In this study, 3D thermal stresses in composite laminates under steady-state through thickness thermal conduction are investigated by means of a stress function-based approach. One-dimensional thermal conduction is solved for composite laminate and the layerwise temperature distribution is calculated first. The principle of complementary virtual work is employed to develop the governing equations. Their solutions are obtained by using the stress function-based approach, where the stress functions are taken from the Lekhnitskii stress functions in terms of in-plane stress functions and out-of-plane stress functions. With the Rayleigh–Ritz method, the stress fields can be solved by first solving a standard eigenvalue problem. The proposed method is not merely computationally efficient and accurate. The stress fields also strictly satisfy the prescribed boundary conditions validated by the results of finite element method (FEM) results. Finally, some of the results will be given for discussion considering different layup stacking sequences, thermal conductivities and overall temperature differences. From the results, we find that the thermal conductivity greatly affects the stress distributions and peak values of stresses increase linearly for the present model. The proposed method can be used for predicting 3D thermal stresses in composite laminates when subjected to thermal loading.

中文翻译：

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稳态全厚度热传导下复合层压板中的 3D 热应力

在这项研究中，通过基于应力函数的方法研究了稳态下通过厚度热传导的复合层压板中的 3D 热应力。求解复合层压板的一维热传导，首先计算分层温度分布。采用互补虚功原理来开发控制方程。他们的解决方案是通过使用基于应力函数的方法获得的，其中应力函数取自 Lekhnitskii 应力函数，包括平面内应力函数和平面外应力函数。使用 Rayleigh-Ritz 方法，可以通过首先求解标准特征值问题来求解应力场。所提出的方法不仅计算效率高且准确。应力场也严格满足有限元法 (FEM) 结果验证的规定边界条件。最后，考虑到不同的叠层堆叠顺序、热导率和整体温差，将给出一些结果以供讨论。从结果中，我们发现热导率对应力分布有很大影响，并且对于当前模型，应力峰值线性增加。所提出的方法可用于预测复合材料层压板在承受热载荷时的 3D 热应力。从结果中，我们发现热导率对应力分布有很大影响，并且对于当前模型，应力峰值线性增加。所提出的方法可用于预测复合材料层压板在承受热载荷时的 3D 热应力。从结果中，我们发现热导率对应力分布有很大影响，并且对于当前模型，应力峰值线性增加。所提出的方法可用于预测复合材料层压板在承受热载荷时的 3D 热应力。