Development of a boundary element method for time-dependent planar thermoelasticity

Abstract A new boundary element method is developed for two-dimensional quasistatic thermoelasticity. This time domain formulation involves only surface quantities. Consequently, volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches. After presenting a brief overview of the governing equations, boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem. Details of a general purpose numerical implementation are then discussed. Next. boundary element methods for the two more practical theories, uncoupled quasistatic and steady-state thermoelasticity, are developed directly from limiting forms of the coupled formulation. Several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems.