Boundary element analysis of finite domains under thermal and mechanical shock with the Lord-Shulman theory

A boundary element method based on the Laplace transform technique is developed for transient coupled thermoelasticity problems with relaxation times in a two-dimensional finite domain. The dynamic thermoelastic model of Lord and Shulman (LS) is selected to show how mechanical and thermal energy conversion takes place in a coupled field. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. The nodal dimensionless temperature and displacements in the transformed domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. The creation and propagation of elastic and thermoelastic waves in a finite domain and their effects on each other are investigated for the first time in this paper. Different relaxation times are chosen to show briefly the events that take place in temperature, displacement and stress fields considering the LS theory. Details of the formulation and numerical implementation are presented.