A geometric construction method for polygonal finite elements

WANG Zhao-qing; LI Shu-cai; LI Shu-chen; WANG Ming-bin

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A geometric construction method for polygonal finite elements

更新时间：2026-06-25

- A geometric construction method for polygonal finite elements
- Vol. 27, Issue S1, (2006)
- 作者机构：
  
  1. 山东建筑大学工程力学研究所,济南,250101
  2. 山东大学岩土与结构工程研究中心,济南,250061
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391
- Online First：15 December 2006，
  
  Published：2006
- 稿件说明：
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WANG Zhao-qing, LI Shu-cai, LI Shu-chen, et al. A geometric construction method for polygonal finite elements[J]. 2006, 27(S1).
DOI：

WANG Zhao-qing, LI Shu-cai, LI Shu-chen, et al. A geometric construction method for polygonal finite elements[J]. 2006, 27(S1). DOI：

摘要

根据非均质材料的细观结构，划分多边形的计算网格。采用多边形单元进行有限元分析，实现了基于材料真实结构的数值模拟。给出了多边形有限单元形函数的几何构造方法，构造了一个辅助多边形，采用散度定理推导出多边形单元形函数的表达式。分析总结了多边形Wachspress插值、Laplace插值和平均值插值的构造方法和性质。

Abstract

Based on the mesostructures of heterogeneous materials to partition meshes and using polygonal elements in finite element analysis

the numerical simulation based on real structures of materials can be realized. A geometric construction method of polygonal interpolation is presented. Constructing an aided polygon

the basis function expressions of polygonal interpolation are given using divergence theorem. The equivalence of geometric construction method and barycentric coordinates method by Floater is proved. The construction methods and properties of Wachspress interpolation

Laplace interpolation and mean value interpolation are compared and analyzed.

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Related Author

WANG Zhao-Qing

LI Shu-Cai

LI Shu-Chen

Related Institution

Institute of Engineering Mechanics, Shandong Jianzhu University

Research Center of Geotechnical and Structural Engineering, Shandong University

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