EVOLUTIONARY TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES -- Contents -- Preface -- 1 Introduction -- 1.1 Structural Optimization -- 1.2 Topology Optimization of Continuum Structures -- 1.3 ESO/BESO and the Layout of the Book -- References -- 2 Evolutionary Structural Optimization Method -- 2.1 Introduction -- 2.2 ESO Based on Stress Level -- 2.2.1 Evolutionary Procedure -- 2.2.2 Example of Two-bar Frame -- 2.2.3 Examples of Michell Type Structures -- 2.3 ESO for Stiffness or Displacement Optimization -- 2.3.1 Sensitivity Number and Evolutionary Procedure -- 2.3.2 Example of a Short Cantilever -- 2.3.3 Example of a Beam Structure -- 2.4 Conclusion -- References -- 3 Bi-directional Evolutionary Structural Optimization Method -- 3.1 Introduction -- 3.2 Problem Statement and Sensitivity Number -- 3.2.1 Problem Statement -- 3.2.2 Sensitivity Number -- 3.3 Filter Scheme and Improved Sensitivity Number -- 3.3.1 Checkerboard and Mesh-dependency Problems -- 3.3.2 Filter Scheme for BESO Method -- 3.3.3 Stabilizing the Evolutionary Process -- 3.4 Element Removal/Addition and Convergence Criterion -- 3.5 Basic BESO Procedure -- 3.6 Examples of BESO Starting from Initial Full Design -- 3.6.1 Topology Optimization of a Short Cantilever -- 3.6.2 Topology Optimization of a Beam -- 3.7 Examples of BESO Starting from Initial Guess Design -- 3.8 Example of a 3D Structure -- 3.9 Mesh-independence Studies -- 3.10 Conclusion -- References -- 4 BESO Utilizing Material Interpolation Scheme with Penalization -- 4.1 Introduction -- 4.2 Problem Statement and Material Interpolation Scheme -- 4.2.1 Problem Statement -- 4.2.2 Material Interpolation Scheme -- 4.3 Sensitivity Analysis and Sensitivity Number -- 4.3.1 Sensitivity Analysis -- 4.3.2 Sensitivity Number -- 4.4 Examples -- 4.4.1 Topology Optimization of a Short Cantilever -- 4.4.2 Topology Optimization of a Beam.

4.4.3 Topology Optimization of a 3D Cantilever -- 4.5 Conclusion -- Appendix 4.1 -- References -- 5 Comparing BESO with Other Topology Optimization Methods -- 5.1 Introduction -- 5.2 The SIMP Method -- 5.3 Comparing BESO with SIMP -- 5.3.1 Comparison of Topology Optimization Algorithms without a Mesh-independency Filter -- 5.3.2 Comparison of Topology Optimization Algorithms with a Mesh-independency Filter -- 5.3.3 Advantages of the BESO Method and Questions yet to be Resolved -- 5.4 Discussion on Zhou and Rozvany (2001) Example -- 5.4.1 Introduction of Zhou and Rozvany (2001) Example -- 5.4.2 Is it a Nonoptimal or a Local Optimal Solution? -- 5.4.3 Avoidance of Highly Inefficient Local Optimum -- 5.5 Conclusion -- References -- 6 BESO for Extended Topology Optimization Problems -- 6.1 Introduction -- 6.2 Minimizing Structural Volume with a Displacement or Compliance Constraint -- 6.2.1 Sensitivity Analysis and Sensitivity Number -- 6.2.2 Determination of Structural Volume -- 6.2.3 Examples -- 6.3 Stiffness Optimization with an Additional Displacement Constraint -- 6.3.1 Sensitivity Number -- 6.3.2 Determination of Lagrangian Multiplier -- 6.3.3 Examples -- 6.4 Stiffness Optimization of Structures with Multiple Materials -- 6.4.1 Sensitivity Number -- 6.4.2 Examples -- 6.5 Topology Optimization of Periodic Structures -- 6.5.1 Problem Statement and Sensitivity Number -- 6.5.2 Examples -- 6.6 Topology Optimization of Structures with Design-dependent Gravity Load -- 6.6.1 Sensitivity Analysis and Sensitivity Number -- 6.6.2 Examples -- 6.7 Topology Optimization for Natural Frequency -- 6.7.1 Frequency Optimization Problem and Material Interpolation Scheme -- 6.7.2 Sensitivity Number -- 6.7.3 Examples -- 6.8 Topology Optimization for Multiple Load Cases -- 6.8.1 Sensitivity Number -- 6.8.2 Examples -- 6.9 BESO Based on von Mises Stress.

6.9.1 Sensitivity Number -- 6.9.2 Examples -- 6.10 Conclusion -- References -- 7 Topology Optimization of Nonlinear Continuum Structures -- 7.1 Introduction -- 7.2 Objective Functions and Nonlinear Analysis -- 7.3 Sensitivity Analysis and Sensitivity Number for Force Control -- 7.4 Sensitivity Analysis and Sensitivity Number for Displacement Control -- 7.5 BESO Procedure for Nonlinear Structures -- 7.6 Examples of Nonlinear Structures under Force Control -- 7.6.1 Geometrically Nonlinear Structure -- 7.6.2 Materially Nonlinear Structure -- 7.6.3 Geometrically and Materially Nonlinear Structures -- 7.6.4 Effects of the Nonlinear Properties and the Magnitude of the Design Load -- 7.6.5 Three-dimensional Geometrically and Materially Nonlinear Structure -- 7.7 Examples of Nonlinear Structures under Displacement Control -- 7.7.1 Results from a Relatively Small Design Displacement -- 7.7.2 Results from Large Design Displacements -- 7.7.3 Example of a 3D Structure -- 7.8 Conclusion -- References -- 8 Optimal Design of Energy Absorption Structures -- 8.1 Introduction -- 8.2 Problem Statement for Optimization of Energy Absorption Structures -- 8.3 Sensitivity Number -- 8.3.1 Criterion 1: Sensitivity Number for the End Displacement -- 8.3.2 Criterion 2: Sensitivity Number for the Whole Displacement History -- 8.4 Evolutionary Procedure for Removing and Adding Material -- 8.5 Numerical Examples and Discussions -- 8.5.1 Example 1 -- 8.5.2 Example 2 -- 8.5.3 Example 3 -- 8.5.4 Example 4 -- 8.6 Conclusion -- References -- 9 Practical Applications -- 9.1 Introduction -- 9.2 Akutagwa River Side Project in Japan -- 9.3 Florence New Station Project in Italy -- 9.4 Sagrada Famı́lia Church in Spain -- 9.5 Pedestrian Bridge Project in Australia -- 9.6 Conclusion -- References -- 10 Computer Program BESO2D -- 10.1 Introduction.

10.2 System Requirements and Program Installation -- 10.2.1 System Requirements -- 10.2.2 Installation of BESO2D -- 10.2.3 Constitutive Parts of BESO2D Package -- 10.3 Windows Interface of BESO2D -- 10.3.1 Overview of the GUI Window -- 10.3.2 Menu Bar -- 10.3.3 Toolbar Area -- 10.3.4 Display Area and Status Bar -- 10.3.5 Status Bar -- 10.4 Running BESO2D from Graphic User Interface -- 10.4.1 Drawing the Design Domain of a Structure -- 10.4.2 Generating a Finite Element Mesh of the Design Domain -- 10.4.3 Specifying Boundary Conditions, Loading Conditions and Material Properties -- 10.4.4 Performing FEA on the Meshed Model and Showing the Analysis Result -- 10.4.5 Performing BESO Optimization -- 10.4.6 Viewing the Final Optimal Design and the Evolution Histories -- 10.4.7 Optimization Continued from a Previously Obtained Design -- 10.5 The Command Line Usage of BESO2D -- 10.5.1 Calling the BESO2D Engine -- 10.5.2 The Model File Format Accepted by the BESO2D Engine -- 10.5.3 Format of BESO Parameter File -- 10.5.4 Result File of an Optimization Run -- 10.6 Running BESO2D from the Command Line -- 10.6.1 Optimize a Structure from an Initial Design -- 10.6.2 Continuing Optimization from a Previously Obtained Design Solution -- 10.7 Files Produced by BESO2D -- 10.8 Error Messages -- Author Index -- Subject Index.