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An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 相似文献
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电动力学电磁场边值问题的广义变分原理 总被引:1,自引:0,他引:1
给出了线性各项异性电磁场边值问题的广义虚功原理表达式,运用钱伟长教授提出的方法建立了该问题的广义变分原理,可直接反映该问题的全部特征,即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件.继而导出了一族有先决条件的广义变分原理.作为例证,导出了两个退化形式的广义变分原理,和已知的广义变分原理等价.此外还导出了两个修正的广义变分原理,可为该问题提供杂交有限元模型.建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础. 相似文献
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