Structural Optimization: Fundamentals and ApplicationsThis book was developed while teaching a graduate course at several universities in the United States. Europe and Israel. during the last two decades. The purpose of the book is to introduce the fundamentals and applications of optimum structural design. Much work has been done in this area recently and many studies have been published. The book is an attempt to collect together selected topics of this literature and to present them in a unified approach. It meets the need for an introductory text covering the basic concepts of modem structural optimization. A previous book by the author on this subject ("Optimum Structural Design". published by McGraw-Hill New York in 1981 and by Maruzen Tokyo in 1983). has been used extensively as a text in many universities throughout the world. The present book reflects the rapid progress and recent developments in this area. A major difficulty in studying structural optimization is that integration of concepts used in several areas. such as structural analysis. numerical optimization and engineering design. is necessary in order to solve a specific problem. To facilitate the study of these topics. the book discusses in detail alternative problem formulations. the fundamentals of different optimization methods and various considerations related to structural design. The advantages and the limitations of the presented approaches are illustrated by numerous examples. |
Contents
1 | |
9 | |
10 | |
3 | 22 |
4 | 35 |
Optimization Methods | 57 |
4 | 97 |
Exercises | 120 |
Design Procedures | 178 |
2 | 185 |
3 | 206 |
4 | 225 |
5 | 246 |
6 | 254 |
Properties of Optimal Topologies | 267 |
Approximations and TwoStage Procedures | 275 |
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Common terms and phrases
A₁ algorithms analysis equations approximations assumed basic feasible solution behavior binomial series bounds on stresses calculated coefficients compatibility conditions considered convergence convex corresponding cross sections cross-sectional areas defined derivatives design procedures design space design variables direction displacement constraints displacement method dual efficient elements equality constraints example feasible design feasible region force method geometry given gradient homogeneous functions inequality constraints iteration Lagrange multipliers linear programming loading conditions LP problem modulus of elasticity nonlinear nonlinear programming nonnegative number of variables objective function obtained optimal design problem optimal solution optimal topologies optimization methods optimization problem P₁ penalty function plastic plastic analysis problem formulation programming problem quadratic quadratic function redundant forces satisfied shown in Fig solution process solving statically determinate statically determinate structure step stress constraints structural optimization Substituting Taylor series truss truss shown unconstrained minimization vector X₁ X₂ Xq+1 Y₁ zero