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E-raamat: Stability and Optimization of Structures: Generalized Sensitivity Analysis

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  • Formaat: PDF+DRM
  • Sari: Mechanical Engineering Series
  • Ilmumisaeg: 10-Jun-2007
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387681849
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Stability and Optimization of Structures: Generalized Sensitivity AnalysisSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Mechanical Engineering Series
  • Ilmumisaeg: 10-Jun-2007
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387681849
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Stability and Optimization of Structures: Generalized Sensitivity Analysis is the first book to address issues of structural optimization against nonlinear buckling. Through the investigation of imperfection sensitivity, worst imperfection and random imperfection based on concrete theoretical framework, it is shown that optimization against buckling does not necessarily produce an imperfection-sensitive structure. This book offers the reader greater insight into optimization-based and computer-assisted stability design of finite-dimensional structures. Using the unified approach to parameter sensitivity analysis, it connects studies of elastic stability, computational mechanics and applied mathematics. Optimization based on stability theory is presented and explained, with 140 figures to illustrate applications in the framework of finite element analysis. This book serves as an illustrative introduction for professional structural and mechanical engineers, graduate students in engineering, as well as applied mathematicians in the field.

This book focuses on the optimization of a geometrically-nonlinear structure under stability constraint. It presents a deep insight into optimization-based and computer-assisted stability design of discrete structures. Coverage combines design sensitivity analysis developed in structural optimization and imperfection-sensitivity analysis developed in stability analysis.

Arvustused

From the reviews:









"The book presents an overview of optimization and stability of geometrically nonlinear structures under stability constraints including sensitivity analysis. Structures with slender members such as latticed frames are considered. The text is divided into three parts with an appendix. The book offers a wide insight into optimization-based and computer-assisted stability design of finite-dimensional structures. It can be recommended to graduate students and research workers in engineering and applied mathematics." (Igor Bock, Zentralblatt MATH, Vol. 1127 (4), 2008)



"The present book provides a uniform treatment of the stability problem of discrete elastic systems and sensitivity analysis . The general conclusions are illustrated by numerous specific examples of optimal designs, providing a deeper insight into the mechanical response of optimal structures. The book constitutes a valuable contribution to the development of the methodology of optimal design of non-linear structures. It can also be useful in teaching graduate courses in structural mechanics." (Z. Mróz, Mathematical Reviews, Issue 2008 m)



"This book is the first monograph that comprehensively presents how the stability theory and optimization methods should be successfully married for optimization of geometrically-nonlinear structure under stability constraint, which is a fast-growing branch of application of both structural and mechanical engineering, and of applied mathematics. This book is wholeheartedly recommended to all engineers who deal with applied mechanics, as well as to applied mathematicians who are interested in real life applications of mathematics. Every engineering & math library ought to have it ." (Isaac Elishakoff, Structural and Multidisciplinary Optimization, Vol. 38, 2009)

Series Preface vi
Preface vii
I Generalized Sensitivity of Nonlinear Elastic Systems 1
1 Introduction to Design Sensitivity Analysis
3
1.1 Introduction
3
1.2 General Framework of Elastic Stability
4
1.2.1 Governing equations and stability
4
1.2.2 Critical state
5
1.2.3 Proportional loading
7
1.3 Design Parameterization
7
1.4 Design Sensitivity Analysis for Linear Response
8
1.5 Design Sensitivity Analyses for Nonlinear Responses
9
1.5.1 Linear buckling load
9
1.5.2 Responses at a regular state
11
1.5.3 Limit point load
12
1.6 Historical Development
13
1.7 Summary
14
2 Methods of Design Sensitivity Analysis
15
2.1 Introduction
15
2.2 Sensitivity of Bifurcation Load: Pedagogic Example
16
2.2.1 Exact analysis
18
2.2.2 Asymptotic analysis
19
2.3 Minor and Major Design Modifications
20
2.3.1 Symmetry and classification of design modifications
20
2.3.2 Regular sensitivity for minor design modification
22
2.3.3 Finite Difference Approach
22
2.4 Linear Eigenvalue Analysis Approach
23
2.5 Interpolation Approach
24
2.5.1 Regular state
24
2.5.2 Bifurcation state
25
2.6 Explicit Diagonalization Approach
26
2.6.1 Simple unstable-symmetric bifurcation point
26
2.6.2 Coincident bifurcation point of a symmetric system
27
2.7 Numerical Examples for Design Sensitivity
29
2.7.1 Five-bar truss
29
2.7.2 Symmetric shallow truss dome
30
2.7.3 Two-degree-of-freedom bar–spring system
32
2.8 Summary
34
3 Imperfection Sensitivity Analysis
35
3.1 Introduction
35
3.2 Mathematical Preliminaries
36
3.2.1 Generalized coordinates
36
3.2.2 D-formulation
38
3.2.3 V-formulation
39
3.2.4 Correspondence between D-formulation and 17-formulation
41
3.3 Classification of Critical Points
41
3.3.1 Simple critical points
42
3.3.2 Coincident critical points
43
3.4 Derivation of Imperfection Sensitivity Laws
45
3.4.1 Power series expansion method
46
3.4.2 Static perturbation method
46
3.5 imperfection Sensitivity for Simple Critical Points
47
3.5.1 Imperfect behaviors
47
3.5.2 Imperfection sensitivity laws
48
3.5.3 Sensitivity coefficients
49
3.6 Imperfection Sensitivity for Coincident Critical Points
50
3.6.1 Hilltop branching point
50
3.6.2 Semi-symmetric double bifurcation point
51
3.6.3 Completely-symmetric double bifurcation point
52
3.6.4 Group-theoretic double bifurcation point
52
3.6.5 Symmetry of a structure
53
3.7 Imperfection Sensitivity of Four-Bar Truss Tent
54
3.8 Historical Development
56
3.9 Summary
57
II Optimization Methods for Stability Design 59
4 Optimization Under Stability Constraints
61
4.1 Introduction
61
4.2 Introduction to Nonlinear Programming Problem
62
4.3 Structural Optimization Problem and Gradient-Based Optimization Algorithm
63
4.3.1 General formulation of structural optimization problem
64
4.3.2 Gradient-based optimization approach
65
4.4 Optimization Under Stability Constraints
67
4.4.1 Direct formulation
67
4.4.2 Formulation with eigenvalue constraints
68
4.5 Optimization of a Symmetric Shallow Truss Dome
69
4.6 Bar–Spring Model
72
4.6.1 Simple degenerate
73
4.6.2 Degenerate hilltop
75
4.7 Historical Development
75
4.8 Summary
76
5 Optimal Structures Under Snaptbrough Constraint
77
5.1 Introduction
77
5.2 Optimization Problems for Structures Undergoing Snapthrough
78
5.3 Two-Bar Truss
78
5.4 Symmetric Shallow Truss Dome
82
5.5 Summary
85
6 Shape Optimization of Compliant Mechanisms
87
6.1 Introduction
87
6.2 Illustrative Examples of Bistable Compliant Mechanisms
89
6.2.1 Two-bar truss
89
6.2.2 Plane grid truss
90
6.3 Shape Optimization Problem for Multistable Compliant Mechanism
92
6.4 Examples of Multistable Compliant Mechanisms
95
6.5 Summary
99
7 Optimal Braced Frames with Coincident Buckling Loads
101
7.1 Introduction
101
7.2 Optimization Problem of a Braced Frame
103
7.2.1 Problem formulation
103
7.2.2 Definition of maximum load factor
104
7.3 Imperfection Sensitivity of Semi-Symmetric Bifurcation Point
105
7.4 Non-Optimal and Optimal Frames
107
7.4.1 Non-optimal unbraced frames
107
7.4.2 Optimal braced frames
109
7.5 Summary
114
8 Hilltop Branching Point I: Simple Bifurcation
115
8.1 Introduction
115
8.2 Imperfection Sensitivity Laws
116
8.2.1 General formulation
117
8.2.2 Trivial fundamental path
118
8.2.3 Perfect and imperfect behaviors
119
8.2.4 Imperfection sensitivity for minor imperfection
119
8.2.5 Imperfection sensitivity for major imperfection
121
8.3 Bar–Spring Model: Hilltop with Asymmetric Bifurcation
123
8.4 Summary
126
9 Hilltop Branching Point II: Multiple Bifurcations
127
9.1 Introduction
127
9.2 Imperfection Sensitivity
128
9.2.1 Hilltop point with many symmetric bifurcations
128
9.2.2 Hilltop point for a system with dihedral-group symmetry
129
9.3 Arch-Type Truss: Hilltop with Multiple Symmetric Bifurcations
129
9.4 Regular-Polygonal Truss Tents: Hilltop with Group-Theoretic Double Point
133
9.5 Summary
135
10 Hilltop Branching Point III: Degenerate
137
10.1 Introduction
137
10.2 Degenerate Behaviors
138
10.3 Four-Bar Truss Tent
139
10.3.1 Without spring
140
10.3.2 With a spring
141
10.4 Symmetric Shallow Truss Dome
143
10.5 Spherical Truss
147
10.5.1 Concentrated load
147
10.5.2 Distributed loads
151
10.6 Summary
151
III Worst and Random Imperfections 153
11 Worst Imperfection: Asymptotic Theory
155
11.1 Introduction
155
11.2 Asymptotic Theory of Worst Imperfection
156
11.2.1 General formulation
156
11.2.2 Simple critical points
157
11.2.3 Hilltop branching with simple bifurcation
158
11.3 Optimization Incorporating Worst Imperfection
160
11.3.1 Formulation of optimization problem
160
11.3.2 Optimization algorithm
160
11.4 Worst Imperfection for Four-Bar Truss: Hilltop Branching Point
161
11.5 Optimum Designs of Trusses with Worst Imperfection
163
11.5.1 Symmetric shallow truss dome
163
11.5.2 Plane tower truss
165
11.6 Summary
167
12 Worst Imperfection: Anti-optimization by LP and QP
169
12.1 Introduction
169
12.2 Numerical Procedure to Obtain Worst Imperfection Mode
170
12.2.1 Minimization of eigenvalues
170
12.2.2 LP formulation
171
12.2.3 QP formulation
172
12.2.4 Dominant worst imperfection
172
12.3 Dominant Worst Imperfection of Braced Column Structures
173
12.3.1 Buckling characteristics of braced column
174
12.3.2 Numerical models
174
12.3.3 Eigenmodes and worst imperfection modes
175
12.3.4 Estimation of buckling loads of imperfect structures
177
12.4 Summary
180
13 Worst Imperfection for Stable Bifurcation
181
13.1 Introduction
181
13.2 Maximum Load Factor for Stable Bifurcation
182
13.3 Anti-Optimization Problem
183
13.3.1 Direct formulation
183
13.3.2 Numerically efficient formulation
184
13.4 Worst Imperfection of Column-Type Trusses
185
13.4.1 Column-type truss
186
13.4.2 Laterally supported truss
189
13.5 Summary
191
14 Random Imperfections: Theory
193
14.1 Introduction
193
14.2 Probability Density Functions of Critical Loads
194
14.3 Numerical Procedure
195
14.4 Probabilistic Variation of Strength of Truss Domes
196
14.4.1 Double-layer hexagonal truss roof: limit point
196
14.4.2 Spherical truss dome: unstable-symmetric bifurcation
197
14.5 Historical Development
200
14.6 Summary
201
15 Random Imperfections of Elasto-Plastic Solids
203
15.1 Introduction
203
15.2 Probability Density Function of Critical Loads
204
15.3 Probabilistic Strength Variation of Steel Blocks
206
15.3.1 Imperfection sensitivity
208
15.3.2 Probabilistic variation of critical loads
209
15.4 Summary
211
16 Random Imperfections: Higher-Order Analysis
213
16.1 Introduction
213
16.2 Higher-Order Asymptotic Theory
214
16.2.1 Generalized sensitivity law
214
16.2.2 Probability density functions of critical loads
214
16.3 Numerical Procedure
215
16.4 Four-Bar Truss Tent
216
16.4.1 Perfect system
216
16.4.2 Generalized imperfection sensitivity law
217
16.4.3 Probability density function of critical loads
218
16.5 Truss Tower Structure
220
16.5.1 Perfect system
220
16.5.2 Generalized imperfection sensitivity law
220
16.5.3 Probabilistic variation of critical loads
223
16.6 Summary
224
Appendix 225
A.1 Introduction
225
A.2 Interpolation Approach for Coincident Critical Points
226
A.3 Derivation of Explicit Diagonalization Approach
228
A.3.1 Simple unstable-symmetric bifurcation point
228
A.3.2 Coincident critical point of symmetric system
230
A.4 Block Diagonalization Approach for Symmetric System
232
A.4.1 Symmetry condition
232
A.4.2 Block diagonalization
232
A.5 Details of Quadratic Estimation of Critical Loads
234
A.6 Differential Coefficients of Bar-Spring Model
235
A.7 Imperfection Sensitivity Law of a Semi-Symmetric Bifurcation Point
236
A.7.1 Limit point load
237
A.7.2 Bifurcation load
238
A.7.3 Imperfect behaviors
238
A.8 Imperfection Sensitivity Laws of Degenerate Hilltop Point I: Asymmetric Bifurcation
239
A.8.1 General formulation
240
A.8.2 Perfect behavior
240
A.8.3 Imperfection sensitivity: minor symmetric
241
A.8.4 Imperfection sensitivity: major antisymmetric
242
A.9 Imperfection Sensitivity Laws of Degenerate Hilltop Point II: Unstable-Symmetric Bifurcation
243
A.9.1 General formulation
243
A.9.2 Perfect behavior
244
A.9.3 Imperfection sensitivity: minor symmetric
244
A.9.4 Imperfection sensitivity: major antisymmetric
246
A.10 Summary
247
Bibliography 249
Index 267


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