Three-dimensional unsteady thermal stress analyses by means of the thermoelastic displacement potential and the boundary element method.

Abstract

The boundary element method (BEM) has been used in various fields because it is convenient in comparison with FEM. BEM does not need a volume integral in three-dimensional elastic problems without body forces, but generally in unsteady three-dimensional thermoelastic problems, the volume integral is necessary. Recently, a method transforming the volume integral in BEM for three-dimensional problems of unsteady thermoelasticity has been reported. However, the time integral was not carried out analytically and a numerical example was not shown in that report. This paper describes the three-dimensional problem of unsteady thermoelasticity can be easily solved without a volume integral by means of a thermoelasticity displacement potential and the boundary element method. It is also shown that the time integral can be carried out analytically and a singularity problem caused by imposing virtual heat sources on the boundary element can be easily solved. Some numerical examples are shown for investigating the accuracy of this method.