非均质材料热传导问题的扩展有限元法

摘要

The extended finite element method （XFEM） for heat transfer of heterogeneous materials is proposed. In the method, the heat conductivity is adopted as the basic parameter for calculation. Mesh can be generated without taking account of the existence of the material interfaces, so the mesh generation can be considerably simplified and the high-quality meshes are obtained correspondingly. When one element contains no material interface, the temperature function will be degenerated into that of the con- ventional finite element. For the element containing material interfaces, the standard temperature based approximation is enriched by incorporating level-set-based enrichment functions which model the interfaces. Results of numerical examples demonstrate the validity and the advantages of the proposed method.%针对非均质材料，提出了以导热系数为基本参数的热传导扩展有限元法。划分网格时不需要考虑材料界面的存在，因此网格的形成可以大大地简化，且可以获得高质量的网格。不含材料界面的单元，其温度场函数将退化为常规有限元的函数。含材料界面的单元，采用基于水平集的加强函数加强常规温度的近似，加强函数用于模拟界面。数值算例结果体现了该方法的有效性和优势。