Probabilistic Methods in the Theory of Structures

Strength of Materials, Random Vibrations, and Random Buckling

Isaac Elishakoff

• Publisher: WSPC
• Year: 2017
• eBook ISBN: 9789813149878
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

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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 Probabilistic Methods in the Theory of Structures: Complete Worked-Through Solutions.

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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Table of contents

• Cover Page
• Title
• Copyright
• Contents
• Preface to the Third Editon
• Preface to the Second Edition
• Preface to the First Edition
• 1. Introduction
• 2. Probability Axioms
• 3. Single Random Variable
• 4. Examples of Probability Distribution and Density Functions. Functions of a Single Random Variable
• 5. Reliability of Structures Described by a Single Random Variable
• 6. Two or More Random Variables
• 7. Reliability of Structures Described by Several Random Variables
• 8. Elements of the Theory of Random Functions
• 9. Random Vibration of Discrete Systems
• 10. Random Vibration of Continuous Structures
• 11. Monte Carlo Method
• Appendix A. Evaluation of Integrals (4.15) and (4.22)
• Appendix B. Table of the Error Function
• Appendix C. Calculation of the Mean Square Response of a Class of Linear Systems
• Appendix D. Some Autocorrelation Functions and Associated Spectral Densities
• Appendix E. Galerkin Method
• Appendix F. First Order — Second — Moment Hasofer-Lind Method
• Additional References (1984–1998)
• Additional References (1999–2016)
• Index