中文摘要：

用积分法和中点材料法形成单元刚度阵对非均匀材料进行结构分析。用函数形式表达材料参数，通过在每个三角形区域里对弹性系数进行积分，得到单元刚度矩阵，从而真实地反映了材料的非均匀性；另一种简化方法是用三角形中心处的材料参数代替整个三角形单元的材料参数，使每一个三角形单元为均匀单元。文章比较了两种方法的计算结果和时间，同时用COMSOL对这两种方法进行了验证。

英文摘要：

PThe integral method and centroid method are used to form the element stiffness matrix for the structural analysis of heterogeneous materials. The material property is expressed as a function of the coordinates, by using the integral of the elasticity coefficients on the triangle, we can obtain the element stiffness matrix, and the Heterogeneous property is truly expressed. Another method is used to replace the integral by using the material of the centroid to represent the material of the triangle, then the element is looked as a homogeneous one. The two methods are compared in computational results and CPU time, and COMSOL is also used to verify the methods of this paper.