含夹杂非均质材料的扩展有限元数值模拟

为了验证含夹杂非均质材料扩展有限元数值模拟的有效性,分别用扩展有限元法和传统有限元法模拟计算了一块含多个圆形夹杂的单轴受拉的板的位移场,并对模拟结果进行了对比分析.结果表明,通过水平集函数来表示夹杂材料的几何界面,利用富集函数来改进被界面切割的单元所在结点的形函数,网格剖分无需考虑内部边界,可大大减少数值模拟前处理的工作量.

Application of extended finite element method in heterogeneous materials with inclusions

In order to test the validity of applying the Extended Finite Element Method(XFEM) in heterogeneous material with inclusions,the displacement field of a plate with multi-circular inclusions under uniaxial tension is simulated with both the XFEM method and the finite element method.Comparative analysis of the test results of the two methods is conducted.The results show that,by employing a level set functions to represent the geometric interfaces and adopting the enrichment functions to improve the shape functions of the nodes of the elements cut by the interfaces,the mesh generation in XFEM can be performed easily,without requiring the mesh to conform to the internal boundaries of the inclusions.Thus,the amount of pre-processing work in numerical simulation is greatly reduced.