颗粒增强复合材料的扩展有限元模拟方法  

Numerical simulation of particle reinforced composite using extended finite element method

作　　者：应宗权[1] 杜成斌[2] 王友元[1] 

机构地区：[1]中交四航工程研究院有限公司水工构造物耐久性技术交通行业重点实验室,广东广州510230 [2]河海大学土木工程学院,江苏南京210098

出　　处：《水利学报》2011年第2期198-203,共6页Journal of Hydraulic Engineering

基　　金：国家自然科学基金重点项目(50539030-1-1);国家自然科学基金项目(50779011)

摘　　要：为了简化颗粒增强复合材料的单元划分问题,采用扩展有限元的富集技术模拟材料的非均质性。在扩展有限元理论框架下,无须严格按照材料的几何边界划分计算网格,从而使单元划分十分简便。利用水平集函数来表征夹杂材料的几何界面,并构造富集函数以修正与材料界面相交单元的形函数。对于包含多种材料的单元,只需要进行单元分解,分区域形成单元刚度矩阵。阐述了扩展有限元位移模式的构造,支配方程的建立以及数值积分方案等。最后,分别应用扩展有限元和常规有限元方法模拟了单轴受拉的颗粒增强材料,计算结果表明扩展有限元方法是简单有效的。To simplify the generation of elements of FEM for particle reinforced composites,the enrichment technique for extended finite element method （XFEM） was used to account for the material interfaces.In the framework of XFEM,it is unnecessary to match the internal features of the inclusions during mesh generation,so it can be performed easily.The geometry of material distribution is described by level set function,which allows one to construct the enrichment function.The enrichment function was used to improve the shape function of classical FEM for the nodes supporting the elements cut by the interface.The key techniques of XFEM were presented,including construction of displacement pattern,establishment of the governing equation and scheme of numerical integration.Finally,the particle reinforced composits with three kinds of distributions of particle under uniaxial tension was simulated by XFEM and FEM,respectively.The comparison of the calculation results show that XFEM is highly effective and efficient.

关 键 词：扩展有限元法 颗粒增强材料 水平集函数 数值积分 

分 类 号：TV431[水利工程—水工结构工程]