Structural Reliability Analysis And Stochastic Finite Element Method

The book provides a self-contained treatment of stochastic finite element methods. It helps the reader to establish a solid background on stochastic and reliability analysis of structural systems and enables practicing engineers to better manage the concepts of analysis and design in the presence of uncertainty. The book covers the basic topics of computational stochastic mechanics focusing on the stochastic analysis of structural systems in the framework of the finite element method. The target audience primarily comprises students in a postgraduate program specializing in structural engineering but the book may also be beneficial to practicing engineers and research experts alike.

The first complete guide to using the Stochastic Finite Element Method for reliability assessment Unlike other analytical reliability estimation techniques, the Stochastic Finite Element Method (SFEM) can be used for both implicit and explicit performance functions, making it a particularly powerful and robust tool for today's engineer. This book, written by two pioneers in SFEM-based methodologies, shows how to use SFEM for the reliability analysis of a wide range of structures. It begins by reviewing essential risk concepts, currently available risk evaluation procedures, and the use of analytical and sampling methods in estimating risk. Next, it introduces SFEM evaluation procedures, with detailed coverage of displacement-based and stress-based deterministic finite element approaches. Linear, nonlinear, static, and dynamic problems are considered separately to demonstrate the robustness of the methods. The risk or reliability estimation procedure for each case is presented in different chapters, with theory complemented by a useful series of examples. Integrating advanced concepts in risk-based design, finite elements, and mechanics, Reliability Assessment Using Stochastic Finite Element Analysis is vital reading for engineering professionals and students in all areas of the field.

This book provides readers with an understanding of the fundamentals and applications of structural reliability, stochastic finite element method, reliability analysis via stochastic expansion, and optimization under uncertainty. It examines the use of stochastic expansions, including polynomial chaos expansion and Karhunen-Loeve expansion for the reliability analysis of practical engineering problems.

This report presents a study of stochastic finite element methods (SFEM) for structural reliability analysis, beginning with a literature review of various SFEM methodologies and subjects relating to probabilistic finite element analysis. The report describes case studies of two existing SFEM-based reliability analysis programs (NESSUS and CALREL-FEAP), with discussion of their methodology, main features, structure, and capabilities. The report then presents the design and implementation of a software package for random field discretization (RANFLD) and a SFEM-based reliability analysis (STOVAST), the latter designed for operation with the commercial VAST finite element analysis system. The package was verified using several beam and plate problems. Finally, the report discusses bias and modelling errors in SFEM-based reliability analysis. Appendices include input formats and output files for RANFLD and STOVAST.

Reliability Calculations with the Stochastic Finite Element presents different methods of reliability analysis for systems. Chapters explain methods used to analyze a number of systems such as single component maintenance system, repairable series system, rigid rotor balance, spring mechanics, gearbox design and optimization, and nonlinear vibration. The author proposes several established and new methods to solve reliability problems which are based on fuzzy systems, sensitivity analysis, Monte Carlo simulation, HL-RF methods, differential equations, and stochastic finite element processing, to name a few. This handbook is a useful update on reliability analysis for mechanical engineers and technical apprentices.

The finite element method (FEM) can be successfully applied to various field problems in solid mechanics, fluid mechanics and electrical engineering. This text discusses finite element methods for structures with large stochastic variations.