Analysis of a contact problem for a viscoelastic Bresse system

Abstract

In this paper, we consider a contact problem between a viscoelastic Bresse beam and a deformable obstacle. The well-known normal compliance contact condition is used to model the contact. The existence of a unique solution to the continuous problem is proved using the Faedo-Galerkin method. An exponential decay property is also obtained defining an adequate Liapunov function. Then, using the finite element method and the implicit Euler scheme, a finite element approximation is introduced. A discrete stability property and a priori error estimates are proved. Finally, some numerical experiments are performed to demonstrate the decay of the discrete energy and the numerical convergence.

Discrete observability of the Bresse system

“…Bernardi and Copetti [12] considered a nonlinear model for a thermoelastic Timoshenko beam that can enter in contact with obstacles, and they performed the a priori analysis of the discrete problem by proposing a discretization by combining an Euler and Crank-Nicolson type schemes in time and finite elements in space. For more numerical studies related to the Bresse type systems we refer to the following papers [13][14][15][16][17].…”

Existence and energy decay of a Bresse system with thermoelasticity of type III

“…In the last years, the asymptotic stability for the Bresse system has attracted the attention of researchers and various damping mechanisms were considered to obtain exponential stability. Among them, Boussouira et al [2], Copetti et al [5], El Arwadi et al [11], Guesmia and Kirane [16], Messaoudi et al [22], Santos et al [23], Soriano et al [25] and others.…”