Abstract

In this paper, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic homogeneous two dimensional media. The coupled thermoelastic equations are derived based on Lord-Shulman (LS) and Green-Lindsay (GL) theories. The temperature and displacement fields are approximated in space domain by linear combinations of Chebyshev polynomials. Also, the direct collocation method is applied to governing differential equations to generate the system of differential equations with respect to time. The resulted set of differential equations are solved in time domain by Wilson method. Both temperature and traction loadings are considered to be applied at the left side of the media. The obtained results from the present paper for the classical coupled thermoelasticity of two dimensional finite domains are compared with the same results extracted analytically in the literature and a very close agreement is observed.

摘要

在本文中，开发了切比雪夫搭配数值方法来解决各向同性均匀二维介质的广义热弹性问题。耦合热弹性方程是基于 Lord-Shulman (LS) 和 Green-Lindsay (GL) 理论推导出来的。温度场和位移场通过切比雪夫多项式的线性组合在空间域中近似。此外，直接搭配方法应用于控制微分方程以生成关于时间的微分方程组。用Wilson方法在时域求解微分方程的结果集。温度和牵引载荷都被认为是施加在介质的左侧。