Boundary element method interior stress/strain analysis for two-dimensional static thermoelasticity involving nonuniform volume heat sources

In the elastostatics analysis of the boundary element method, strains at interior points of an elastic body are calculated using the respective Somigliana identity after the boundary integral equation is solved for boundary displacements and tractions. In the presence of a nonuniform volume heat source, an extra line integral depending on the spatial location of the source point will appear in the boundary integral equation for displacements. Therefore, the usual spatial differentiations of the boundary integral equation for displacements will not yield proper strains if the source point is inside the domain. Somigliana's identity is derived for the interior strains in an anisotropic medium loaded with a nonuniform volume heat source. By coupling the associated thermal field with elasticity, this work provides an alternative and effective numerical approach of analyzing the interior thermal stresses in a fully anisotropic medium loaded with arbitrary nonuniform volume heat sources.