Abstract

In the context of the fractional-order theory of thermoelastic diffusion, the problem of a thermoelastic infinitely long hollow cylinder is considered. The outer surface of the cylinder is taken traction free and subjected to thermal shock, while the inner surface is taken to be in contact with a rigid surface and is thermally insulated. The governing equations of the problem are formulated. Laplace transform technique and a direct approach method are used to obtain the solution in transformed domain. A numerical method is used to get the inversion of the Laplace transform of the solutions. The temperature, displacement, stress, and concentration as well as the chemical potential are represented graphically.

摘要

在热弹性扩散的分数阶理论的背景下，考虑了热弹性无限长的空心圆柱体的问题。圆柱体的外表面不受牵引并受到热冲击，而内表面则与刚性表面接触并被隔热。制定了问题的控制方程。使用拉普拉斯变换技术和直接方法来获得变换域中的解。使用数值方法来获得解的拉普拉斯变换的反演。用图形表示温度，位移，应力和浓度以及化学势。