Abstract

This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study, a systematic method is used to decouple the elasticity and heat equations. Hence one sixth-order differential equation and two second-order differential equations are obtained. Completeness of the solution is proved using a retarded logarithmic Newtonian potential function for functionally graded transversely isotropic domain. To verify the obtained solution, in a simpler case, potential functions are generated for homogeneous transversely isotropic media that coincide with respective equations. Presented potential functions can be used to solve the problems in various media like infinite and semi-infinite space, beams and columns, plates, shells, etc., with arbitrary boundary conditions and subjected to arbitrary mechanical and thermal loads.

中文翻译：

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热弹动力学问题中受热源影响的功能梯度横向各向同性介质的势函数

摘要

本文开发了一组新颖的位移温度势函数来解决热源作用下功能梯度横向各向同性介质中的热弹动力学问题。为此，考虑三维热方程和波动方程来获得功能梯度材料的位移温度运动方程。在本研究中，采用系统方法来解耦弹性方程和热方程。由此得到1个六阶微分方程和2个二阶微分方程。使用功能梯度横向各向同性域的延迟对数牛顿势函数证明了解的完整性。为了验证所获得的解，在更简单的情况下，生成与各自方程一致的均匀横观各向同性介质的势函数。所提出的势函数可用于解决各种介质中的问题，例如无限和半无限空间、梁和柱、板、壳等，具有任意边界条件并承受任意机械和热载荷。