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**Probabilistic methods in the theory of structures.**
*(English)*
Zbl 0572.73094

A Wiley-Interscience Publication. New York etc.: John Wiley & Sons. XII, 489 p. (1983).

This book is written both to serve as a first-course text on probabilistic methods in the theory of structures and to provide a more advanced treatment of random vibration and buckling. It is intended in particular for the student in aeronautical engineering, mechanical engineering, or theoretical and applied mechanics, and may also be used by practicing engineers and research workers as a reference. In fact, it combines the features of a textbook and a monograph.

Chapter 1 introduces the role of probabilistic methods in the theory of structures. Chapters 2 through 4 deal exclusively with elements of the theory of probability for a single random variable. This apparent preoccupation with the single random variable stems from my own feeling that it would be unfair to offer the reader a mere taste of the theory of probability and then immediately confront him or her with a wide range of applications. Chapter 5 is devoted to the reliability of structures described by a single random variable. Chapter 6 discusses elements of the theory of probability of two or more random variables, while Chapter 7 examines the reliability of such multivariable structures. Chapter 8 introduces the theory of random functions. Chapter 9 deals with random vibration of single- and multi-degree-of-freedom structures, and Chapter 10 with random vibration of continuous systems. These chapters concentrate on the role of modal cross correlations in random vibration analysis, usually overlooked in literature, as well as treat point-driven structures, and random vibration and flutter. These chapters constitute, among others, a prerequisite to study the fatigue life of structures - a topic which is outside the scope of this book. The reader interested in this subject is referred to other sources where it is adequately treated. Finally, Chapter 11 is devoted to the Monte Carlo method for treating problems incapable of exact solution. Special emphasis is placed on buckling of nonlinear structures where random imperfections may be responsible for drastic reduction of the buckling loads.

Ample examples are included in the book, because it is my experience that much of the material in question may be taught most effectively by this means. An additional purpose of the examples is to examine the validity of some widely accepted simplifying assumptions concerning the probabilistic nature of the output quantities and to observe the errors that these assumptions may cause. Numerous exercises are provided with each chapter, to deepen the reader’s grasp of the subject and widen his or her perspectives.

Chapter 1 introduces the role of probabilistic methods in the theory of structures. Chapters 2 through 4 deal exclusively with elements of the theory of probability for a single random variable. This apparent preoccupation with the single random variable stems from my own feeling that it would be unfair to offer the reader a mere taste of the theory of probability and then immediately confront him or her with a wide range of applications. Chapter 5 is devoted to the reliability of structures described by a single random variable. Chapter 6 discusses elements of the theory of probability of two or more random variables, while Chapter 7 examines the reliability of such multivariable structures. Chapter 8 introduces the theory of random functions. Chapter 9 deals with random vibration of single- and multi-degree-of-freedom structures, and Chapter 10 with random vibration of continuous systems. These chapters concentrate on the role of modal cross correlations in random vibration analysis, usually overlooked in literature, as well as treat point-driven structures, and random vibration and flutter. These chapters constitute, among others, a prerequisite to study the fatigue life of structures - a topic which is outside the scope of this book. The reader interested in this subject is referred to other sources where it is adequately treated. Finally, Chapter 11 is devoted to the Monte Carlo method for treating problems incapable of exact solution. Special emphasis is placed on buckling of nonlinear structures where random imperfections may be responsible for drastic reduction of the buckling loads.

Ample examples are included in the book, because it is my experience that much of the material in question may be taught most effectively by this means. An additional purpose of the examples is to examine the validity of some widely accepted simplifying assumptions concerning the probabilistic nature of the output quantities and to observe the errors that these assumptions may cause. Numerous exercises are provided with each chapter, to deepen the reader’s grasp of the subject and widen his or her perspectives.

### MSC:

74H50 | Random vibrations in dynamical problems in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

60G35 | Signal detection and filtering (aspects of stochastic processes) |

74G60 | Bifurcation and buckling |