Solid Mechanics and Its Applications

By: Peter W. Christensen, Anders Klarbring

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Hardcover | 20 October 2008

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224 Pages

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24.13 x 15.88 x 1.27

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This book has grown out of lectures and courses given at Link¶ping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying-frequently very many- variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.

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"This book represents a good introduction to structural optimization. It covers the main methods used for the optimization of discrete and distributed parametric systems. ... Due to numerous practical examples, this book can be strongly recommended to young specialists and students in mechanical engineering." (Sergiu T. Chiriacescu, Zentralblatt MATH, Vol. 1180, 2010)

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You Can Find This Book In

Non-Fiction Engineering & Technology Civil Engineering Structural Engineering Mechanical Engineering & Materials Mechanical Engineering Mathematics Applied Mathematics Technology in General Technical Design Calculus & Mathematical Analysis Numerical Analysis

Building Construction & Materials Heating Engineering in General Optimisation

Introduction	p. 1
The Basic Idea	p. 1
The Design Process	p. 1
General Mathematical Form of a Structural Optimization Problem	p. 3
Three Types of Structural Optimization Problems	p. 5
Discrete and Distributed Parameter Systems	p. 7
Examples of Optimization of Discrete Parameter Systems	p. 9
Weight Minimization of a Two-Bar Truss Subject to Stress Constraints	p. 9
Weight Minimization of a Two-Bar Truss Subject to Stress and Instability Constraints	p. 12
Weight Minimization of a Two-Bar Truss Subject to Stress and Displacement Constraints	p. 14
Weight Minimization of a Two-Beam Cantilever Subject to a Displacement Constraint	p. 18
Weight Minimization of a Three-Bar Truss Subject to Stress Constraints	p. 21
Weight Minimization of a Three-Bar Truss Subject to a Stiffness Constraint	p. 31
Exercises	p. 33
Basics of Convex Programming	p. 35
Local and Global Optima	p. 35
Convexity	p. 37
KKT Conditions	p. 41
Lagrangian Duality	p. 46
Lagrangian Duality for Convex and Separable Problems	p. 47
Exercises	p. 52
Sequential Explicit, Convex Approximations	p. 57
General Solution Procedure for Nested Problems	p. 57
Sequential Linear Programming (SLP)	p. 58
Sequential Quadratic Programming (SQP)	p. 59
Convex Linearization (CONLIN)	p. 59
The Method of Moving Asymptotes (MMA)	p. 66
Exercises	p. 72
Sizing Stiffness Optimization of a Truss	p. 77
The Simultaneous Formulation of the Problem	p. 77
The Nested Formulation and Some of Its Properties	p. 84
Convexity of the Nested Problem	p. 85
Fully Stressed Designs	p. 87
Minimization of the Volume Under a Compliance Constraint	p. 88
Numerical Solution of the Nested Problem Using MMA	p. 91
Sensitivity Analysis	p. 97
Numerical Methods	p. 97
Analytical Methods	p. 98
Direct Analytical Method	p. 98
Adjoint Analytical Method	p. 99
Analytical Calculation of Pseudo-loads	p. 100
Bars	p. 101
Plane Sheets	p. 104
Exercises	p. 112
Two-Dimensional Shape Optimization	p. 117
Shape Representation	p. 117
Bezier Splines	p. 118
B-Splines	p. 120
Treatment of Geometrical Design Constraints	p. 127
C[superscript 1] Continuity Between Bezier Splines	p. 128
C[superscript 1] Continuity at a Point on a Line of Symmetry	p. 129
A Composite Circular Arc	p. 131
Mesh Generation and Calculation of Nodal Sensitivities	p. 132
B-Spline Surface Meshes	p. 133
Coons Surface Meshes	p. 134
Unstructured Meshes	p. 137
Summary of Sensitivity Analysis for Two-Dimensional Shape Optimization	p. 139
Exercises	p. 143
Stiffness Optimization of Distributed Parameter Systems	p. 147
Calculus of Variations	p. 147
Optimality Conditions and Gateaux Derivatives	p. 149
Handling a Constraint	p. 153
Equilibrium Principles for Distributed Parameter Systems	p. 156
One-Dimensional Elasticity	p. 156
Beam Problem	p. 158
Two-Dimensional Elasticity	p. 159
Abstract Equilibrium Principles	p. 162
The Design Problem	p. 163
Optimality Conditions	p. 166
The Stiffest Rod	p. 168
Beam Stiffness Optimization	p. 170
Exercises	p. 174
Topology Optimization of Distributed Parameter Systems	p. 179
The Variable Thickness Sheet Problem	p. 179
Problem Statement and FE-Discretization	p. 179
The Optimality Criteria (OC) Method	p. 182
Penalization of Intermediate Thickness Values	p. 188
Solid Isotropic Material with Penalization (SIMP)	p. 188
Other Penalizations	p. 190
Well-Posedness and Potential Numerical Problems	p. 190
The Archetype Problem and an Analogy	p. 190
Numerical Instabilities	p. 191
Restriction of the Archetype Problem	p. 193
Bounds on the Design Gradient	p. 194
Filters	p. 195
Relaxation of the Archetype Problem	p. 198
Exercises	p. 200
Answers to Selected Exercises	p. 203
References	p. 207
Index	p. 209
Table of Contents provided by Ingram. All Rights Reserved.

Solid Mechanics and Its Applications

At a Glance

Hardcover

Industry Reviews

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