磁电圆柱壳修正后的H-R变分原理及其正则方程

磁电弹性材料应与纯弹性材料一样，也有对应的Hellinger-Reissner（H-R）变分原理和正则方程．以纯弹性材料的H-R变分原理为基础，建立了柱坐标系下三维磁电体修正后的广义H-R变分原理，通过变分运算推导了磁电材料圆柱壳的Hamilton正则方程．并指出，纯弹性材料圆柱壳、单一压电材料圆柱壳或压磁材料圆柱壳相应的变分原理是磁电材料圆柱壳变分原理的特例．修正后的H-R变分原理是研究复杂边界条件下磁电材料圆柱壳和智能结构力学行为半解析法的理论基础．

H-R Mixed Variational Principle for Magnetoelectroelastic Shell and Its Hamilton Canonical Equation

There exits a corresponding Hellinger-Reissner ( H-R) mixed variational principle and canonical equation for Magnetoelectroelastic material, which should be the same as pure elastic. Based upon the H-R mixed variational principle for elastic materials, modified H-R mixed variational theorem for three-dimensional magnetoelectroelastic materials in the cylindrical coordinates was established, and the Hamilton canonical equation of magnetoelectroelastic cylindrical shell was derived from the present variational formulation by using the variational operations. Finally, it is emphasized that the principle for the pure elastic, single piezoelectric or single piezomagnetic shells is the special cases of the present variational principle. The proposed principle is the theoretical basis for the semi-analytical solution applied the mechanical behaviors of the complicated magnetoelectroelastic cylindrical shells and smart structures in engineering area.