Application of Chebyshev collocation method to unified generalized thermoelasticity of a finite domain
Jaber Alihemmati, Yaghoub Tadi Beni, Y. Kiani
Abstract
In this article, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic layer. The coupled thermoelastic equations are derived based on Lord-Shulman (LS), Green-Lindsay (GL) and Green-Naghdi (GN) theories. Two kinds of shock loading are considered. In the first model, a temperature shock is applied at the left side of the layer, and in the second model a heat flux shock is applied at the mentioned side. The displacement and temperature fields are approximated in the layer by Chebyshev polynomials and then the collocation is imposed on some collocation points to derive the system of ordinary differential equations from the coupled partial differential equations. The derived system of differential equations is then solved by the Wilson method to achieve the displacement and temperature and also stress at any location and time. The obtained results from the present article are compared with the same results in the open literature and a very close agreement is observed. Finally, it is concluded that the Chebyshev collocation numerical method can be utilized as a very strong method for solving the transient wave propagation problems.