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

• 综合研究 • 上一篇    下一篇

九节点Hamilton等参元列式

  

  1. 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. 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: 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

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