准静态电磁热弹性体余能原理和广义变分原理

The complementary energy principle and generalized variational principles of quasi-static electro-magneto-thermo-elasticity

具有多场耦合性质的电磁热弹性体的基本方程很复杂,即使考虑最简单的情况也难求其解析解,所以需采用近似计算方法.变分原理是有限元法等近似计算方法的理论基础.按照广义力和广义位移之间的对应关系,将基本方程乘上相应的虚量,积分代数相加,建立了准静态电磁热弹性体的余能原理和第一类H-R型广义变分原理,为电磁热弹多场问题的近似计算提供理论依据.驻值条件的推导结果表明,驻值条件和先决条件一起构成了适定的微分方程组,加上温度场方程和补充条件则构成了电磁热弹性体全部的微分方程,从而验证了这2个变分原理的正确性.

The basic equations of coupled electro-magneto-thermo-elasticity are very complicated.Therefore,it is hard to obtain analytical solutions,even in the simplest conditions,so approximate computational methods are used.However,variational principles are the foundation of the finite element method and other approximate computational methods.According to the corresponding relations between generalized forces and generalized displacements,basic equations were multiplied by corresponding virtual quantities,then integrated with volume and area and added algebraically.Complementary energy principles and the first H-R generalized variational principles of quasi-static electro-magneto-thermo-elasticity were established,offering theoretical support for approximate calculation of multi-physics field problems of electro-magneto-thermo-elasticity.Results of stationary value conditions show that the suitable differential equations are composed of stationary value conditions and various pre-conditions.All differential equations are composed of these suitable differential equations,including temperature field equations and supplementary conditions.Thus the validity of these two variational principles is verified.