Spillers / Macbain Structural Optimization

1. Auflage 2009
ISBN: 978-0-387-95865-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten

Structural Optimization is intended to supplement the engineer's box of analysis and design tools making optimization as commonplace as the finite element method in the engineering workplace. It begins with an introduction to structural optimization and the methods of nonlinear programming such as Lagrange multipliers, Kuhn-Tucker conditions, and calculus of variations. It then discusses solution methods for optimization problems such as the classic method of linear programming which leads to the method of sequential linear programming. It then proposes using sequential linear programming together with the incremental equations of structures as a general method for structural optimization. It is furthermore intended to give the engineer an overview of the field of structural optimization.

Autoren/Hrsg.

Spillers, William R.

Macbain, Keith M.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Contents of the CD;12
3.1;Readme;12
3.2;Computer Programs;12
3.3;Tools;14
4;1 Introduction;15
4.1;1.1 Problem Statement;15
4.2;1.2 An Optimization Problem;16
4.3;1.3 Elementary Calculus;19
4.4;1.4 Optimal Slope for Truss Bars;20
4.5;1.5 An Arch Problem;21
4.6;1.6 The Gradient of a Function;22
4.7;1.7 The Lagrange Multiplier Rule;25
4.8;1.8 Newton’s Method;26
4.9;1.9 Solving Linear Equations;28
4.10;1.10 Linear Systems Versus Optimization;28
4.11;1.11 Equations of Structures;29
4.12;1.12 Plastic Analysis;32
4.13;1.13 A Beam Problem;33
4.14;1.14 Quadratic Programming;34
4.15;1.15 Embedding;35
4.16;1.16 Geometric Programming;35
4.17;1.17 Plastic Design of Plane Frames;36
4.18;1.18 Problems;38
5;2 Some Tools of Optimization;42
5.1;2.1 The Lagrange Multiplier Rule;42
5.2;2.2 The Kuhn–Tucker Conditions;44
5.3;2.3 Calculus of Variations;47
5.4;2.4 Newton’s Method;49
5.5;2.5 Linear Programming;53
5.6;2.6 Sequential Linear Programming;57
5.7;2.7 Other Methods of Mathematical Programming;59
5.8;2.8 Genetic Algorithms;60
5.9;2.9 Problems;61
6;3 Sequential Linear Programming and the Incremental Equations of Structures;62
6.1;3.1 Introduction;62
6.2;3.2 The Incremental Equations of Structures;62
6.3;3.3 Application to Structural Optimization;64
6.4;3.4 An Example with a Displacement Constraint;65
6.5;3.5 Adding Stress Constraints;69
6.6;3.6 The 25-Bar Truss;70
6.7;3.7 A Frame Example;73
6.8;3.8 A Buckling Example;76
6.9;3.9 The Incremental Equations when Shape Change is Allowed;80
6.10;3.10 A Beam Example;85
6.11;3.11 A Plate Bending Problem;87
6.12;3.12 Problems;89
7;4 Optimality Criteria Methods;90
7.1;4.1 Introduction;90
7.2;4.2 The Most Simple Optimality Criteria Problem;91
7.3;4.3 Monotone Behavior;92
7.4;4.4 An Application;93
7.5;4.5 Sandwich Beams;97
7.6;4.6 A Generalization of the Truss Problem;97
7.7;4.7 Plastic Design of Frames;99
7.8;4.8 Sandwich Plate Design;101
7.9;4.9 Truss Design;102
7.10;4.10 A Plane Stress Problem;104
7.11;4.11 Prager and His Co-Workers;108
7.12;4.12 A Plate Problem;110
7.13;4.13 Problems;113
8;5 Some Basic Optimization Problems;115
8.1;5.1 Multiple Loading Conditions;115
8.2;5.2 Deflection Constraints;121
8.3;5.3 Optimal Shape;134
8.4;5.4 Generating New Designs Automatically;140
8.5;5.5 Problems;149
9;6 Beams and Plates: The Work of Rozvany;150
9.1;6.1 Introduction;150
9.2;6.2 Design of Plates;157
9.3;6.3 Problems;160
10;7 Some Problems of Dynamic Structural Optimization;161
10.1;7.1 Introduction;161
10.2;7.2 Optimization for Transient Vibrations;162
10.3;7.3 Steady-State Problems;172
11;8 Multicriteria Optimization;185
11.1;8.1 Introduction;185
11.2;8.2 Solving Multicriteria Optimization Problems;187
12;9 Practical Matters: The Work of Farkas and Jarmai;189
12.1;9.1 Introduction;189
12.2;9.2 Sizing Member Cross Sections;189
12.3;9.3 Tubular Trusses;192
12.4;9.4 Problems;196
13;10 On Going Work;197
13.1;10.1 Design of Tall Buildings;197
13.2;10.2 Heuristic Algorithms;202
13.3;10.3 Extending the Design Process;203
13.4;10.4 Design Theory;203
14;A Using the Computer;206
14.1;A.1 Using Computer Languages and Programs;206
14.2;A.2 Matlab;208
14.3;A.3 Microsoft Excel;209
14.4;A.4 Freeware;214
14.5;A.5 Graphical Interface Applications;214
15;B The Node Method for Trusses;215
15.1;B.1 Introduction;215
15.2;B.2 A Formal Description of the Truss Problem;216
15.3;B.3 A Decomposition;220
16;C Convex Sets and Functions: Homogeneous Functions;227
16.1;C.1 Convex Sets and Functions;227
16.2;C.2 Homogeneous Functions;228
17;D Structural Optimization Classics;231
17.1;D.1 Michell Trusses;231
17.2;D.2 Keller’s Optimal Column;241
17.3;D.3 The Paper of Venkayya, Khot, and Berke;253
18;References;297
19;Index;306