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2007, 2007(Special): 201-211. doi: 10.3934/proc.2007.2007.201

Numerical solution of a time-dependent Signorini contact problem

María Teresa Cao-Rial 1, , Peregrina Quintela 1, and  Carlos Moreno 2,

1. 

Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Campus Universitario Sur, 15782, Spain, Spain
2. 

Department of Statistics OR and Numerical Analysis a Distancia, Universidad Nacional de Educación, Madrid, 28040, Spain

Received  September 2006 Revised  May 2007 Published  September 2007

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.
Keywords: elasto-dynamic problems, existence of solutions, unilateral contact, numerical resolution..
Mathematics Subject Classification: 74B05, 74H15, 74H20, 74S0.
Citation: María Teresa Cao-Rial, Peregrina Quintela, Carlos Moreno. Numerical solution of a time-dependent Signorini contact problem. Conference Publications, 2007, 2007 (Special) : 201-211. doi: 10.3934/proc.2007.2007.201
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