压电材料壳的广义变分原理和状态向量方程

General Variation Principle Behind Piezoelectric Shell and State Vector Equation

将三维弹性材料的H-R变分原理引入到具有机-电耦合效应的三维压电弹性材料圆柱壳问题中,建立了对应于正交各向异性压电材料圆柱壳的Hamilton型广义变分原理。通过变分运算得到了柱坐标系下的状态向量方程,该状态向量方程也是Hamilton正则方程。最后指出纯正交各向异性弹性材料壳Hamilton型广义变分原理是变分公式的特例。变分原理的建立将有利于压电材料圆柱壳静力学和动力学问题的有限元方法或半解析法的推导。

The Hellinger-Reissner (H-R) variation-principle for three-dimensional elastic materials introduced into the cylindrical shell problems of three-dimensional elastic piezoelectric materials with mechanical-electric coupling effect.The Hamilton type generalized variation principle for piezoelectric,cylindrical shells is established. The state vector equation is derived from the present variation algorithm after performing variation operations,and the state vector equation can be also called Hamilton canonical equation.The article emphasizes that the Hamilton type generalized variation principle for the purely elastic shell formula is of a special case of the present variation formula. The establishment of variation-principle is of benefit to deriving the finite element method or semi-analytical solution to the cylindrical shell static-dynamical problems of piezoelectric materials.