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.
出处
《应用数学和力学》
EI
CSCD
北大核心
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)
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
magnetoelectroelastic body
variational principle
laminated plates
state-vector equation
semi-analytical solution