Numerical solution of a time-dependent Signorini contact problem

María Teresa Cao-Rial; Peregrina Quintela; Carlos Moreno

doi:10.3934/proc.2007.2007.201

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2007, Volume 2007: 201-211. Doi: 10.3934/proc.2007.2007.201 open access

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Numerical solution of a time-dependent Signorini contact problem

1.
Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Campus Universitario Sur, 15782
2.
Department of Statistics OR and Numerical Analysis a Distancia, Universidad Nacional de Educación, Madrid, 28040

Received: August 31, 2006

Revised: April 30, 2007

Published: August 2007

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Abstract

The purpose of this work is to study the dynamic frictionless contact problem between an elastic body and a rigid foundation. In order to model the contact we consider Signorini conditions. A numerical algorithm is proposed to approximate the solution; the algorithm involves a contact multiplier, which is a fixed point of a nonlinear equation solved by using a generalized Newton method. We use one of the Newmark methods for time discretization and a finite element method for space discretization. The convergence of the method is numerically studied, and a simple test problem is used to validate the methodology.

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Mathematics Subject Classification: 74B05, 74H15, 74H20, 74S05.

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