Adaptive Random Field Mesh Refinements in Stochastic Finite Element Reliability Analysis of Structures

A technique for adaptive random field refinement for stochastic finite element reliability analysis of structures is presented in this paper. Refinement indicator based on global importance measures are proposed and used for carrying out adaptive random field mesh refinements. Reliability index based error indicator is proposed and used for assessing the percentage error in the estimation of notional failure probability. Adaptive mesh refinement is carried out using hierarchical graded mesh obtained through bisection of elements. Spatially varying stochastic system parameters (such as Young's modulus and mass density) and load parameters are modeled in general as non-Gaussian random fields with prescribed marginal distributions and covariance functions in conjunction with Nataf's models. Expansion optimum linear estimation method is used for random field discretisation. A framework is developed for spatial discretisation of random fields for system/load parameters considering Gaussian/non-Gaussian nature of random fields, multidimensional random fields, and multiple-random fields. Structural reliability analysis is carried out using first order reliability method with a few refined features, such as, treatment of multiple design points and/or multiple regions of comparable importance. The gradients of the performance function are computed using direct differentiation method. Problems of multiple performance functions, either in series, or in parallel, are handled using the method based on product of conditional marginals. The efficacy of the proposed adaptive technique is illustrated by carrying out numerical studies on a set of examples covering linear static, free vibration and forced vibration problems.