Criteria and Methods of Structural Optimization

Criteria and Methods of Structural Optimization

by Andrzej M Brandt (Editor)

Paperback(Softcover reprint of the original 1st ed. 1984)

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Product Details

ISBN-13: 9789401175197
Publisher: Springer Netherlands
Publication date: 03/26/2012
Series: Developments in Civil and Foundation Engineering , #1
Edition description: Softcover reprint of the original 1st ed. 1984
Pages: 556
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

I: Criteria of Structural Optimization.- 1 Aims, Basic Concepts and Assumptions.- 1.1 The aims and scope of optimization.- 1.2 Basic concepts and definitions.- 1.3 Preliminary assumptions.- 2 Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability.- 2.1 The optimality criterion.- 2.2 Wasiuty?ski’s theorems.- 2.3 Deformability of a structure and the free surface.- 2.4 The necessary and sufficient conditions of minimum deformability.- 2.5 Optimization of plane bar structures.- 2.6 Optimization of plates.- 2.7 Optimization of spatial lattice bar structures.- 3 Uniform Strength Design.- 3.1 Strength hypotheses.- 3.2 The criterion of uniform strength.- 3.3 Uniform-strength design of structures under multiple loading conditions.- 3.4 Uniform-strength design of bar structures.- 3.5 Uniform-strength design of beams with cross-sections defined up to m parameters.- 3.6 Uniform-strength design of plates.- 4 Optimization for Minimum Volume, Weight or Cost.- 4.1 The criterion of optimization.- 4.2 Optimum elastic design.- 4.3 Examples of optimum elastic design.- 4.4 Optimum limit design.- 4.5 Examples of optimum limit design.- 4.6 Probabilistic approach to optimum design.- II: Methods of Structural Optimization.- 5 Introduction to Mathematical Methods of Optimization.- 5.1 Problem formulation in optimum structural design.- 5.2 Classical extremum theory.- 5.3 Convex regions and convex functions.- 6 Linear Programming.- 6.1 The linear programming problem.- 6.2 Constrained extrema of a linear function.- 6.3 The graphical method of linear programming.- 6.4 Determination of an initial basic feasible solution.- 6.5 The simplex method.- 6.6 Duality in linear programming.- 6.7 Other important methods of linear programming.- 6.8 Linear discrete programming.- 6.9 Examples of linear programming in optimum structural design.- 7 Non-linear Programming.- 7.1 Problem statement.- 7.2 Kuhn-Tucker conditions.- 7.3 Quadratic programming.- 7.4 Duality in quadratic programming.- 7.5 Beale’s method.- 7.6 Wolfe’s method.- 7.7 Geometric programming: unconstrained problem.- 7.8 Geometric programming: constrained problem.- 7.9 Non-linear integer programming.- 7.10 Unconstrained optimization: direct search methods.- 7.11 Unconstrained optimization: descent methods.- 7.12 Constrained optimization: direct methods.- 7.13 Constrained optimization: indirect methods.- 7.14 Choosing a method.- 7.15 Applications of non-linear programming methods to structural optimization.- 8 Dynamic Programming.- 8.1 Introduction.- 8.2 Multi-stage decision process.- 8.3 Bellman’s principle of optimality.- 8.4 The variant method of dynamic programming.- 8.5 Applications of dynamic programming to structural optimization.- 8.6 Final to initial value problem conversion.- 8.7 Continuous dynamic programming.- 9 Stochastic Programming.- 9.1 Linear stochastic programming.- 9.2 Non-linear stochastic programming.- 9.3 Reliability-based structural optimization: a stochastic programming approach.- 10 Classical Variational Methods. Examples of Application to Optimum Structural Design.- 10.1 Introductory remarks and fundamental concepts.- 10.2 Necessary conditions for an extremum of a functional.- 10.3 Variational problems with side conditions.- 10.4 Sufficient conditions for a minimum of a functional.- 10.5 Direct methods in the calculus of variations.- 10.6 Examples of application of the calculus of variations to structural optimization.- 11 Non-classical Variational Methods of Optimization.- 11.1 Assumptions and problem formulations.- 11.2 Optimality conditions: necessary and sufficient.- 11.3 Trukhaev-Khomenyuk operator equations.- 11.4 Elimination of inequality constraints.- 11.5 Minimax formulation for non-classical variational problems.- 11.6 Approximate methods for non-classical variational problems.- 12 Mathematical Theory of Extremum Problems.- 12.1 Introduction.- 12.2 Cones and dual cones.- 12.3 Necessary extremum conditions.- 12.4 Directions of decrease.- 12.5 Feasible directions.- 12.6 Tangent directions.- 12.7 Calculation of dual cones.- 12.8 The Lagrange multiplier rule and the Kuhn-Tucker theorem.- 12.9 Optimal control problems. Local maximum principle. Pontryagin maximum principle.- 12.10 Sufficient extremum conditions.- 13 Iterative and Experimental Methods of Shape Optimization of Structures.- 13.1 Iterative and experimental approaches to shape optimization.- 13.2 Types of iterations.- 13.3 Iteration vs. imitation and the trial and error method.- 13.4 Designing a column for uniform strain.- 13.5 Designing an arch bridge for uniform strain.- 13.6 Determination of an optimum profile of the junction between a beam and a column by means of photo-elastic modelling.- 13.7 Determination of the optimum shape of plane structures.- 13.8 Shape optimization of shells.- III: Bibliographical Survey and Bibliography.- 14 Survey of the Literature of Structural Optimization.- 14.1 Scope and aim of the survey.- 14.2 Survey works and general studies on structural optimization.- 14.3 Optimization of beams.- 14.4 Optimization of plates.- 14.5 Optimization of trusses.- 14.6 Optimization of columns, arches and frames.- 14.7 Optimization of shells, hanging structures and lattice structures.- Bibliography of Structural Optimization.- Author index.

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