基于二次移动单元的边界点法解弹性力学问题

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (6): 581-585.

基于二次移动单元的边界点法解弹性力学问题

马杭，周鹃

（上海大学理学院，上海 200444）

收稿日期:2009-06-19 出版日期:2009-12-28 发布日期:2009-12-28
通讯作者: 马杭（1951～），男，教授，博士，研究方向为计算固体力学. Email:hangma@staff.shu.edu.cn
作者简介:马杭（1951～），男，教授，博士，研究方向为计算固体力学. Email:hangma@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(10772106)

Boundary Point Method Based on Quadratic Moving Elements for Elasticity

MA Hang,ZHOU Juan

(College of Sciences, Shanghai University, Shanghai 200444, China)

Received:2009-06-19 Online:2009-12-28 Published:2009-12-28

摘要/Abstract

摘要：

边界点法是一种结合基本解法和边界元法二者优点的新的边界型无网格数值方法.将边界点法推广到弹性力学问题的数值求解中,在边界点法原有的常数移动单元基础上，引入了二次移动单元，解决了后处理过程中由于近奇异性而产生的边界附近应力的计算精度问题以及薄壁构件的分析问题.用改进的边界点法对弹性力学平面问题的典型算例进行了分析，结果表明数值解与精确解吻合良好.

关键词: 边界点法；二次移动单元；基本解；单点计算；弹性力学

Abstract:

The boundary point method (BPM) is a newly developed boundarytype meshless method with favorable features of both the method of fundamental solution (MFS) and the boundary element method (BEM). The present paper extends the BPM to the numerical analysis of linear elasticity. In order to improve accuracy of stresses near boundaries due to the near singularity in postprocessing and in the analysis of thinwall structures, quadratic moving elements are introduced into BPM in addition to the original constant moving elements. Numerical tests are carried out with benchmark examples in the two dimensional elasticity. Good agreement is observed between the numerical results and the rigorous solutions.

Key words: boundary point method （BPM）; quadratic moving element; fundamental solution; onepoint computing;elasticity

中图分类号:

O 241

马杭，周鹃. 基于二次移动单元的边界点法解弹性力学问题[J]. 上海大学学报(自然科学版), 2009, 15(6): 581-585.

MA Hang,ZHOU Juan. Boundary Point Method Based on Quadratic Moving Elements for Elasticity[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(6): 581-585.