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Evolutionary Structural Optimization


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Table of Contents

1 Introduction.- 1.1 Background.- 1.2 The Engineering Design Process.- 1.3 Illustration: A Simply Supported Beam.- 1.4 Wish List for Structural Optimization.- 1.5 Finite Element Analysis (FEA).- 1.6 References.- 2 Basic Evolutionary Structural Optimization.- 2.1 Introduction.- 2.2 Material Removal Based on Stress Level.- 2.3 Example of Two-Bar Frame.- 2.4 Examples of Michell Type Structures.- 2.5 Structures with Uniform Surface Stress.- 2.6 Conclusion.- 2.7 References.- 3 ESO for Multiple Load Cases and Multiple Support Environments.- 3.1 Introduction.- 3.2 ESO for Multiple Load Cases.- 3.3 ESO for Multiple Support Environments.- 3.4 Examples of ESO for Multiple Load Cases.- 3.4.1 A Bearing Pedestal.- 3.4.2 A Bridge with a Moving Load.- 3.4.3 Design of Bicycle Frames.- 3.5 Examples of ESO for Multiple Support Environments.- 3.5.1 Fixed and Rolling Arch Supports.- 3.5.2 Sinking Bridge Support.- 3.6 Conclusion.- 3.7 References.- 4 Structures with Stiffness or Displacement Constraints.- 4.1 Overall Stiffness Constraint.- 4.2 Displacement Constraint.- 4.3 Examples of Optimization with a Displacement Constraint.- 4.3.1 A Short Cantilever.- 4.3.2 A Michell Type Structure.- 4.3.3 The MBB Beam.- 4.3.4 A Plate in Bending.- 4.4 Constraint on the Difference of Two Displacements.- 4.5 Multiple Displacement Constraints.- 4.6 Example of Optimization with Multiple Displacement Constraints.- 4.7 Minimizing Weight of Plate by Reducing Element Thickness.- 4.8 Example of Least Weight Design of Plate with Variable Thicknesses.- 4.9 Keeping Weight Constant Through Material Shifting.- 4.10 Example of Optimal Design of Plate Subject to Constant Weight.- 4.11 Conclusion.- 4.12 References.- 5 Frequency Optimization.- 5.1 Introduction.- 5.2 Sensitivity Number for Frequency.- 5.3 Evolutionary Procedures for Frequency Optimization.- 5.3.1 Increase a Chosen Frequency ?n.- 5.3.2 Reduce a Chosen Frequency ?n.- 5.3.3 Keep a Chosen Frequency ?n Constant.- 5.3.4 Increase the Gap Between Two Frequencies.- 5.3.5 Optimization with Multiple Frequency Constraints.- 5.4 Examples.- 5.4.1 A Short Beam.- 5.4.2 A Rectangular Plate.- 5.4.3 A Square Plate.- 5.4.4 A Short Beam with Lumped Mass.- 5.5 Conclusion.- 5.6 References.- 6 Optimization Against Buckling.- 6.1 Introduction.- 6.2 Sensitivity Number for Buckling Load.- 6.3 Bimodal and Multimodal Problems.- 6.4 Evolutionary Procedure for Buckling Optimization.- 6.5 Example of Column Optimization.- 6.6 Example of Frame Optimization.- 6.7 Plate Optimization.- 6.8 Conclusion.- 6.9 References.- 7 ESO for Pin- and Rigid-Jointed Frames.- 7.1 Introduction.- 7.2 ESO Algorithm for Pin-Jointed Frames.- 7.3 ESO Algorithm for Rigid-Jointed Frames.- 7.4 Examples of Size Optimization of Pin-Jointed Frames.- 7.4.1 The Ten Bar Truss.- 7.4.2 Michell Arch.- 7.4.3 Three Dimensional Pin-Jointed Frames.- 7.5 Topology Optimization of Pin-Jointed Frames.- 7.6 Size Optimization for Beams and Rigid-Jointed Frames.- 7.7 Conclusion.- 7.8 References.- 7.9 Appendix.- 8 ESO for Shape Optimization and the Reduction of Stress Concentrations.- 8.1 Introduction.- 8.2 ESO for Shape Optimization.- 8.3 Examples.- 8.3.1 Fillet in Plane Stress under Tension.- 8.3.2 Cantilever with a Tip Load.- 8.3.3 An Open Ended Spanner.- 8.3.4 Optimum Shape of Holes.- 8.3.5 An Adhesive Joint.- 8.4 Conclusion.- 9 ESO Computer Program Evolve97.- 9.1 Introduction.- 9.2 System Requirements and Installation of Evolve97.- 9.3 Overview of the Evolve97 Interface.- 9.3.1 Title Bar.- 9.3.2 Menu Bar.- 9.3.3 Button Bar.- 9.3.4 Display Area.- 9.3.5 Status Bar.- 9.3.6 Drawing Tools Button Bar.- 9.3.7 Mesh and ESO Parameter Button Bar.- 9.3.8 Finite Element Button Bar.- 9.3.9 Evolve Structure Button Bar.- 9.4 To Get Started.- 9.4.1 Drawing a Structural Domain.- 9.4.2 Generate Finite Element Mesh.- 9.4.3 Specifying Properties, Loads, Freedoms and ESO Parameters.- 9.4.4 Carry out FEA of Initial Structure.- 9.4.5 Evolving the Structure.- 9.4.6 Viewing the Evolution History.- 9.5 Evolve97 Data Storage Files.- 9.6 Error Messages.- Author Index.

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