九节点Hamilton等参元列式

广东工业大学学报 ›› 2012, Vol. 29 ›› Issue (1): 27-31.

九节点Hamilton等参元列式

1.广州民航职业技术学院机务工程系，广东广州 510403；2.中国民航大学航空工程学院，天津 300300

出版日期:2012-03-25 发布日期:2012-03-25
作者简介:邢瑞山（1982-）,男，实验师，硕士，主要研究方向为飞机结构与复合材料.

node Isoparametric Element of Hamilton Canonical Equation 

1. Department of Aircraft Engineering, Guangzhou Civil Aviation College, Guangzhou 510403, China；2. College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China

Online:2012-03-25 Published:2012-03-25

摘要/Abstract

摘要： 结合弹性材料修正后的HR变分原理和九节点四边形等参元二次插值函数，建立了九节点Hamilton等参元列式的正则方程.简要地介绍了弹性材料修正后的HR变分原理.基于变分原理使用3×3的高斯积分详细地推导了Hamilton正则方程的九节点等参元列式，使得九节点等参元在有限元法中的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合.数值实例的结果证明了本文九节点Hamilton等参元列式的正确性.
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关键词: Hamilton正则方程；九节点等参元；半解析法；高斯积分

Abstract: The 9node isoparametric element of Hamiltonian canonical equation has been established by combining the modified HellingerReissner (HR) variational principle of elastic material and quadratic interpolation function of 9node quadrilateral isoparametric element. Firstly, the modified HR variational principle for the elastic material was briefly presented. Then, based on the variational principle and the 3×3 Guass integration, the Hamilton canonical equation of 9node isoparametric element was derived in detail. The advantages of 9node isoparametric element in finite element were combined with the semianalytical method of elasticity Hamilton canoncial equation organically. The results of numerical examples prove the correctness of the 9node isoparametric element formulation.

Key words: Hamilton canonical equation; 9node isoparametric element; semianalytical method; Gauss integral

邢瑞山1,卿光辉2. 九节点Hamilton等参元列式[J]. 广东工业大学学报, 2012, 29(1): 27-31.

Xing Ruishan1, Qing Guanghui2 . node Isoparametric Element of Hamilton Canonical Equation [J]. Journal of Guangdong University of Technology, 2012, 29(1): 27-31.

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