An accurate mixed-form global-local higher-order theory including transverse normal thermal deformation is developed for thermo-mechanical analysis of multilayered composite beams. Although transverse normal deformation is considered, the number of displacement parameters is not increased. The proposed mixed-form global-local higher-order theory is derived using the displacement assumptions of global-local higher-order theory in conjunction with the Reissner mixed variational theorem. Moreover, the mixed-form global-local higher-order theory retains a fixed number of displacement variables regardless of the number of layers. In order to obtain the improved transverse shear stresses, the three-dimensional equilibrium equation is used. It is significant that the second-order derivatives of in-plane displacement variables have been eliminated from the transverse shear stress field, such that the finite element implementation is greatly simplified. The benefit of the proposed mixed-form global-local higher-order theory is that no post-processing integration procedure is needed to accurately calculate the transverse shear stresses. The equilibrium equations and analytical solution of the proposed model can be obtained based on the Reissner mixed variational equation. The performance of the proposed model is assessed through different numerical examples, and the results show that the proposed model can better predict the thermo-mechanical responses of multilayered composite beams.

中文翻译：

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基于新的全局-局部混合模型的多层复合梁的热力学分析

为多层复合梁的热机械分析开发了一种精确的混合形式全局-局部高阶理论，包括横向法向热变形。虽然考虑了横向法向变形，但并没有增加位移参数的数量。所提出的混合形式全局-局部高阶理论是使用全局-局部高阶理论的位移假设并结合 Reissner 混合变分定理推导出来的。此外，混合形式的全局-局部高阶理论保留了固定数量的位移变量，而不管层数如何。为了获得改进的横向剪应力，使用了三维平衡方程。重要的是，平面内位移变量的二阶导数已从横向剪应力场中消除，从而大大简化了有限元实现。所提出的混合形式全局-局部高阶理论的好处是不需要后处理集成程序来准确计算横向剪应力。基于Reissner混合变分方程可以得到所提出模型的平衡方程和解析解。通过不同的数值算例评估了所提出模型的性能，结果表明所提出的模型可以更好地预测多层复合梁的热机械响应。所提出的混合形式全局-局部高阶理论的好处是不需要后处理集成程序来准确计算横向剪应力。基于Reissner混合变分方程可以得到所提出模型的平衡方程和解析解。通过不同的数值算例评估了所提出模型的性能，结果表明所提出的模型可以更好地预测多层复合梁的热机械响应。所提出的混合形式全局-局部高阶理论的好处是不需要后处理集成程序来准确计算横向剪应力。基于Reissner混合变分方程可以得到所提出模型的平衡方程和解析解。通过不同的数值算例评估了所提出模型的性能，结果表明所提出的模型可以更好地预测多层复合梁的热机械响应。