压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程。给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的。这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析。变分原理将有利于压电材料问题相应的半解析法或有限元法的推导。

MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR PIEZOELECTRIC MATERIAL AND EXACT SOLUTION OF PIEZOELECTRIC LAMINATES

The Hellinger-Reissner(H-R) mixed variational principle for three-dimensional purely elastic bodies is introduced into the static analysis of piezoelectric material with mechanical-electric coupling effect.The modified H-R mixed variational principle for piezoelectric material is established and a state-vector equation of piezoelectric material is derived from the principle.Analytical solution is presented for the static behavior of the state-vector equation of laminated piezoelectric plates with simply supported edges.Numerical results obtained by present method are in good agreement with other available solutions.The present theory and solution can also be applied to the static analysis of hybrid laminates made of conversational elastic material and piezoelectric material.The proposed variational principle will facilitate the derivation of corresponding semi-analytical or finite element method for piezoelectric laminated plates.