Non-Classical Problems in the Theory of Elastic Stability

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

• ISBN13: 9780521020107
• ISBN10: 0521020107
• Format: Paperback
• Copyright: 2005-09-15
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface: Why Still Another Book on Stability?	ix
1 Mode Localization in Buckling of Structures	1	(42)
1.1 Localization in Elastic Plates Due to Misplacement in the Stiffener Location	1	(16)
1.2 Localization in a Multi-Span Periodic Column with a Disorder in a Single Span	17	(13)
1.3 Localization Phenomenon of Buckling Mode in Stiffened Multi-Span Elastic Plates	30	(13)
2 Deterministic Problems of Shells with Variable Thickness	43	(64)
2.1 Introductory Remarks	43	(10)
2.1.1 Basic Equations for Homogeneous Shells	44	(2)
2.1.2 Hybrid Perturbation-Weighted Residuals Method	46	(4)
2.1.3 Solution by Finite Difference Method	50	(2)
2.1.4 Solution by Godunov-Conte Shooting Method	52	(1)
2.1.5 Numerical Results and Discussion	52	(1)
2.2 Buckling of an Axially Compressed Imperfect Cylindrical Shell of Variable Thickness	53	(18)
2.2.1 Direct Discussion of Energy Criterion	54	(3)
2.2.2 Numerical Technique	57	(14)
2.3 Axial Buckling of Composite Cylindrical Shells with Periodic Thickness Variation	71	(18)
2.4 Effect of the Thickness Variation and Initial Imperfection on Buckling of Composite Cylindrical Shells	89	(10)
2.5 Effect of the Dissimilarity in Elastic Moduli on the Buckling	99	(8)
2.5.1 Analysis	99	(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