Non-Classical Problems in the Theory of Elastic Stability

, by Isaac Elishakoff , Yiwei Li , James H. Starnes, Jr

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ISBN: 9780521020107 | 0521020107
Cover: Paperback
Copyright: 9/15/2005

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When a structure is put under an increasing compressive load, it becomes unstable and buckling occurs. This important work discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that exist in real systems. The techniques are based on two complementary theories that are developed in the text: the probabilistic theory of stability and "anti-optimization," a theory that is valid when the necessary information for probabilistic analysis is absent, that is, when only scant data are available. Design engineers, researchers, and graduate students in aerospace, mechanical, marine, and civil engineering concerned with issues of structural integrity will find this book a useful reference source.

Preface: Why Still Another Book on Stability?

1 Mode Localization in Buckling of Structures

(42)

1.1 Localization in Elastic Plates Due to Misplacement in the Stiffener Location

(16)

1.2 Localization in a Multi-Span Periodic Column with a Disorder in a Single Span

(13)

1.3 Localization Phenomenon of Buckling Mode in Stiffened Multi-Span Elastic Plates

(13)

2 Deterministic Problems of Shells with Variable Thickness

(64)

2.1 Introductory Remarks

(10)

2.1.1 Basic Equations for Homogeneous Shells

(2)

2.1.2 Hybrid Perturbation-Weighted Residuals Method

(4)

2.1.3 Solution by Finite Difference Method

(2)

2.1.4 Solution by Godunov-Conte Shooting Method

(1)

2.1.5 Numerical Results and Discussion

(1)

2.2 Buckling of an Axially Compressed Imperfect Cylindrical Shell of Variable Thickness

(18)

2.2.1 Direct Discussion of Energy Criterion

(3)

2.2.2 Numerical Technique

(14)

2.3 Axial Buckling of Composite Cylindrical Shells with Periodic Thickness Variation

(18)

2.4 Effect of the Thickness Variation and Initial Imperfection on Buckling of Composite Cylindrical Shells

(10)

2.5 Effect of the Dissimilarity in Elastic Moduli on the Buckling

(8)

2.5.1 Analysis

(6)

2.5.2 Discussion

105

(2)

3 Stochastic Buckling of Structures: Monte Carlo Method

107

(68)

3.1 Introductory Remarks

107

(2)

3.2 Reliability Approach to the Random Imperfection Sensitivity of Columns

109

(18)

3.2.1 Motivation for the Reliability Approach

109

(1)

3.2.2 The Linear Problem

110

(2)

3.2.3 Deterministic Imperfection Sensitivity: Mixed Quadratic-Cubic Foundation

112

(2)

3.2.4 Single-Mode Solution

114

(2)

3.2.5 Multi-Mode Solution

116

(1)

3.2.6 Buckling Under Random Imperfections– Monte Carlo Method

117

(3)

3.2.7 Numerical Examples

120

(7)

3.3 Non-Linear Buckling of a Structure with Random Imperfection and Random Axial Compression by a Conditional Simulation Technique

127

(10)

3.3.1 Deterministic Procedure

127

(2)

3.3.2 Formulation of Basic Random Variables

129

(1)

3.3.3 Probabilistic Analysis

130

(4)

3.3.4 Numerical Example and Discussion

134

(3)

3.4 Reliability of Axially Compressed Cylindrical Shells with Random Axisymmetric Imperfections

137

(24)

3.4.1 Preliminary Considerations

137

(2)

3.4.2 Probabilistic Properties of Initial Imperfections

139

(5)

3.4.3 Simulation of Random Imperfections with Given Probabilistic Properties

144

(4)

3.4.4 Simulation of Random Initial Imperfections from Measured Data

148

(6)

3.4.5 Computation of the Buckling Loads

154

(3)

3.4.6 Comparison of the Monte Carlo Method with the Benchmark Solution

157

(4)

3.5 Reliability of Axially Compressed Cylindrical Shells with Nonsymmetric Imperfections

161

(14)

3.5.1 Probabilistic Properties and Simulation of the Initial Imperfections for a Finite Shell

161

(4)

3.5.2 Multi-Mode Deterministic Analysis for Each Realization of Random Initial Imperfections

165

(2)

3.5.3 Numerical Results and Discussion

167

(8)

4 Stochastic Buckling of Structures: Analytical and Numerical Non-Monte Carlo Techniques

175

(47)

4.1 Asymptotic Analysis of Reliability of Structures in Buckling Context

175

(11)

4.1.1 Overview of the Work by Ikeda and Murota

177

(2)

4.1.2 Finite Column on a Non-Linear Foundation

179

(2)

4.1.3 Application of Ikeda-Murota Theory

181

(2)

4.1.4 Axially Compressed Cylindrical Shells

183

(3)

4.2 Second-Moment Analysis of the Buckling of Isotropic Shells with Random Imperfections

186

(7)

4.3 Use of STAGS to Derive Reliability Functions by Arbocz and Hol

193

(3)

4.4 Reliability of Composite Shells by STAGS

196

(4)

4.5 Buckling Mode Localization in a Probabilistic Setting

200

(10)

4.6 Finite Element Method for Buckling of Structures with Stochastic Elastic Modulus

210

(4)

4.7 Stochastic Finite Element Formulation by Zhang and Ellingwood

214

(8)

5 Anti-Optimization in Buckling of Structures

222

(35)

5.1 incorporation of Uncertainties in Elastic Moduli

223

(15)

5.1.1 Basic Equations

223

(5)

5.1.2 Extremal Buckling Load Analysis

228

(3)

5.1.3 Determination of Convex Set from Measured Data

231

(2)

5.1.4 Numerical Examples and Discussion

233

(4)

5.1.5 Numerical Analysis by Non-Linear Programming

237

(1)

5.2 Critical Contrasting of Probabilistic and Convex Analyses

238

(19)

5.2.1 Is There a Contradiction Between Two Methodologies?

238

(3)

5.2.2 Deterministic Analysis of a Model Structure for a Specified Initial Imperfection

241

(6)

5.2.3 Probabilistic Analysis

247

(4)

5.2.4 Non-Stochastic, Anti-Optimization Analysis

251

(6)

6 Application of the Godunov-Conte Shooting Method to Buckling Analysis

257

(11)

6.1 Introductory Remarks

257

(3)

6.2 Brief Outline of Godunov-Conte Method As Applied to Eigenvalue Problems

260

(1)

6.3 Application to Buckling of Polar Orthotropic Annular Plate

261

(7)

7 Application of Computerized Symbolic Algebra in Buckling Analysis

268

(22)

7.1 Introductory Remarks

268

(3)

7.2 Brief Review of MATHEMATICA®

271

(3)

7.3 Buckling of Polar Orthotropic Circular Plates on Elastic Foundation by Computerized Symbolic Algebra

274

(16)

7.3.1 Results Reported in the Literature

274

(2)

7.3.2 Statement of the Problem

276

(1)

7.3.3 Buckling of Clamped Polar Orthotropic Plates

277

(8)

7.3.4 Buckling of Simply Supported Polar Orthotropic Plates

285

(3)

7.3.5 Buckling of Free Polar Orthotropic Plates

288

(2)

Bibliography

290

(37)

Author Index

327

(4)

Subject Index

331

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Non-Classical Problems in the Theory of Elastic Stability

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