular structures using the variable linking approach}{80}{section.4.2}%
\contentsline {subsection}{\numberline {4.2.1}On the equivalence of multi-load cases and modular structures}{80}{subsection.4.2.1}%
\contentsline {subsection}{\numberline {4.2.2}Parametric study on the number of subdomains and the complexity of the module}{82}{subsection.4.2.2}%
\contentsline {paragraph}{\nonumberline Influence of the number of the subdomains}{83}{paragraph*.140}%
\contentsline {paragraph}{\nonumberline Influence of the complexity of the module}{85}{figure.caption.149}%
\contentsline {paragraph}{\nonumberline Design of experiments}{87}{paragraph*.155}%
\contentsline {paragraph}{\nonumberline Discussion on the DOE}{89}{paragraph*.161}%
\contentsline {subsection}{\numberline {4.2.3}Comparison with the optimized octet-truss}{90}{subsection.4.2.3}%
\contentsline {subsection}{\numberline {4.2.4}Using multiple module topologies}{92}{subsection.4.2.4}%
\contentsline {section}{\numberline {4.3}Conclusion}{96}{section.4.3}%
\contentsline {mtocsection}{\numberline {4.3}Conclusion}{96}{section.4.3}%
\contentsline {chapter}{\numberline {5}Optimizing the spatial layout of the modules}{99}{chapter.5}%
\etoc@startlocaltoc {10}
\etoc@startlocaltoc {11}
\contentsline {section}{\numberline {5.1}Optimizing the modules' layout using a modified DMO algorithm}{99}{section.5.1}%
\contentsline {mtocsection}{\numberline {5.1}Optimizing the modules' layout using a modified DMO algorithm}{99}{section.5.1}%
\contentsline {subsection}{\numberline {5.1.1}Definition of the subdomains cross-sectional areas}{99}{subsection.5.1.1}%
\contentsline {subsection}{\numberline {5.1.2}Variables penalization schemes}{100}{subsection.5.1.2}%
\contentsline {subsection}{\numberline {5.1.3}The optimization formulation and resolution strategy}{102}{subsection.5.1.3}%
\contentsline {subsection}{\numberline {5.1.4}Optimization initialization: a clustering algorithm to identify similarly behaving subdomains}{104}{subsection.5.1.4}%
\contentsline {section}{\numberline {5.2}Optimization of the topology and layout of modular structures}{106}{section.5.2}%
\contentsline {mtocsection}{\numberline {5.2}Optimization of the topology and layout of modular structures}{106}{section.5.2}%
\contentsline {subsection}{\numberline {5.2.1}Layout optimization of fixed topology modules}{107}{subsection.5.2.1}%
\contentsline {subsection}{\numberline {5.2.2}Optimizing topology and layout of the modules}{110}{subsection.5.2.2}%
\contentsline {subsection}{\numberline {5.2.3}A benchmark case study: a simply supported modular bridge}{113}{subsection.5.2.3}%
\contentsline {subsection}{\numberline {5.2.4}Simply supported 3D beam}{118}{subsection.5.2.4}%
\contentsline {section}{\numberline {5.3}Conclusion}{119}{section.5.3}%
\contentsline {mtocsection}{\numberline {5.3}Conclusion}{119}{section.5.3}%
\contentsline {chapter}{\numberline {6}Design of real-size aeronautical wing structures}{121}{chapter.6}%
\etoc@startlocaltoc {12}
\etoc@startlocaltoc {13}
\contentsline {section}{\numberline {6.1}3D CRM wingbox with multiple load cases}{121}{section.6.1}%
\contentsline {mtocsection}{\numberline {6.1}3D CRM wingbox with multiple load cases}{121}{section.6.1}%
\contentsline {subsection}{\numberline {6.1.1}Advanced thresholding}{122}{subsection.6.1.1}%
\contentsline {subsection}{\numberline {6.1.2}Numerical optimization of the CRM wingbox}{123}{subsection.6.1.2}%
\contentsline {paragraph}{\nonumberline Maximum Displacement Constraints}{124}{paragraph*.207}%
\contentsline {paragraph}{\nonumberline Multiple materials}{126}{paragraph*.211}%
\contentsline {paragraph}{\nonumberline Enriching the mesh}{128}{paragraph*.217}%
\contentsline {paragraph}{\nonumberline Active mechanical constraints}{130}{paragraph*.221}%
\contentsline {paragraph}{\nonumberline Discussion on the modular CRM}{130}{paragraph*.225}%
\contentsline {section}{\numberline {6.2}NACA 0012 modular UAV wing}{132}{section.6.2}%
\contentsline {mtocsection}{\numberline {6.2}NACA 0012 modular UAV wing}{132}{section.6.2}%
\contentsline {subsection}{\numberline {6.2.1}Modular ground structure generation for irregular volumes}{132}{subsection.6.2.1}%
\contentsline {subsection}{\numberline {6.2.2}Numerical optimization of the modular NACA 0012 \gls {uav} wing}{133}{subsection.6.2.2}%
\contentsline {section}{\numberline {6.3}Conclusion}{141}{section.6.3}%
\contentsline {mtocsection}{\numberline {6.3}Conclusion}{141}{section.6.3}%
\etoc@startlocaltoc {14}
\etoc@startlocaltoc {15}
\contentsline {chapter}{Conclusion and perspectives}{143}{section*.238}%
\contentsline {chapter}{Communications}{149}{section*.242}%
\contentsline {chapter}{\nonumberline Bibliography}{151}{chapter*.246}%
\contentsline {part}{\nonumberline Appendix}{177}{part*.248}%
\contentsline {chapter}{\nonumberline Sensitivity analysis of the modular lattice structure optimization algorithm}{179}{chapter*.249}%
\contentsline {section}{\numberline {1}Optimization formulation, objective function and constraints}{179}{section.6.1}%
\contentsline {mtocsection}{\numberline {1}Optimization formulation, objective function and constraints}{179}{section.6.1}%
\contentsline {section}{\numberline {2}Common derivatives}{180}{section.6.2}%
\contentsline {mtocsection}{\numberline {2}Common derivatives}{180}{section.6.2}%
\contentsline {section}{\numberline {3}Gradient}{181}{section.6.3}%
\contentsline {mtocsection}{\numberline {3}Gradient}{181}{section.6.3}%
\contentsline {section}{\numberline {4}Jacobian matrix}{181}{section.6.4}%
\contentsline {mtocsection}{\numberline {4}Jacobian matrix}{181}{section.6.4}%
\contentsline {section}{\numberline {5}Hessian matrix}{183}{section.6.5}%
\contentsline {mtocsection}{\numberline {5}Hessian matrix}{183}{section.6.5}%