电磁弹性动力学初边值问题12类变量广义变分原理

Twelve-field generalized variational principles for initial-boundary-value problem of magneto-electroelasto dynamics

基于Yao建立的电磁弹性固体广义变分原理,运用关于非传统Hamilton型广义变分原理的方法,建立了电磁弹性动力学初边值问题的12类变量广义变分原理,可反映该问题的全部特征,其独立变分变量为该问题的全部变量,即位移、速度、动量、应变、应力、电位移、磁感应强度、电场强度、磁场强度、电标量势、磁标量势和磁矢量势。本文建立的广义变分原理可为电磁弹性动力学提供建立杂交或混合有限元等变分近似解法的理论基础。

Based on the generalized variational principles（GVPs） established by Yao for magnetoelectroelastic solids,the twelve-field GVPs for the initial-boundary-value problem of magneto-electro-elasto dynamics are established by using the method on unconventional Hamilton-type GVPs.The new GVPs can fully characterize this dynamics.The independent variables are all variables of the discussed problem,such as displacements,velocities,momentums,strains,stresses,electric displacements,magnetic inductions,electric field intensities,magnetic field intensities,electric scalar potential,magnetic scalar potential and magnetic vector potentials.The proposed GVPs can provide the theoretical basis for establishment of various approximate methods,such as hybrid or mixed finite element method,in magnetoelectro-elasto dynamics.