Time domain boundary elements for dynamic contact problems

• Published in: Computer methods in applied mechanics and engineering Vol. 333; pp. 147 - 175
• Main Authors: Gimperlein, Heiko, Meyer, Fabian, Özdemir, Ceyhun, Stephan, Ernst P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2018; Elsevier BV; Elsevier
• Subjects: A priori error estimates; Approximation; Boundary conditions; Boundary element method; Contact problems; Dirichlet problem; Engineering Sciences; Finite element analysis; Friction; Galerkin method; Mathematical models; Mixed method; Numerical analysis; Saddle points; Time domain analysis; Variational inequality; Wave equation; Wave equations; Wave equation; A priori error estimates; Variational inequality; Mixed method; Boundary element method; variational inequality; boundary element method; mixed method; a priori error estimates; wave equation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.01.025

This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using boundary elements in the time domain. As a model problem, also a variational inequality for the single layer operator is considered. A priori estimates are obtained for Galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area, where the existence of solutions to the continuous problem is known. Numerical experiments demonstrate the performance of the proposed mixed method. They indicate the stability and convergence beyond flat geometries.