Consistent thermal stress evaluation in finite elements

Abstract

The computation of thermal stresses in displacement finite elements through a formal theoretical basis using the minimum potential principle leads to oscillating stress predictions. Many finite element packages have therefore used an average temperature in simple elements; thermal stresses were computed only at the centroids of such elements to avoid these problems. In this paper we trace this difficulty to a consistency requirement-the requirement that stress fields derived from temperature fields (or initial strains) must be consistent with the total strain field interpolations used in the finite element formulation. The principle governing the problem is developed from the minimum total potential theorem and the Hu-Washizu theorem. This gives it a formal rational basis and leads to an orthogonality condition that provides the procedure for determining consistent, thermal stresses in a variationally correct manner. The princple is demonstrated using some simple problems. A four-noded laminated plane-shell element is also considered to prove the rigour and generality of the approach presented here.