A novel method for solving nonlinear stochastic mechanics problems using FETI‐DP

Abstract

AbstractSolution of large‐scale nonlinear stochastic mechanics problems such as plasticity is generally very expensive. In this work, a domain decomposition based scalable method is proposed for solving such problems. The mechanics problem and random fields are discretized using finite element (FE) bases and Karhunen–Loève expansion, respectively. The FE mesh is partitioned that offers (i) both spatial and stochastic dimensionality reduction and (ii) an inherent framework for parallelization. Then a stochastic collocation based surrogate model is built for each subdomain wherein at each collocation point a deterministic nonlinear problem is solved. The deterministic nonlinear problem is solved using Newton–Raphson method. The linear system of equations involving the Jacobian is solved using the dual‐primal version of the FE tearing and interconnecting (FETI‐DP) method, due to its demonstrated scalability for deterministic problems. Stochastic collocation and FETI‐DP are inherently and independently parallelizable. Finally, at the post‐processing stage, a statistical sampling from the surrogate model is performed by preserving the structure of the input random field. The proposed method is numerically tested for p‐Laplace and plain‐strain plasticity problems, and found to be computationally efficient and accurate. In parallel implementation, the method showed good scalability.