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准静态电磁热弹性体余能原理和广义变分原理

DOI: doi:10.3969/j.issn.1006-7043.2011.01.007

Keywords: 电磁热弹性体, 余能原理, 广义变分原理, 准静态

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Abstract:

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.

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