压电材料修正后的变分原理及智能板的精确解

建立了压电材料修正后的H-R混合变分原理，并从该变分原理直接推导了压电材料的状态向量方程，同时给出了与广义位移和广义应力相关的边界条件表达式。为了验证本文的理论，给出了简支压电材料矩形板静力和自由振动问题的无穷级数精确解形式。并对两个具有代表性的实例进行了数值分析，部分结果与已有的文献进行了比较，并给出了分广义位移和广义应力的分布图，它们直观地展示了精确解的优点。本文的变分公式将用采构造新颖的适应工程领域复杂压电材料问题的半解析法。

Modified Mixed Variational Principle for Piezoelectric Materials and Exact Solution for Smart Laminated Plates

A modified mixed variational principle for piezoelectric plates is established and the state-vector equation is deduced directly from the principle. The explicit forms of the generalized displacements and stresses with respect to boundary conditions are given, To validate the theory,the exact solutions of the static problem and free vibration analysis of the simply supported piezoelectric rectangular plate are put in terms of an infinite series. Two representative examples are analyzed numerically. Some of the results are compared with published papers. Some distribution figures of the generalized displacements and stresses are given to demonstrate the advantage of the exact solutions. The present variational formulation will be used to achieve a novel seml-analytical formulation for more complex piezoelectric material problems in engineering applications.