弹性力学问题的加权Nitsche间断伽辽金有限元法  

Weighted Nitsche Discontinuous Galerkin Finite Element Method of Elasticity Problems

作　　者：王明威 张健飞[1] 邓小蔚 

机构地区：[1]河海大学力学与材料学院,江苏南京211100

出　　处：《河南科技大学学报（自然科学版）》2018年第3期83-88,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(51679077);中央高校基本科研业务费专项基金项目(2016B06414)

摘　　要：结合传统间断伽辽金有限元法和加权Nitsche法,将内界面上的通量计算由传统的算术平均改进为加权平均,推导了弹性力学问题的加权Nitsche间断伽辽金有限元法公式,并给出了界面稳定系数的取值公式。数值试验表明:随着单元尺寸的逐步减少,对于均质和非均质材料问题,加权Nitsche间断伽辽金有限元法的解逐步收敛于精确解。尤其是对于非均质材料问题,其稳定系数取值比传统方法更加合理和稳定,且可以避免由于稳定系数过大引起的数值不稳定问题。By combining the traditional discontinuous Galerkin finite element method with the weighted Nistche method,a weighted Nistche discontinuous Galerkin finite element method was developed for elasticity problems. In this method,the traditional arithmetic flux average on interface was replaced by the weighted average,and the formula to compute the interface stability parameter was given. The numerical tests show that the solution of weighted Nistche discontinuous Galerkin finite element method converges to exact solution with the refinement of element size for both homogeneous and heterogeneous material problems. Especially for the heterogeneous material problem,the stability parameter is more reasonable and stable than traditional method,which can avoid the unstable numerical problem resulting from the excessively large stability parameter.

关 键 词：间断伽辽金有限元法 加权Nitsche法 稳定系数 非均质材料 

分 类 号：O343[理学—固体力学]