Reliability analysis of plane elasticity problems by stochastic spline fictitious boundary element method

In this paper a stochastic spline fictitious boundary element method (SFBEM) is proposed for reliability analysis of plane elasticity problems in conjunction with the advanced first-order-second-moment (AFOSM) method. The AFOSM method has been demonstrated to be a reliable and practical approach to the structural reliability analysis, yielding results of reasonable accuracy for the engineering applications. And as a modified method for the conventional indirect boundary element method, SFBEM can provide accurate numerical solutions at high efficiency in deterministic analyses. For the purpose of structural reliability analysis, SFBEM is introduced during the iteration process of the AFOSM method, to obtain the required values of structural responses and their derivations with respect to the random variables considered. The use of SFBEM in the formulation of the AFOSM method makes it unnecessary to construct an explicit expression to the implicit limit state function of the problem, leading to a higher efficiency and better accuracy. The present approach is validated by comparing calculated solutions with those of Monte Carlo simulation for a number of example problems and a good agreement of the results is achieved.