[1]丁胜勇,邵国建.Wachspress型多边形有限元法积分方案[J].东南大学学报(自然科学版),2013,43(1):216-220.[doi:10.3969/j.issn.1001-0505.2013.01.039]
 Ding Shengyong,Shao Guojian.Integration scheme of Wachspress interpolation polygonal finite element method[J].Journal of Southeast University (Natural Science Edition),2013,43(1):216-220.[doi:10.3969/j.issn.1001-0505.2013.01.039]
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Wachspress型多边形有限元法积分方案()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
43
期数:
2013年第1期
页码:
216-220
栏目:
计算机科学与工程
出版日期:
2013-01-20

文章信息/Info

Title:
Integration scheme of Wachspress interpolation polygonal finite element method
作者:
丁胜勇邵国建
河海大学工程力学系, 南京210098
Author(s):
Ding Shengyong Shao Guojian
Department of Engineering Mechanics, Hohai University, Nanjing 210098, China
关键词:
多边形单元 多边形有限元 Wachspress插值 Gauss积分
Keywords:
polygonal element polygonal finite element Wachspress interpolation Gauss integration
分类号:
TP391
DOI:
10.3969/j.issn.1001-0505.2013.01.039
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.
Abstract:
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 studied. 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 rationality 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.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 丁胜勇(1987—),男,博士生;邵国建(联系人),男,博士,教授,博士生导师,gjshao@hhu.edu.cn.
基金项目: 国家自然科学基金资助项目(50978083).
引文格式: 丁胜勇,邵国建.Wachspress型多边形有限元法积分方案[J].东南大学学报:自然科学版,2013,43(1):216-220. [doi:10.3969/j.issn.1001-0505.2013.01.039]
更新日期/Last Update: 2013-01-20