Locking of the Finite Element Method in Thermoelasticity

摘要

The paper is concerned with the solution mu to the stationary problem ofthermoelasticity and with the approximation mu(sub n) of u obtained with a standard Galerkin method. In the incompressible limit, when the Lame coefficient lambda becomes infinite, mu(sub n) is subject to a divergence constraint, div mu(sub n) = P(sub n)T, where Pn is a given approximation operator acting on the temperature field T. This mechanism provokes a locking phenomenon similar to the one observed in elasticity and studied by Babuska and Suri in another paper. The purpose of the work is to give a sufficient and necessary condition on the discrete spaces V(sub n), used in the Galerkin formulation, to avoid locking and get an estimation of the error which is optimal and independant of lambda. The criterion will be used to construct two practical examples of methods free from locking for the usual thermoelasticity problem where the temperature field is solution of a Poisson equation. The first example is based on the h-version of the finite element method, the second one on the p-version.