A new modeling scheme has been developed for the analysis of thermo-mechanical stresses in structural problems of fiber-reinforced composite materials with mixed mode of physical conditions. In contrast with conventional approaches, the coupled thermal and mechanical problems of structural mechanics are integrated here using a single scalar function of space variables, which is defined in terms of the displacement components of plane elasticity. The displacement-function is governed by a single partial-differential equation of equilibrium that takes into account the two orthogonal gradients of the resulting non-uniform temperature field through two different versions of the formulation. The temperature-dependent elastic field is determined using a two-step solution scheme that utilizes the two versions of displacement-function formulations in two sequential steps. The scheme is developed in such a flexible fashion that even the solution of the corresponding isotropic problems can readily be obtained with thermal and/or mechanical loading as a limiting case of the formulation. The application of the proposed modeling scheme is demonstrated through the solution of a number of problems of structural mechanics, namely plates and beams subjected to thermal as well as thermo-mechanical loadings with both uniform and mixed mode of physical conditions. An attempt is also made to verify the soundness and accuracy of the resulting thermoelastic fields by comparing them with the corresponding analytical as well as computational solutions available in the literature. Moreover, the correspondence between the versions of the displacement-function formulation is also verified by solving identical problems using different versions or different combinations of the versions of the formulation.

开发了一种新的建模方案，用于分析具有混合物理条件模式的纤维增强复合材料结构问题中的热机械应力。与传统方法相比，结构力学的热耦合和机械耦合问题在这里使用空间变量的单个标量函数进行整合，该函数根据平面弹性的位移分量进行定义。位移函数由平衡的单个偏微分方程控制，该方程考虑了通过两个不同版本的公式产生的非均匀温度场的两个正交梯度。温度相关弹性场是使用两步求解方案确定的，该方案在两个连续步骤中利用两个版本的位移函数公式。该方案是以一种灵活的方式开发的，即使是相应的各向同性问题的解决方案也可以很容易地通过热和/或机械负载作为公式的限制情况来获得。所提出的建模方案的应用通过解决结构力学的许多问题来证明，即板和梁承受热载荷以及具有均匀和混合物理条件模式的热机械载荷。还尝试通过将它们与文献中可用的相应分析和计算解决方案进行比较来验证所得热弹性场的健全性和准确性。此外，还通过使用不同版本或不同版本的公式组合解决相同的问题来验证位移函数公式版本之间的对应关系。