Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling
The first edition of this book appeared over three decades ago (Wiley-Interscience, 1983), whereas the second one saw light on the verge of new millennium (Dover, 1999). This is third, corrected and expanded edition that appears in conjunction with its companion volume .Thus, the reader is able to both get acquainted with the theoretical material and be able to master some of the problems, following Chinese dictum: I hear and I forget. I see and I remember. I do and I understand — Confucius.The main idea of the book lies in the fact that three topics: probabilistic strength of materials, random vibrations, and probabilistic buckling are presented in a single package allowing one to see the forest in between the trees. Indeed, these three topics usually are presented in separate manners, in different specialized books. Here, the reader gets a feeling of true unity of the subject at large in order to appreciate that in the end what one wants is reliability of the structure, in conjunction with its operating conditions.As the author describes in the Preface of the second edition, this book was not conceived ab initio, as a book that author strived to compose. Rather, it was forced, as it were, upon me due to two reasons. One was rather a surprising but understandable requirement in the venerable Delft University of Technology, The Netherlands to prepare the lecture notes for students with the view of reducing skyrocketing costs of acquisition of textbooks by the students. The other one was an unusually warm acceptance of the notes that the author prepared while at Delft University of Technology and later in Haifa, at the Technion-Israel Institute of Technology by the legendary engineering scientist Warner Tjardus Koiter (1914-1997). The energy necessary to prepare the second and third editions came from enthusiastic reviews that appeared in various sources. Author embraced the simplicity of exposition as the main virtue following Isaac Newton's view that 'Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.'
1133772367
Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling
The first edition of this book appeared over three decades ago (Wiley-Interscience, 1983), whereas the second one saw light on the verge of new millennium (Dover, 1999). This is third, corrected and expanded edition that appears in conjunction with its companion volume .Thus, the reader is able to both get acquainted with the theoretical material and be able to master some of the problems, following Chinese dictum: I hear and I forget. I see and I remember. I do and I understand — Confucius.The main idea of the book lies in the fact that three topics: probabilistic strength of materials, random vibrations, and probabilistic buckling are presented in a single package allowing one to see the forest in between the trees. Indeed, these three topics usually are presented in separate manners, in different specialized books. Here, the reader gets a feeling of true unity of the subject at large in order to appreciate that in the end what one wants is reliability of the structure, in conjunction with its operating conditions.As the author describes in the Preface of the second edition, this book was not conceived ab initio, as a book that author strived to compose. Rather, it was forced, as it were, upon me due to two reasons. One was rather a surprising but understandable requirement in the venerable Delft University of Technology, The Netherlands to prepare the lecture notes for students with the view of reducing skyrocketing costs of acquisition of textbooks by the students. The other one was an unusually warm acceptance of the notes that the author prepared while at Delft University of Technology and later in Haifa, at the Technion-Israel Institute of Technology by the legendary engineering scientist Warner Tjardus Koiter (1914-1997). The energy necessary to prepare the second and third editions came from enthusiastic reviews that appeared in various sources. Author embraced the simplicity of exposition as the main virtue following Isaac Newton's view that 'Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.'
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Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling

Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling

by Isaac E Elishakoff
Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling

Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling

by Isaac E Elishakoff

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Overview

The first edition of this book appeared over three decades ago (Wiley-Interscience, 1983), whereas the second one saw light on the verge of new millennium (Dover, 1999). This is third, corrected and expanded edition that appears in conjunction with its companion volume .Thus, the reader is able to both get acquainted with the theoretical material and be able to master some of the problems, following Chinese dictum: I hear and I forget. I see and I remember. I do and I understand — Confucius.The main idea of the book lies in the fact that three topics: probabilistic strength of materials, random vibrations, and probabilistic buckling are presented in a single package allowing one to see the forest in between the trees. Indeed, these three topics usually are presented in separate manners, in different specialized books. Here, the reader gets a feeling of true unity of the subject at large in order to appreciate that in the end what one wants is reliability of the structure, in conjunction with its operating conditions.As the author describes in the Preface of the second edition, this book was not conceived ab initio, as a book that author strived to compose. Rather, it was forced, as it were, upon me due to two reasons. One was rather a surprising but understandable requirement in the venerable Delft University of Technology, The Netherlands to prepare the lecture notes for students with the view of reducing skyrocketing costs of acquisition of textbooks by the students. The other one was an unusually warm acceptance of the notes that the author prepared while at Delft University of Technology and later in Haifa, at the Technion-Israel Institute of Technology by the legendary engineering scientist Warner Tjardus Koiter (1914-1997). The energy necessary to prepare the second and third editions came from enthusiastic reviews that appeared in various sources. Author embraced the simplicity of exposition as the main virtue following Isaac Newton's view that 'Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.'

Product Details

ISBN-13: 9789813149854
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 05/23/2017
Pages: 524
Product dimensions: 6.10(w) x 8.90(h) x 1.00(d)

Table of Contents

Preface to the Third Editon vii

Preface to the Second Edition ix

Preface to the First Edition xiii

1 Introduction 1

2 Probability Axioms 8

2.1 Random Event 8

2.2 Sample Space 12

2.3 Probability Axioms 17

2.4 Equiprobable Events 21

2.5 Probability and Relative Frequency 23

2.6 Conditional Probability 25

2.7 Independent Events 28

2.8 Reliability of Statically Determinate Truss 31

2.9 Overall Probability and Bayes' Formula 34

Problems 36

3 Single Random Variable 39

3.1 Random Variable 39

3.2 Distribution Function 40

3.3 Properties of the Distribution Function 42

3.4 Mathematical Expectation 49

3.5 Moments of Random Variable; Variance 52

3.6 Characteristic Function 58

3.7 Conditional Probability Distribution and Density Functions 61

3.8 Inequalities of Bienaymé and Tchebycheff 64

Problems 65

4 Examples of Probability Distribution and Density Functions. Functions of a Single Random Variable 68

4.1 Causal Distribution 61

4.2 Discrete Uniform Distribution 69

4.3 Binomial or Bernoulli Distribution 70

4.4 Poisson Distribution 72

4.5 Rayleigh Distribution 74

4.6 Exponential Distribution 75

4.7 χ2 (Chi-Square) Distribution with m Degrees of Freedom 76

4.8 Gamma Distribution 76

4.9 Weibull Distribution 77

4.10 Normal or Gaussian Distribution 78

4.11 Truncated Normal Distribution 83

4.12 Function of a Random Variable 84

4.13 Moments of a Function of a Random Variable 85

4.14 Distribution and Density Functions of a Function of a Random Variable (Special Case) 86

4.15 Linear Function of a Random Variable 87

4.16 Exponents and Logarithms of a Random Variable 88

4.17 Distribution and Density Functions of a Function of a Random Variable (General Case) 90

4.18 Example of Application of the Probabilistic Approach in an Engineering Decision Problem 97

Problems 101

5 Reliability of Structures Described by a Single Random Variable 104

5.1 A Bar under Random Force 104

5.2 A Bar with Random Strength 113

5.3 A Bar with a Random Cross-Sectional Area 114

5.4 A Beam under a Random Distributed Force 115

5.5 Static Imperfection-Sensitivity of a Nonlinear Model Structure 120

5.6 Dynamic Imperfection-Sensitivity of a Nonlinear Model Structure 133

5.7 Axial Impact of a Bar with Random Initial Imperfections 145

Problems 160

6 Two or More Random Variables 174

6.1 Joint Distribution Function of Two Random Variables 174

6.2 Joint Density Function of Two Random Variables 179

6.3 Conditional Probability Distribution and Density Functions 183

6.4 Multidimensional Random Vector 186

6.5 Functions of Random Variables 187

6.6 Expected Values, Moments, Covariance 198

6.7 Approximate Evaluation of Moments of Functions 209

6.8 Joint Characteristic Function 211

6.9 Pair of Jointly Normal Random Variables 215

6.10 Several Jointly Normal Random Variables 220

6.11 Functions of Random Variables 224

6.12 Complex Random Variables 231

Problems 233

7 Reliability of Structures Described by Several Random Variables 236

7.1 Fundamental Case 236

7.2 Bending of Beams under Several Random Concentrated Forces 251

7.3 Bending of Beams under Several Random Concentrated Moments 259

7.4 The Central Limit Theorem and Reliability Estimate 262

Problems 266

8 Elements of the Theory of Random Functions 271

8.1 Definition of a Random Function 271

8.2 First- and Second-order Distribution Functions 273

8.3 Moment Functions 275

8.4 Properties of the Autocovariance Function 276

8.5 Probability Density Function 277

8.6 Normal Random Function 278

8.7 Joint Distribution of Random Functions 279

8.8 Complex Random Functions 281

8.9 Stationary Random Functions 284

8.10 Spectral Density of a Stationary Random Function 288

8.11 Differentiation of a Random Function 297

8.12 Integration of a Random Function 304

8.13 Ergodicity of Random Functions 306

Problems 314

9 Random Vibration of Discrete Systems 317

9.1 Response of a Linear System Subjected to Deterministic Excitation 317

9.2 Response of a Linear System Subjected to Random Excitation 324

9.3 Random Vibration of a Multidegree-of-Freedom System 349

9.4 Illustration of the Role of Modal Cross Correlations 361

Problems 378

10 Random Vibration of Continuous Structures 384

10.1 Random Fields 384

10.2 Normal Mode Method 389

10.3 Determination of Joint and Cross Acceptances 402

10.4 Case Capable of Closed-Form Solution 406

10.5 Crandall's Problem 408

10.6 Random Vibration Due to Boundary-Layer Turbulence 416

10.7 Analytic Approximations for Pressure Fluctuations in a Turbulent Boundary Layer 419

10.8 Flutter and Random Vibration of Beams-Approximate Solution 421

Problems 429

11 Monte Carlo Method 433

11.1 Description of the Method 433

11.2 Generation of Random Numbers 436

11.1 Simulation of Continuous Random Variables 438

11.1 Simulation of Random Vectors 441

11.2 Method of Linear Transformation 442

11.3 Simulation of Random Functions 446

11.4 Buckling of a Bar on a Nonlinear Foundation 450

Problems 466

Appendix A Evaluation of Integrals (4.15) and (4.22) 469

Appendix B Table of the Error Function 471

Appendix C Calculation of the Mean Square Response of a Class of Linear Systems 472

Appendix D Some Autocorrelation Functions and Associated Spectral Densities 477

Appendix E Galerkin Method 477

Appendix F First Order - Second - Moment Hasofer-Lind Method 483

Additional References (1984-1998) 493

Additional References (1999-2016) 496

Index 498

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