Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation
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摘要: 以三维弹性体的Hellinger-Reissner(H-R)混合变分原理为基础，建立了三维磁电弹性体修正后的H-R混合变分原理，通过变分运算得到了磁电弹性板的状态向量方程，并应用该原理导出了平面内离散元素的状态向量方程，为半解析法在磁电弹性板问题上的应用奠定了理论基础．最后指出：纯弹性体、单一压电体或单一压磁体修正后的H-R混合变分原理都是目前原理的特例．Abstract: Based upon the Hellinger-Reissner(H-R) mixed variational principle for three-dimensional elastic bodies,the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established.The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations.To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates,the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle.Finally,it is pointed out that the modified H-R mixed variational principle for pure elastic,single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.
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