Abstract
This paper deals with the problem of dynamical frictionless contact or impact of an elastic body with a rigid foundation. The contact is modelled by a normal compliance condition. It is assumed that the Hertz approximation is valid. The resulting problem has the form of a coupled system, a static elastic (elliptic) contact problem for the deformations in the body and an ordinary differential equation for the projected rigid body motion. We prove the existence of the unique weak solution of this non coercive problem. A numerical algorithm based on implicit time discretization and preconditioned projected-gradient method is presented. The convergence of iterations at each time step is proved. Numerical experiments show the effectiveness of this approach.
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