A coupled FETI-BDNM for solving 3D elastic frictional contact problem

Abstract

Based on the B-differentiable Newton method (BDNM) and finite element tearing and interconnecting (FETI) algorithm, a coupled approach named FETI-BDNM is developed to solve the 3D elastic contact problem with friction. In this method, the contact bodies are decomposed into a number of subdomains. The interfaces between the two adjacent substructures will be skillfully considered as the special contact surfaces that are always in the stick state. By resorting to the generalized inverse of stiffness matrices of the subdomains, the relationships between the relative displacements and forces on contact/interface, i.e., contact flexibility matrices will be computed efficiently. The contact equations, displacement continuity equations and equilibrium equations for each subdomain are expressed in the form of B-differentiable equations (BDEs) uniformly, which can be solved by the damped Newton-Raphson method with 1D Armijo type linear search. The proposed method makes it possible to solve large-scale contact problems without compromising the solution accuracy compared to the original BDNM, and the good convergence of BDEs and parallel scalability of the FETI algorithm will be preserved. Numerical examples validate the accuracy, efficiency, robustness and effects of the number of subdomains on the computational time of the proposed method.