Basic Formulation for Elastic-Plastic Stochastic Finite Element Method : Sensitivity Analysis of Nonlinear FEM

Abstract

An analysis method to evaluate the gradient of structural response is developed for nonlinear systems which are governed by incremental finite element equations. The formulation originates in the perturbation method and retains its advantage. Namely a nonlinear finite element analysis needs to be done only once; based on which the gradients are evaluated. Although the formulation is written for elasto-plastic problems in the present paper, it is also applicable to a wider class of nonlinear problems, the solutions of which depend on the load paths. An elastic-plastic truss structure is solved to examine the validity of the method, and satisfactory results are obtained. The proposed formulation forms the foundation of the nonlinear stochastic finite element method.