General finite-element stress formulation of dynamic thermoelastic problems using the galerkin method

TLDR: In this article, the Galerkin method was used to obtain the general form of the finite-element equations of dynamic thermoelasticity in terms of stresses and temperature.

Abstract: The general, governing equations of dynamic thermoelasticity in terms of stresses are considered. Applying the approximation field to the stresses and temperature, the general form of the finite-element equations are obtained using the Galerkin method. The general traction boundary conditions are discussed. The formulations are then reduced to the one-dimensional case, and the problem of bars subjected to mechanical and thermal shocks is discussed. Assuming an isoparametric simplex element, the submatrices for the base element e are obtained and simplified. As an example, a bar of two ends free subjected to a mechanical shock at one end is considered and the plots of stress and temperature waves are obtained. The results are compared with those of the displacement formulation. While both formulations compare well, the stress formulation predicts a slightly lower value for the computed stress field that is a lower bound to the solution and offers a stiffer model.