The FETI Based Domain Decomposition Method for Solving 3D-Multibody Contact Problems with Coulomb Friction

Abstract

Summary. The contribution deals with the numerical solving of contact problems with Coulomb friction for 3D bodies. A variant of the FETI based domain decomposition method is used. Numerical experiments illustrate the efficiency of our algorithm.

Domain Decomposition Method with an Interface Preconditioner for Frictionless Contact Problem

“…The problem (8) is solved by an iterative procedure to determine the unknown of the problem and the reel contact regions using the augmented Lagrangian method [19]. must satisfy the contact conditions.…”

“…An algorithm is introduced to solve the resulting finite element system by a non-overlapping domain decomposition method. Using this equivalence, the interface problem is transformed to an equivalent problem which is solved with adequate mathematical programming methods [11] [19]. The central aspect of this work is to construct preconditioners for the interface problem and the adaptation of a preconditioner construction developped in [2] [4] for non-overlapping decomposition domain method to the contact problem.…”

Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

“…When nonlinearities are restricted to the boundaries, small-strain concept is adopted, and the material in the bulk is linear and homogeneous (so that the fundamental solutions of the underlying operators are at disposal), the Boundary Element Method (BEM) can be an efficient and very accurate alternative to the Finite Element Method (FEM) usually employed in engineering computations, e.g. [13,21,22,25,27,29,31,58]. In this paper, we confine ourselves to the mentioned situation in the bulk, so that all nonlinearities arising from the normalcompliance model and the Coulomb friction will be indeed only on the boundary or interfaces between the bodies.…”