Influence of higher orders of Neumann expansion on accuracy of stochastic linear elastic finite element method with random physical parameters

The objective of this study is to quantify the influence of higher orders of expansion in the formulation of stochastic finite elements method on the linear elastic response in 2-dimensional problems with random physical parameters in the left hand side term. Neumann expansion was used to get an explicit expression of the result. Young’s modulus was considered as a random variable following normal distribution. The coefficient of variance (COV) of this input parameter ranged in this study up to 0.3 (30%), and mainly 20% of COV was analyzed. The displacement was selected as the quantity of interest. The difference in distribution function of the displacement for different orders of expansion was observed in the tail distribution. A fundamental example revealed the limitation of the applicability of first, second and third orders being approximately 3%, 12% and 20% of COV of input parameter. In the analysis of 2-phase composite material, the influence of geometrical random morphology was larger than that of physical parameter, but the latter was not negligible in the microscopic response.