基于哈密顿体系的平面无限解析元

孙雁; 周钢; 刘正兴

基于哈密顿体系的平面无限解析元

1.
上海交通大学, 工程力学系, 上海, 200030;
2.
上海交通大学, 应用数学系, 上海, 200030

基金项目: 国家自然科研基金资助项目(10132020);上海市科学技术委员会资助项目(00QA14013)

详细信息

作者简介:
孙雁(1965- ),女,上海人,副教授,博士(E-mail:sunyan07@sh163c.sta.net.cn)

中图分类号: O343
计量
- 文章访问数: 2274
- HTML全文浏览量: 138
- PDF下载量: 560
- 被引次数: 0
出版历程
- 收稿日期: 2001-02-10
- 修回日期: 2002-12-24
- 刊出日期: 2003-05-15

Plane Infinite Analytical Element and Hamiltonian System

1.
Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P.R.China;
2.
Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, P.R.China

摘要

摘要: 在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。
- 无限域 /
- 无限元 /
- 哈密顿体系 /
- 本征向量展开 /
- 有限元
Abstract: It is not convenient to solve those engineering problems defined in an infinite field by using FEM.An infinite area can be divided into a regular infinite external area and a finite internal area.The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate.All governing equations were transformed into the Hamiltonian system.The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element,like a super finite element,can be combined with commonly used finite elements.The proposed method was verified by numerical case studies.The results show that the preparation work is very simple,the infinite analytical element has a high precision,and it can be used conveniently.The method can also be easily extended to a three-dimensional problem.
- infinite field /
- infinite analytical element /
- Hamiltonian system /
- method of eigenfunction expansion /
- FEM

HTML全文

参考文献(8)

[1]	徐芝纶.弹性力学[M].北京:高等教育出版社,1990.
[2]	Timoshenko S P,Goodier J N.Theory of Elasticity[M].3rd Ed.New York:McGraw-Hill,1970.
[3]	Sokolnikoff I S.Mathematical Theory of Elasticity[M].2nd Ed.New York:McGraw-Hill,1956.
[4]	Zienkiewiz O C,Taylor R W.The Finite Element Method[M].Vol 2.4th Ed.New York:McGraw-Hill,1989.
[5]	应隆安.无限元方法[M].北京:北京大学出版社,1992.
[6]	ZHONG Wan-xie,Williams F W.Physical interpretation of the symplectic orthogonality of the eigensolutions of a Hamiltonian or symplectic matrix[J].Computers & Structures,1993,49(4):749-750.
[7]	ZHONG Wan-xie.LIN Jia-hao.QIU Chun-hang.The eigenvalue problem of the chain of identical substructures[J].Acta Mechanica Sinica,1991,7(2):169-177.
[8]	钟万勰.弹性平面扇形域问题及哈密顿体系[J].应用数学和力学,1994,15(12):1057-1066.