Evolutionary Structural Optimization

Evolutionary Structural Optimization (ESO) is a design method based on the simple concept of gradually removing inefficient material from a structure as it is being designed. Through this method, the resulting structure will evolve towards its optimum shape. The latest techniques and results of ESO are presented here, illustrated by numerous clear and detailed examples. Sections cover the fundamental aspects of the method, the application to multiple load cases and multiple support environments, frequency optimization, stiffness and displacement constraints, buckling, jointed frame structures, shape optimization, and stress reduction. This is followed by a section describing Evolve97, a software package which will allow readers to try the ideas of ESO themselves and to solve their optimization problems. This software is provided on a computer diskette which accompanies the book.

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.