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Generic Topology Optimization Based on Local State Features / Titelei/Inhaltsverzeichnis
Generic Topology Optimization Based on Local State Features / Titelei/Inhaltsverzeichnis
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I–XVIII
Titelei/Inhaltsverzeichnis
I–XVIII
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1–7
1 Introduction
1–7
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8–28
2 Fundamentals
8–28
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2.1 Background: Topology Optimization of Continuum Structures
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2.1.1 General ProblemFormulation
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2.1.2 Early Topology Optimization
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2.1.3 Topology Optimization Approaches
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2.2 Density-based Topology Optimization
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2.2.1 ProblemFormulation
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2.2.2 The Minimum Compliance Problem
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2.3 Evolutionary Computation
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2.3.1 Evolution Strategies
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2.3.2 Covariance-Matrix Adaptation Evolutionary Strategy
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2.4 Summary
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29–47
3 Structure Representations for Evolutionary Computation
29–47
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3.1 Representing the Structure
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3.2 Grid Representation
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3.2.1 Bit-Array Encoding
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3.2.2 Real-Valued Array Encoding
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3.3 Geometric Representation
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3.3.1 Voronoi-cells
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3.3.2 Material-Mask Overlay
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3.3.3 Graph Representation
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3.3.4 Level SetMethods
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3.4 Indirect Representation
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3.4.1 Lindenmayer System
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3.4.2 Gene Regulatory Network
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3.4.3 Compositional Pattern Producing Network
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3.5 Discussion
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3.6 Summary of Contribution
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48–83
4 Topology Optimization by Predicting Sensitivities
48–83
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4.1 Generic Update-SignalModel
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4.1.1 Introduction
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4.1.2 Replacing Sensitivities
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4.1.3 Local State Features
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4.2 Enclosing Topology Optimization
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4.2.1 Improvement Threshold
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4.3 Explicit Evolutionary Learning
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4.3.1 Neural Network ApproximationModel
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4.3.2 Piecewise-Constant Model
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4.3.3 Optimization with CMA-ES
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4.3.4 Computational Flow
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4.4 Sampling and Supervised Learning
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4.4.1 Sensitivity Estimation by Finite-Difference Sampling
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4.4.2 Aggregated Sensitivity-Sampling
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4.4.3 Sensitivity Regression Model
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4.4.4 Computational Flow
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4.5 Summary of Contribution
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84–120
5 Studies on the Minimum Compliance Problem
84–120
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5.1 Reference Problem
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5.1.1 Linear Static LSF
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5.2 NE/PCM-TOPS Experiments
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5.2.1 Results LSF Vector I
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5.2.2 Results LSF Vector II
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5.2.3 NE/PCM-TOPS Results Discussion
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5.3 SVR/LIN-TOPS Experiments
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5.3.1 Results LSF Vector I
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5.3.2 Results LSF Vector II
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5.3.3 Intermediate LIN/SVR-TOPS Results Discussion
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5.3.4 Mesh-Independency Study
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5.3.5 Alternative LSF
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5.3.6 Experiments with Aggregated Sampling
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5.4 Overall Discussion
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5.5 Summary of Contribution
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121–149
6 Topology Optimization of Crashworthiness Objectives
121–149
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6.1 State-of-the-art
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6.2 Maximum Energy Absorption Beam
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6.2.1 Beam Model and Optimization Set-up
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6.2.2 Optimization Results
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6.3 MinimumIntrusion Frame
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6.3.1 Frame Model and Optimization Set-up
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6.3.2 Optimization Results
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6.4 Summary of Contribution
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150–154
7 Conclusions
150–154
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7.1 Main Results
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7.2 Future Directions
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155–160
A Theory
155–160
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A.1 Adjoint Sensitivities
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A.2 Sensitivity RegressionModels
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A.2.1 Linear Regression
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A.2.2 Support Vector Regression
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A.3 Compliance Topology Optimization
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A.4 Correlation Coefficient
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161–171
B Compliance Studies Results
161–171
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172–176
C Crashworthiness
172–176
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177–202
Bibliography
177–202
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Generic Topology Optimization Based on Local State Features , page I - XVIII
Titelei/Inhaltsverzeichnis
Autoren
Nikola Aulig
DOI
doi.org/10.51202/9783186468208-I
ISBN print: 978-3-18-346820-1
ISBN online: 978-3-18-646820-8
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