Time domain boundary elements for dynamic contact problems

verfasst von: Heiko Gimperlein, Fabian Meyer, Ceyhun Özdemir, Ernst P. Stephan
Abstract: 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.
Organisationseinheit(en): Institut für Angewandte Mathematik
Externe Organisation(en): Heriot-Watt University
Universität Paderborn
Universität Stuttgart
Typ: Artikel
Journal: Computer Methods in Applied Mechanics and Engineering
Band: 333
Seiten: 147-175
Anzahl der Seiten: 29
ISSN: 0045-7825
Publikationsdatum: 01.05.2018
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik
Elektronische Version(en): http://arxiv.org/pdf/1801.09792 (Zugang: Offen)
https://doi.org/10.1016/j.cma.2018.01.025 (Zugang: Geschlossen)

BibTeX

@article{922f7fdc68994c67b6d3017359ca5176,
title = "Time domain boundary elements for dynamic contact problems",
abstract = "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.",
keywords = "A priori error estimates, Boundary element method, Mixed method, Variational inequality, Wave equation",
author = "Heiko Gimperlein and Fabian Meyer and Ceyhun {\"O}zdemir and Stephan, {Ernst P.}",
note = "Funding Information: H.G. acknowledges support by ERC Advanced Grant HARG 268105 and the EPSRC Impact Acceleration Account EP/K503915/1 . C.O. is supported by a scholarship of the Avicenna Foundation . ",
year = "2018",
month = may,
day = "1",
doi = "10.1016/j.cma.2018.01.025",
language = "English",
volume = "333",
pages = "147--175",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}