A new hybrid fundamental-solution-based finite element method (HFS-FEM) is developed for the transient heat conduction analysis of two-dimensional orthotropic materials. By using coordinate transformation and time-stepping approximation, the governing equation of the original problem is converted to the modified Helmholtz equation. In the solution procedure, the homogeneous solutions of the problem are sought by employing HFS-FEM while the particular solutions are approximated with the aid of radial basis function. HFS-FEM has many attractive features compared to the conventional FEM. The computational efficiency and convergence of the present method are examined through several numerical examples.

中文翻译：

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二维正交各向异性材料瞬态热传导分析的基于混合基本解的有限元方法

开发了一种新的基于混合基本解的有限元方法 (HFS-FEM)，用于二维正交各向异性材料的瞬态热传导分析。通过坐标变换和时间步逼近，将原问题的控制方程转化为修正的亥姆霍兹方程。在求解过程中，采用HFS-FEM寻求问题的齐次解，而特定解则借助径向基函数逼近。与传统 FEM 相比，HFS-FEM 具有许多吸引人的特点。通过几个数值例子检验了本方法的计算效率和收敛性。