Computational Analysis of Randomness in Structural Mechanics

This high-quality book captures in one concise volume the importance of probabilistic analysis of structures, the theory behind such analysis, and practical methods for solving structural mechanics problems that contain uncertainty. It provides a crucial gateway to probabilistic structural mechanics for instructors and students as well as researchers and practitioners who may have directed most of their efforts towards deterministic problems. The book provides an excellent, self-contained introduction to random vibrations, stochastic finite elements, and reliability analysis while also preparing the reader for more advanced study based on the many more specialized texts available in these topics. The first three chapters form the first part of the book, in which the elements of probability and statistics are introduced with sufficient rigour to prepare the reader with even limited experience in probability and statistics to benefit from the second part of the book. Chapter 1 motivates the study of randomness in structural mechanics through a series of fully worked example problems that immediately illustrate the key concepts of the remainder of the book. Chapter 2 presents the key elements of probability and statistics, such as random variables and distributions, expectation, estimation and Monte Carlo sampling. These concepts are used freely throughout the rest of the book, and provision of this chapter renders the book fully self-contained. Chapter 3 introduces regression, and the related idea of the response surface for complex probabilistic systems. The next and final three chapters form the technical core of the book. Chapter 4, on random vibrations, covers the solution of single and multi-degree of freedom systems using numerical, exact and approximate methods. Chapter 5 provides a concise, accessible description of how the stochastic finite element method may be used to solve problems involving spatial uncertainty and an introduction to the theory of random fields. Methods for calculating structural reliability, such as first-order reliability and Monte Carlo simulation with importance sampling are the focus of chapter 6, which also shows how response surfaces can be applied to reliability analysis. Aside from the timely, rigourous and thorough technical content, the book has several features to recommend it. First, it focuses intently on problems and examples of obvious relevance to students and practitioners of structural engineering. Second, the theoretical developments introduced are thoroughly illustrated with fully worked examples, and a smattering of exercises left for the reader give the reader the opportunity to practice implementing the presented techniques. Third, most of the analysis techniques described are accompanied by listings of Octave computer code designed to solve relevant examples. These listings are fully compatible with MATLAB and are a very valuable component of the book. A fine semester-long graduate course could be designed around the content of this book, and some of the material could even be reasonably included in the upper-level undergraduate curriculum, providing the connection between the probability and statistics course and the analysis and design classes that is too often lacking. At the graduate level, the book will have particular value as the basis for a general course in probabilistic structural mechanics in those departments where faculty staffing and expertise do not allow the offering of individual specialty courses in random vibrations, reliability and stochastic finite elements. In short, Computational Analysis of Randomness in Structural Mechanics will prove a valuable resource to any student or practitioner of structural engineering and mechanics.