Efficient computation of boundary stresses and error indicators in two-dimensional thermoelasticity

Abstract

In this paper the tangent derivative boundary integral equations (TDBIEs) are used to implement an efficient formulation for the computation of stresses and error indicators in two-dimensional, steady-state, thermoelastic problems. The basis for this work is a global reanalysis technique in which, as a post-processing activity, the functional representation for the displacements is changed from Lagrangian to Hermite. The new unknowns introduced in the model, namely the tangential derivatives of the displacements, are obtained by solving a second system of equations generated by collocating the TDBIEs at the functional nodes of the Lagrangian elements. This approach provides more accurate values for the boundary stresses due to the improved functional representation used for the displacements. Also, once the new values for stresses have been obtained using the global reanalysis technique, the difference between them and the ones corresponding to the original solution with Lagrangian elements is used to obtain an efficient error indicator suitable for leading adaptive processes.