多边形单元的构造新方法及实现

A New Construction and Implementation of Polygonal Elements

摘要:

针对任意多边形单元生成困难的问题，提出了一种利用传统的三角形有限元网格生成形状合理的多边形单元网格的方法.该方法能够直接利用已经成熟的三角形网格生成算法，且具有消耗时间少、程序实施简单、稳定可靠等优点.详细介绍了该多边形网格的生成算法，进行了程序实现，并用算例证实了该方法的正确性.

关键词:多边形单元; 有限元; Wachspress 插值函数; 自然单元; 无网格

Abstract:

A study is made of the difficulty of generating n polygonal element and a generalized polygonal mesh construction method is proposed for generating acceptable polygonal elements by using the conventional triangular mesh.The well developed triangularization algorithm is directly used in the method.It is highly robust,reliable,easy to be implemented and less time consuming.The proposed polygonal meshing algorithm is described in detail and is coded in Standard C++.To demonstrate the validities of constructing element,numerical examples of the patch test and the cantilever beam are discussed.

Key words:polygonal finite element method; finite element method; Wachspress basis functions; natural element; meshless methods