| Preface | 6 |
|---|
| Contents | 8 |
|---|
| Contents of the CD | 12 |
|---|
| Readme | 12 |
| Computer Programs | 12 |
| Tools | 14 |
| 1 Introduction | 15 |
|---|
| 1.1 Problem Statement | 15 |
| 1.2 An Optimization Problem | 16 |
| 1.3 Elementary Calculus | 19 |
| 1.4 Optimal Slope for Truss Bars | 20 |
| 1.5 An Arch Problem | 21 |
| 1.6 The Gradient of a Function | 22 |
| 1.7 The Lagrange Multiplier Rule | 25 |
| 1.8 Newton s Method | 26 |
| 1.9 Solving Linear Equations | 28 |
| 1.10 Linear Systems Versus Optimization | 28 |
| 1.11 Equations of Structures | 29 |
| 1.12 Plastic Analysis | 32 |
| 1.13 A Beam Problem | 33 |
| 1.14 Quadratic Programming | 34 |
| 1.15 Embedding | 35 |
| 1.16 Geometric Programming | 35 |
| 1.17 Plastic Design of Plane Frames | 36 |
| 1.18 Problems | 38 |
| 2 Some Tools of Optimization | 42 |
|---|
| 2.1 The Lagrange Multiplier Rule | 42 |
| 2.2 The Kuhn Tucker Conditions | 44 |
| 2.3 Calculus of Variations | 47 |
| 2.4 Newton s Method | 49 |
| 2.5 Linear Programming | 53 |
| 2.6 Sequential Linear Programming | 57 |
| 2.7 Other Methods of Mathematical Programming | 59 |
| 2.8 Genetic Algorithms | 60 |
| 2.9 Problems | 61 |
| 3 Sequential Linear Programming and the Incremental Equations of Structures | 62 |
|---|
| 3.1 Introduction | 62 |
| 3.2 The Incremental Equations of Structures | 62 |
| 3.3 Application to Structural Optimization | 64 |
| 3.4 An Example with a Displacement Constraint | 65 |
| 3.5 Adding Stress Constraints | 69 |
| 3.6 The 25-Bar Truss | 70 |
| 3.7 A Frame Example | 73 |
| 3.8 A Buckling Example | 76 |
| 3.9 The Incremental Equations when Shape Change is Allowed | 80 |
| 3.10 A Beam Example | 85 |
| 3.11 A Plate Bending Problem | 87 |
| 3.12 Problems | 89 |
| 4 Optimality Criteria Methods | 90 |
|---|
| 4.1 Introduction | 90 |
| 4.2 The Most Simple Optimality Criteria Problem | 91 |
| 4.3 Monotone Behavior | 92 |
| 4.4 An Application | 93 |
| 4.5 Sandwich Beams | 97 |
| 4.6 A Generalization of the Truss Problem | 97 |
| 4.7 Plastic Design of Frames | 99 |
| 4.8 Sandwich Plate Design | 101 |
| 4.9 Truss Design | 102 |
| 4.10 A Plane Stress Problem | 104 |
| 4.11 Prager and His Co-Workers | 108 |
| 4.12 A Plate Problem | 110 |
| 4.13 Problems | 113 |
| 5 Some Basic Optimization Problems | 115 |
|---|
| 5.1 Multiple Loading Conditions | 115 |
| 5.2 Deflection Constraints | 121 |
| 5.3 Optimal Shape | 134 |
| 5.4 Generating New Designs Automatically | 140 |
| 5.5 Problems | 149 |
| 6 Beams and Plates: The Work of Rozvany | 150 |
|---|
| 6.1 Introduction | 150 |
| 6.2 Design of Plates | 157 |
| 6.3 Problems | 160 |
| 7 Some Problems of Dynamic Structural Optimization | 161 |
|---|
| 7.1 Introduction | 161 |
| 7.2 Optimization for Transient Vibrations | 162 |
| 7.3 Steady-State Problems | 172 |
| 8 Multicriteria Optimization | 185 |
|---|
| 8.1 Introduction | 185 |
| 8.2 Solving Multicriteria Optimization Problems | 187 |
| 9 Practical Matters: The Work of Farkas and Jarmai | 189 |
|---|
| 9.1 Introduction | 189 |
| 9.2 Sizing Member Cross Sections | 189 |
| 9.3 Tubular Trusses | 192 |
| 9.4 Problems | 196 |
| 10 On Going Work | 197 |
|---|
| 10.1 Design of Tall Buildings | 197 |
| 10.2 Heuristic Algorithms | 202 |
| 10.3 Extending the Design Process | 203 |
| 10.4 Design Theory | 203 |
| A Using the Computer | 206 |
|---|
| A.1 Using Computer Languages and Programs | 206 |
| A.2 Matlab | 208 |
| A.3 Microsoft Excel | 209 |
| A.4 Freeware | 214 |
| A.5 Graphical Interface Applications | 214 |
| B The Node Method for Trusses | 215 |
|---|
| B.1 Introduction | 215 |
| B.2 A Formal Description of the Truss Problem | 216 |
| B.3 A Decomposition | 220 |
| C Convex Sets and Functions: Homogeneous Functions | 227 |
|---|
| C.1 Convex Sets and Functions | 227 |
| C.2 Homogeneous Functions | 228 |
| D Structural Optimization Classics | 231 |
|---|
| D.1 Michell Trusses | 231 |
| D.2 Keller s Optimal Column | 241 |
| D.3 The Paper of Venkayya, Khot, and Berke | 253 |
| References | 297 |
|---|
| Index | 306 |
|---|
