中文摘要：

针对线性压电效应只适合低电场下压电层合板弯曲问题研究的情况，基于考虑电致伸缩和电致弹性效应的非线性本构关系，建立了压电非线性分析模型，研究压电层合板的非线性弯曲问题。根据压电非线性模型分析了正压电效应对板弯曲挠度的影响，探讨了强电场作用下考虑压电非线性效应后板位移控制效果的变化规律。研究结果表明：电场作用下的线性解受正压电效应的影响很小，但是随着电压、机械荷载及板宽厚比增加，正压电效应对压电非线性解的影响逐渐增大；机械荷载作用下，若分别在基板上、下层压电片施加电压控制板的位移，线性解是唯一的，非线性解则表现出不同的控制效果。在实际工程应用中，可以根据需要选择电荷载施加方案。

英文摘要：

Linear piezoelectric effect only occurs in the bending of piezoelectric laminated plates under low electric fields. The nonlinear constitutive relationship caused by eleetrostriction and elas- tostriction was used to establish a nonlinear total potential energy functional of the piezoelectric lami- nates. According to the model, nonlinear bending analysis of the piezoelectric laminates was carried out. The impact of direct piezoelectric effect on the plate bending deflection was studied. And the variation of the displacement control was explored considering the piezoelectric nonlinear effects when the plate was subjected to a strong electric field. The results show that the impact of direct pie- zoelectric effect on the linear bending deflection is small, while its impact on the nonlinear bending deflection increases with the increase of voltage, mechanical load or plate thickness ratio. Under theaction of mechanical force, the voltage is applied to the upper piezoelectric sheet or the lower one, the linear displacement solution is unique, but the nonlinear solutions vary. In engineering, the ap- plication method of electric load can be selected according to needs.