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.

摘要

在本文中，Chebyshev配置数值方法被开发用于解决各向同性层的广义热弹性问题。耦合热弹性方程是根据Lord-Shulman（LS），Green-Lindsay（GL）和Green-Naghdi（GN）理论推导的。考虑两种冲击载荷。在第一个模型中，在层的左侧施加温度冲击，在第二个模型中，在所述侧面施加热通量冲击。通过Chebyshev多项式在层中近似位移和温度场，然后将配位强加到某些配位点上，以从耦合的偏微分方程导出常微分方程组。然后通过Wilson方法求解导出的微分方程组，以实现位移和温度以及任意位置和时间的应力。将本文获得的结果与公开文献中的相同结果进行比较，并观察到非常接近的一致性。最后，得出结论，切比雪夫搭配数值方法可以作为解决瞬态波传播问题的一种非常强大的方法。