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文章将单一的弹性或塑性力学中的变分原理应用到压电、压磁和电磁耦合弹性介质材料中,通过对某一泛函的驻值求解,即一阶变分为零并满足一定的边界条件,建立各种变分原理。并由此推出各向异性压电、压磁弹性板的变分方程,进而导出板的平衡方程和边界条件。该方法可为材料的有限元分析模型提供依据。
In this paper, the principle of variational principle in a single elastic or plastic mechanics is applied to piezoelectric, piezomagnetic and electromagnetic coupling elastic medium materials. By solving the value of a functional in terms of first-order variational zero and satisfying certain Boundary conditions, the establishment of various variational principles. And then the variational equation of the anisotropic piezoelectric and piezomagnetic elastic plates is deduced, and then the balance equation and the boundary condition of the plate are deduced. This method can provide the basis for the finite element analysis of the material.