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磁电弹性体修正后的H-R混合变分原理和状态向量方程
引用本文:卿光辉,邱家俊,刘艳红.磁电弹性体修正后的H-R混合变分原理和状态向量方程[J].应用数学和力学,2005,26(6):665-670.
作者姓名:卿光辉  邱家俊  刘艳红
作者单位:1. 中国民用航空学院,机电分院,天津,300300
2. 天津大学,机械工程学院,力学系,天津,300072
基金项目:国家自然科学基金资助项目(10072038),教育部博士点基金资助项目(2000005616)
摘    要:以三维弹性体的Hellinger_Reissner(H_R)混合变分原理为基础,建立了三维磁电弹性体修正后的H_R混合变分原理,通过变分运算得到了磁电弹性板的状态向量方程,并应用该原理导出了平面内离散元素的状态向量方程,为半解析法在磁电弹性板问题上的应用奠定了理论基础· 最后指出:纯弹性体、单一压电体或单一压磁体修正后的H_R混合变分原理都是目前原理的特例·

关 键 词:磁电弹性体  变分原理  层合板  状态向量方程  半解析法
文章编号:1000-0887(2005)06-0665-06
修稿时间:2004年5月8日

Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation
QING Guang-hui,QIU Jia-jun,LIU Yan-hong.Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation[J].Applied Mathematics and Mechanics,2005,26(6):665-670.
Authors:QING Guang-hui  QIU Jia-jun  LIU Yan-hong
Institution:QING Guang-hui~1,QIU Jia-jun~2,LIU Yan-hong~1
Abstract:Based upon the Hellinger_Reissner (H_R) mixed variational principle for three_dimensional elastic bodies, the modified H_R mixed variational theorem for magnetoelectroelastic bodies was established. The state_vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi_analytical solution applied with the magnetoelectroelastic plates,the state_vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H_R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.
Keywords:magnetoelectroelastic body  variational principle  laminated plates  state-vector equation  semi-analytical solution
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