中文摘要：

一个新奇混合分级的元素模型为调查机能上地分级的材料(FGM ) 的热行为在这份报纸被开发。模型能处理 FGM 的一块空间地变化的材料性质地。在建议途径，一新变化功能首先为产生相应有限元素模型被构造。然后，一个分级的元素基于独立温度地的二个集合被提出。一个人作为在元素领域以内定义的 intra 元素温度地被知道；其它是仅仅在元素边界上定义的所谓的框架地。intra 元素温度域用基本解决方案的线性联合被构造，当独立框架域独立被用作在内部元素的边界上保证域连续性的元素的边界插值函数时。由于基本答案的性质，出现在变化功能的罐头的领域积分被变换成罐头显著地简化概括元素僵硬矩阵的计算的边界积分。建议模型能模仿性质自然地由于在有限元素(FE ) 的分级的元素的使用建模的分级的材料。而且，它继承混合 Trefftz 有限元素方法的所有优点(HT 女性) 在上常规女性并且边界元素方法(BEM ) 。最后，几个例子被举估计建议方法的表演，并且获得的数字结果显示出好数字精确性。

英文摘要：

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element （FE） model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional FEM and boundary element method （BEM）. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.