hp‐Mortar boundary element method for two‐body contact problems with friction

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Abstract

Abstract We construct a novel hp ‐mortar boundary element method for two‐body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss–Lobatto points using the hp ‐mortar projection operator. The problem is reformulated as a variational inequality with the Steklov–Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as 𝒪(( h / p ) 1/4 ) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet‐to‐Neumann algorithm. The original two‐body formulation is rewritten as a one‐body contact subproblem with friction and a one‐body Neumann subproblem. Then the original two‐body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd.

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