杂交应力元的应力子空间和柔度矩阵<em>H</em>对角化方法

张灿辉; 冯伟; 黄黔

杂交应力元的应力子空间和柔度矩阵H对角化方法

上海大学, 上海市应用数学和力学研究所, 上海, 200072

基金项目: 教育部留学回国人员资助基金资助项目;教育部高等学校骨干教师计划基金资助项目;上海市教育基金会"曙光计划"的资助项目(99SG38)

详细信息

作者简介:
张灿辉(1967- ),男,福建惠安人,博士(E-mail:oudeezhang@sohu.com).

中图分类号: O242.21
计量
- 文章访问数: 2198
- HTML全文浏览量: 131
- PDF下载量: 651
- 被引次数: 0
出版历程
- 收稿日期: 2001-10-09
- 修回日期: 2002-08-03
- 刊出日期: 2002-11-15

The Stress Subspace of Hybrid Stress Element and the Diagonalization Method for Flexibility Matrix H

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 证明了:1)杂交元假设应力模式线性无关是柔度矩阵非奇异的充分必要条件;以及2)等价假设应力模式形成相同的杂交元。在此基础上建立了假设应力模式的希尔伯特应力子空间,从而可以利用斯密特方法简单地得到等价的正交归一化应力模式,实现了柔度矩阵对角化,使得杂交元形成过程中完全避免了繁杂的矩阵求逆运算,极大地提高了杂交元分析的计算效率,数值算例表明该方法是确实有效的。
- 杂交应力有限元 /
- 希尔伯特应力子空间 /
- 柔度矩阵对角化方法
Abstract: The following is proved:1)The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix.2)The equivalent assumed stress modes lead to the identical hybrid element.The Hilbert stress subspace of the assumed stress modes is established.So,it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method.Because of the resulting diagonal flexibility matrix,the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly.The numerical examples show that the method is effective.
- hybrid stress finite element /
- Hilbert stress subspace /
- diagonalization method for flexibility matrix

HTML全文

参考文献(11)

[1]	Pian T H H. Derivation of element stiffness matrices[J]. AIAA,1964,2(3):576-577.
[2]	Hoa S V, FENG Wei. Hybrid Finite Element Method for Stress Analysis of Laminated Composites[M]. Boston/Dordrecht/London:Kluwer Academic Publihsers,1998.
[3]	HUANG Qian. Modal analysis of deformable bodies with finite degree of deformation freedom-An approach to determination of natural stres modes in hybrid finite elements[A]. In: Chien Wei-zang, Fu Zi-zhi, Eds. Advances in Applied Mathematics & Mechancis in China[C]. IAP,1991,3:283-303.
[4]	FENT Wei, Hoa S V, HUANG Quan. Classification of stress modes in assumed stress fields of hybrid finite elements[J]. International Journal for Numerical Methods in Engineering,1997,40(23):4313-4339.
[5]	吴长春,卞学. 非协调数值分析与杂交元方法[M]. 北京:科学出版社,1997.
[6]	焦兆平. 简化杂交应力元H阵的一种方法[J]. 计算结构力学及其应用,1991,8(2):214-216.
[7]	H.卡得斯赛. 有限元法手册[M]. 诸得超,傅子智译,北京:科学出版社,1995.
[8]	Saether Erik, Explicit determination of element stiffness matrix in the hybrid stress method[J]. International Journal for Numerical Methods in Engineering,1995,38(15):2547-2571.
[9]	Han J, Hoa S V. A three-dimensional multilayer composite finite element for stress analysis of composite laminates[J].International Journal for Numerical Methods in Engineering,1993,36(22):3903-3914.
[10]	MacNeal R H, Harder R L. A proposed standard set of problems to test finite element accuracy[J]. Finite Element in Analysis and Design,1985,1(1):3-20.
[11]	MacNeal R H. A theorem regarding the locking of tapered four-noded membrane elements [J]. International Journal for Numerical Methods in Engineering,1987,24(9):1793-1799.