Stochastic Static Analysis of Planar Elastic Structures with Multiple Spatially Uncertain Material Parameters

Engineering structures are often assembled from parts with different materials. When uncertainty quantification techniques are applied, the curse of dimensionality increases the computational complexity. Here, a stochastic Galerkin method for planar elasticity allowing for multiple regions with independent uncertain materials is introduced. The method allows for efficient solution of linear systems both in fully assembled and matrix-free formulations. The selection of the stochastic basis polynomials is performed using a priori knowledge of the decay of the random fields. The statistical quantities of interest are the expected solution and variance, both of which can be computed efficiently after the Galerkin system has been solved. Analysis of the results indicates that the proposed method is highly efficient in terms of both computational resource requirements and discretization of the stochastic dimensions. The results were verified with Monte Carlo and quasi-Monte Carlo methods.