Structural and System Reliability

Based on material taught at the University of California, Berkeley, this textbook offers a modern, rigorous and comprehensive treatment of the methods of structural and system reliability analysis. It covers the first- and second-order reliability methods for components and systems, simulation methods, time- and space-variant reliability, and Bayesian parameter estimation and reliability updating. It also presents more advanced, state-of-the-art topics such as finite-element reliability methods, stochastic structural dynamics, reliability-based optimal design, and Bayesian networks. A wealth of well-designed examples connect theory with practice, with simple examples demonstrating mathematical concepts and larger examples demonstrating their applications. End-of-chapter homework problems are included throughout. Including all necessary background material from probability theory, and accompanied online by a solutions manual and PowerPoint slides for instructors, this is the ideal text for senior undergraduate and graduate students taking courses on structural and system reliability in departments of civil, environmental and mechanical engineering.

Projection methods for stochastic structural dynamics

A set of novel hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. An optimal basis for the response of a stochastic system has been computed from the eigen modes of the parametrized structural dynamic system. The hybrid projection methods are obtained by applying appropriate approximations and by reducing the modal basis. These methods have been further improved by an implementation of a sample based Galerkin error minimization approach. In total four methods are presented and compared for numerical accuracy and efficiency by analysing the bending of a Euler-Bernoulli cantilever beam.

Anchored analysis of variance Petrov–Galerkin projection schemes for linear stochastic structural dynamics

In this paper, we propose anchored functional analysis of variance Petrov–Galerkin (AAPG) projection schemes, originally developed in the context of parabolic stochastic partial differential equations (Audouze C, Nair PB. 2014 Comput. Methods Appl. Mech. Eng. 276, 362–395. ( doi:10.1016/j.cma.2014.02.023 )) for solving a class of problems in linear stochastic structural dynamics. We consider the semi-discrete form of the governing equations in the time-domain and the proposed formulation involves approximating the dynamic response using a Hoeffding functional analysis of variance decomposition. Subsequently, we design a set of test functions for a stochastic Petrov–Galerkin projection scheme that enables the original high-dimensional problem to be decomposed into a sequence of decoupled low-dimensional subproblems that can be solved independently of each other. Numerical results are presented to demonstrate the efficiency and accuracy of AAPG projection schemes and comparisons are made to approximations obtained using Monte Carlo simulation, generalized polynomial chaos-based stochastic Galerkin projection schemes and the generalized spectral decomposition method. The results obtained suggest that the proposed approach holds significant potential for alleviating the curse of dimensionality encountered in tackling high-dimensional problems in stochastic structural dynamics with a large number of spatial and stochastic degrees of freedom.