A hybrid finite element method is proposed for the heat conduction analysis with variable thermal conductivities. A linear combination of fundamental solutions is employed to approximate the intra-element temperature field while standard one-dimensional shape functions are utilized to independently define the frame temperature field along the element boundary. The influence of variable thermal conductivities embeds in the intra-element temperature field via the fundamental solution. A hybrid variational functional, which involves integrals along the element boundary only, is developed to link the two assumed fields to produce the thermal stiffness equation. The advantage of the proposed method lies that the changes in the thermal conductivity are captured inside the element domain. Numerical examples demonstrate the accuracy and efficiency of the proposed method and also the insensitivity to mesh distortion.

中文翻译：

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变热导率正交各向异性介质中热传导的混合有限元分析

提出了一种混合有限元法用于变热导率的热传导分析。基本解的线性组合用于近似单元内温度场，而标准一维形状函数用于独立定义沿单元边界的框架温度场。可变热导率的影响通过基本解嵌入到单元内温度场中。开发了一种混合变分泛函，它仅涉及沿单元边界的积分，以连接两个假设场以产生热刚度方程。所提出方法的优点在于在单元域内捕获了热导率的变化。