Stochastic finite element analysis in computation of reliability of frames

Real life situations contain uncertainties of different levels, which lead to off-target performance. The study and assurance of performance under probabilistic environment is the main aim of reliability analysis. Finite Element Analysis is a tool which analyzes structures, among other things, for different criteria and simulates the failure modes revealing weakest sections. Stochastic Finite Element Method (SFEM) is sophisticated reliability analysis method which considers uncertainties in the variables involved in the problems to estimate the risk associated with any structure or frame that can be represented by finite elements. With a case of framed structure, methodology of SFEM is demonstrated in this paper. Performance function determining the probability of failure is constructed. Using deterministic analysis the value of g(X) is obtained. Gradient vector ∇g(X) is evaluated through sensitivity analysis. Using these two quantities, reliability analysis is performed.