Based on the method of sampling surfaces, a hybrid finite-element model is developed for a three-dimensional analysis of laminated composite plates with piezoelectric patches. According to this method, the sampling surfaces inside the layers and piezoelectric patches parallel to the middle surface are selected, and displacements and electric potentials of these surfaces are introduced as unknown functions. The sampling surfaces are located inside the layers and patches at the nodes of Chebyshev polynomials that allows one to obtain numerical solutions asymptotically approaching the solutions of electroelasticity as the number of sampling surfaces tends to infinity. A method to determine the optimal voltages applied to the electrodes of piezoelectric patches that makes it possible to bring the plate to the desired shape by using the inverse piezoelectric effect is proposed.

中文翻译：

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具有三维公式的分布式压电致动器复合板的形状控制

基于采样表面的方法，开发了一种混合有限元模型，用于对带有压电贴片的层压复合板进行三维分析。根据该方法，选取层内采样面和与中间面平行的压电贴片，将这些面的位移和电位作为未知函数引入。采样表面位于 Chebyshev 多项式节点处的层和补丁内部，当采样表面的数量趋于无穷大时，这允许人们获得逐渐接近电弹性解的数值解。