Application of 2D base force element method with complementary energy principle for arbitrary meshes
Application of 2D base force element method with complementary energy principle for arbitrary meshes
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DOI：
10.1108/ec-10-2011-0125
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发表时间：
2014-07
影响因子：
1.6
通讯作者：
Yijiang Peng;Nana Zong;Lijuan Zhang;Jiwei Pu
中科院分区：
文献类型：
--
作者：
Yijiang Peng;Nana Zong;Lijuan Zhang;Jiwei Pu
目的：提出一种基于余能原理的基体力单元法的二维模型。提出了一种适用于任意网格问题的边界元模型。设计/方法/方法--BFE使用Gao(2003)给出的基本力作为基本变量来描述弹性系统的应力状态。利用基本力的概念，推导出单元柔度矩阵的显式表达式。利用拉格朗日乘子法，给出了边界元控制方程的详细公式。给出了节点位移的显式表达式。为了验证二维有限元模型的正确性，用MatLab语言编制了有限元程序，并给出了任意多边形网格和变异网格的算例。结果-数值结果和理论结果之间有很好的一致性。通过研究发现，互补能边界元的二维列式可以有效地提高边界元的精度。
Purpose – The purpose of this paper is to present a two-dimensional (2D) model of the base force element method (BFEM) based on the complementary energy principle. The study proposes a model of the BFEM for arbitrary mesh problems. Design/methodology/approach – The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM are given using the Lagrange multiplier method. The explicit displacement expression of nodes is given. To verify the 2D model, a program on the BFEM using MATLAB language is made and a number of examples on arbitrary polygonal meshes and aberrant meshes are provided to illustrate the BFEM. Findings – A good agreement is obtained between the numerical and theoretical results. Based on the studies, it is found that the 2D formulation of BFEM with complementary energy pr...