Differential-algebraic approach to coupled problems of dynamic thermoelasticity

Wang, L. and Melnik, R.V.N.

Applied Mathematics and Mechanics,  27 (9), 1185-1196, 2006


An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm.. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.