Stochastic Finite Element Methods for Structural Reliability Analysis

Abstract : A research and development study of stochastic finite element methods (SFEM) for structural reliability analysis is presented. A detailed state-of-the-art literature review of various SFEM methodologies and the diverse technical subjects relating to probabilistic finite element analysis is summarized. Case studies of two existing SFEM-based reliability analysis computer programs were conducted, with a discussion of the methodology, main features, structure, and capabilities of both systems. The design and implementation of a software package for random field discretization (RANFLD) and SFEM-based reliability analysis (STOVAST) is then presented. The package, developed on the basis of the finite element reliability method (FERM) approach, and designed for operation with the VAST commercial finite element analysis system, was verified using several problems. Also, in this work, the quantification and analysis of bias and modelling errors/uncertainties in engineering analysis are discussed. Sources of bias and modelling errors/uncertainties in SFEM based reliability analysis are identified and suggestions are offered for the application of realistic formulations for accounting for this class of uncertainties. Finally, recommendations are given on requirements for further development work that will broaden the analysis scope of the STOV AST system and permit straight forward applications to ship structures.