磁电弹性体修正后的H-R混合变分原理和状态向量方程  

Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation

作　　者：卿光辉[1] 邱家俊[2] 刘艳红[1] 

机构地区：[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

出　　处：《应用数学和力学》2005年第6期665-670,共6页Applied Mathematics and Mechanics

基　　金：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。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.

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 

分 类 号：O343.2[理学—固体力学] O176[理学—力学]