An introduction to structural optimization (Solid Mechanics and Its Applications)

✍ Scribed by Peter W. Christensen, A. Klarbring

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 214
• Edition: 1
• Category: Library

✦ Synopsis

This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered. The mathematical prerequisites are kept to a bare minimum, making the book suitable for undergraduate, or beginning graduate, students of mechanical or structural engineering. Practicing engineers working with structural optimization software would also benefit from reading this book.

✦ Table of Contents

cover-large.TIF......Page 1
front-matter.pdf......Page 2
Preface......Page 6
Contents......Page 8
The Design Process......Page 11
General Mathematical Form of a Structural Optimization Problem......Page 13
Three Types of Structural Optimization Problems......Page 15
Discrete and Distributed Parameter Systems......Page 17
Weight Minimization of a Two-Bar Truss Subject to Stress Constraints......Page 18
Weight Minimization of a Two-Bar Truss Subject to Stress and Instability Constraints......Page 21
Weight Minimization of a Two-Bar Truss Subject to Stress and Displacement Constraints......Page 23
Weight Minimization of a Two-Beam Cantilever Subject to a Displacement Constraint......Page 27
Weight Minimization of a Three-Bar Truss Subject to Stress Constraints......Page 30
Weight Minimization of a Three-Bar Truss Subject to a Stiffness Constraint......Page 40
Exercises......Page 42
Local and Global Optima......Page 44
Convexity......Page 46
KKT Conditions......Page 50
Lagrangian Duality......Page 55
Lagrangian Duality for Convex and Separable Problems......Page 56
Exercises......Page 61
General Solution Procedure for Nested Problems......Page 65
Sequential Linear Programming (SLP)......Page 66
Convex Linearization (CONLIN)......Page 67
The Method of Moving Asymptotes (MMA)......Page 74
Exercises......Page 80
The Simultaneous Formulation of the Problem......Page 84
The Nested Formulation and Some of Its Properties......Page 91
Convexity of the Nested Problem......Page 92
Fully Stressed Designs......Page 94
Minimization of the Volume Under a Compliance Constraint......Page 95
Numerical Solution of the Nested Problem Using MMA......Page 98
Numerical Methods......Page 103
Direct Analytical Method......Page 104
Adjoint Analytical Method......Page 105
Analytical Calculation of Pseudo-loads......Page 106
Bars......Page 107
Shape Optimization......Page 108
Plane Sheets......Page 110
Sizing and Topology Optimization......Page 112
Shape Optimization......Page 113
Exercises......Page 118
Shape Representation......Page 122
Bézier Splines......Page 123
B-Splines......Page 125
Treatment of Geometrical Design Constraints......Page 132
C1 Continuity Between Bézier Splines......Page 133
C1 Continuity at a Point on a Line of Symmetry......Page 134
A Composite Circular Arc......Page 136
Mesh Generation and Calculation of Nodal Sensitivities......Page 137
B-Spline Surface Meshes......Page 138
Coons Surface Meshes......Page 139
Unstructured Meshes......Page 142
Summary of Sensitivity Analysis for Two-Dimensional Shape Optimization......Page 144
Exercises......Page 148
Calculus of Variations......Page 152
Optimality Conditions and Gateaux Derivatives......Page 154
Examples of Gateaux Derivatives......Page 155
Solution of a Simple Example......Page 157
Handling a Constraint......Page 158
Solution of an Example Including a Constraint......Page 159
One-Dimensional Elasticity......Page 161
Beam Problem......Page 163
Two-Dimensional Elasticity......Page 164
Abstract Equilibrium Principles......Page 167
The Design Problem......Page 168
Example: One-dimensional elasticity......Page 169
Example: Two-dimensional elasticity......Page 170
Optimality Conditions......Page 171
The Stiffest Rod......Page 173
Beam Stiffness Optimization......Page 175
Exercises......Page 179
Problem Statement and FE-Discretization......Page 183
The Optimality Criteria (OC) Method......Page 186
Solid Isotropic Material with Penalization (SIMP)......Page 192
The Archetype Problem and an Analogy......Page 194
Numerical Instabilities......Page 195
Restriction of the Archetype Problem......Page 197
Bounds on the Design Gradient......Page 198
Filters......Page 199
Relaxation of the Archetype Problem......Page 202
Exercises......Page 204
Answers to Selected Exercises......Page 206
References......Page 210
Index......Page 212