Multiple reciprocity boundary element analysis of two-dimensional anisotropic thermoelasticity involving an internal arbitrary non-uniform volume heat source

In the direct boundary element method (BEM) formulation of anisotropic thermoelasticity, thermal loads manifest themselves as additional volume integral terms in the boundary integral equation (BIE). Conventionally, this requires internal cell discretisation throughout the whole domain. In this paper, the multiple reciprocity method in BEM analysis is employed to treat the general 2D thermoelasticity problem when the thermal loading is due to an internal non-uniform volume heat source. By successively performing the "volume-to-surface" integral transformation, the general formulation of the associated BIE for the problem is derived. The successful implementation of such a scheme is illustrated by three numerical examples.