摘要
本文采用多边形单元的平均值坐标,构造任意节点分布的多边形单元无理函数形式的插值函数,提出了一种求解微分方程边值问题的多边形有限元方法.对于曲线边界问题的数值求解,通过适当的节点配置,多边形单元网格能够逼近任意形状的求解区域.不同形状多边形单元的形函数表达式形式统一,方便计算程序的编写.数值算例验证了多边形有限元法的求解精度和有效性.
The irrational function forms interpolation on a polygonal element with arbitrary nodal distribution was constructed by using mean value coordinates of polygonal elements. The polygonal finite element method for solving boundary value problems of differential equations was presented. For a curved boundary, the polygonal meshes can exactly approximate the arbitrary geometric shape by proper nodal distribution. The expressions of shape function within different elements are uniform. It is convenient to program the computer codes for finite element analysis. Numerical examples on second order elliptical boundary value problems are presented to demonstrate the accuracy and effectiveness of the proposed method.
出处
《山东大学学报（工学版）》
CAS
2008年第2期66-70,共5页
Journal of Shandong University（Engineering Science）
基金
国家自然基金重点项目(50539080)
山东建筑大学博士基金及科研基金资助项目(XN050103)
关键词
无理函数插值
多边形单元
多边形有限元
重心坐标
平均值坐标
irrational function interpolation
polygonal element
polygonal finite element method
barycentric coordinates
mean value coordinates
