基于参数变分原理的非均质材料弹塑性有限元分析的Voronoi单元法  

Parametric Variational Principle Based Elastic-Plastic Analysis of Heterogeneous Materials With Voronoi Finite Element Method

作　　者：张洪武[1] 王辉[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024

出　　处：《应用数学和力学》2006年第8期904-912,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金;创新群体基金资助项目(10225212;10421002;10332010);长江学者和创新团队发展计划资助项目;国家基础性发展规划项目(2005CB321704)

摘　　要：在非均质材料的有限元数值模拟中,采用了Voronoi单元(VCFEM)以克服经典位移元的局限性.基于参数变分原理和二次规划法进行了Voronoi单元的二维弹塑性分析.推导了有限元列式并形成最终的二次规划求解模型.研究了非均质材料微观夹杂对整体力学性能的影响.数值算例证明了该方法的正确和可行性.The Voronoi cell finite element method （VCFEM） is adopted to overcome the limitations of the classic displacement based finite element method in numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method were developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations were derived and a standard quadratic programming model was deduced flom the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

关 键 词：Voronoi单元 参数变分原理 二次规划法 

分 类 号：O344.3[理学—固体力学] O242.21[理学—力学]