LAUSR

Abstract We present a formulation for the extension of the stochastic finite element method with non-linear material models. Stress and stiffness fields, as well as displacements at each degree of freedom, are modeled as random processes and are expanded along the Polynomial Chaos (PC). PC terms of displacements are solved incrementally under load control by performing stochastic Galerkin projections on the equilibrium equation. PC terms of stress and stiffness are updated between each load increment from the resulting strains inside each elements, which follow a stochastic constitutive algorithm that performs stochastic Galerkin projections on the local level. The proposed approach is similar to the traditional deterministic non-linear finite element method and is consistent with the linear stochastic finite element method. The PC terms of stiffness are directly updated between increments of loading, and the stochastic tangent stiffness matrix is reconstructed at each increment. We illustrate the method to solve for the distribution of displacements caused by gravity loading in an earth dam with uncertain shear modulus and shear strength. The method gives similar results and, for the same level of accuracy, is computationally faster than the classical Monte-Carlo approach by several orders of magnitude.