Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation

Abstract

In the present paper innovative solution strategies for parallel computer implementation have been developed in connection with the Monte Carlo Simulation (MCS) and the weighted integral method to produce efficient numerical handling of stochastic finite element analysis for 2D plane stress/strain problems. Furthermore, MCS in conjunction with the local average method is also used to extend the stochastic finite element analysis to 3D solid structures. Although MCS approaches have the major advantage that accurate solutions can be obtained for any type of problem whose deterministic solution is known either numerically or analytically their applicability is hindered by the high computational effort that is required. The implementation of innovative parallel solution techniques in this study resulted in cost effective treatment of these highly computationally demanding problems. One- and two-level domain decomposition methods have been implemented. Numerical results revealed that the proposed approaches permit an efficient treatment of stochastic finite element analysis for real-scale 2D plane stress/strain and 3D solid structures.