Time domain boundary elements for dynamic contact problems

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 mo...

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Bibliographic Details
Published inComputer 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
LanguageEnglish
Published Amsterdam Elsevier B.V 01.05.2018
Elsevier BV
Elsevier
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2018.01.025