A FETI B-differentiable equation method for elastic frictional contact problem with nonconforming mesh

Abstract

In this study, a novel approach is proposed by integrating the finite element tearing and interconnecting (FETI) method into the B-differentiable equations (BDEs) method for the analysis of 3D elastic frictional contact problem with small deformations. The contact blocks are divided into several nonoverlapping substructures with nonconforming meshes on the contact surface and the interface between two adjacent substructures. The enforcement of contact conditions and interface continuity conditions is achieved by using dual Lagrange multipliers discretized on the slave surface, typically defined with fine meshes. The modified Boolean transformation matrix is utilized to convert the contact stress into the equivalent nodal force. For large-scale elastic contact problems, the equilibrium equations for substructures and the relationship between the relative displacements and contact stresses on the contact surfaces and interfaces (i.e., the contact flexibility matrix) are efficiently computed using the FETI method. Subsequently, the governing equations consisting of the contact equations, interface continuity equations, and equilibrium equations for each floating substructure are uniformly formulated as the BDEs. These BDEs can be solved using the B-differentiable damped Newton method (BDNM). The proposed method harnesses the parallel scalability of the FETI method and extends the applicability of the BDEs algorithm, benefiting from its ability to precisely satisfy the contact constraints and theoretically ensure convergence when solving large-scale contact problems. The Hilber/Hughes/Taylor (HHT) time integration scheme is employed to investigate elastic dynamic contact problems. Numerical examples demonstrate the accuracy, convergence rate, and parallel scalability of the proposed algorithm.