Wachspress型多边形有限元法积分方案  

Integration scheme of Wachspress interpolation polygonal finite element method

作　　者：丁胜勇[1] 邵国建[1] 

机构地区：[1]河海大学工程力学系,南京210098

出　　处：《东南大学学报（自然科学版）》2013年第1期216-220,共5页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(50978083)

摘　　要：针对3种基于Wachspress插值的多边形单元形函数,讨论其各自的特点,选取其中最合理的形函数构造形式进行其偏导数公式推导,建立多边形有限元的数值列式.对现行多边形有限元法的积分方案进行探讨,将传统有限元法常用的Gauss积分运用到多边形有限元法积分方案中,结合数值算例验证了该积分方案的合理性和可行性,并给出了在不同类型网格中Gauss积分点数选取的建议.验证在混合型网格中多边形有限元法的合理性,对多边形单元在疏密网格中作为一种过渡单元使用的可行性进行初步探讨,为解决有限元计算中疏密网格的过渡问题提供了一种新的思路.According to three kinds of Wachspress interpolation based shape function of polygonal element, the characteristics of their structural forms are discussed. The formula of partial derivative is derived by applying the best reasonable structural form and the polygonal FEM （finite element method） formulations are established. The current integration scheme in the polygonal FEM is stud- ied. Based on this, the Gaussian integration, which is widely used in traditional FEM, is applied to the integration scheme of polygonal FEM. Numerical examples are presented to demonstrate the ra- tionality and effectiveness of the proposed method. And the suggestion of selecting the number of the Gaussian integration points in different grids is given. The rationality of the polygonal FEM in mixed mesh is tested, and the feasibility of using the polygonal element as transition element in the coarse mesh and fine mesh is preliminarily discussed. This study provides a new idea to solve the transition problem of the coarse mesh and fine mesh in the FEM calculation.

关 键 词：多边形单元 多边形有限元 Wachspress插值 GAUSS积分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]