梁板结构埋入压电片的深度和厚度优化研究

根据梁的弯曲变形理论，以及压电材料的压电效应，对压电复合材料梁结构的应变和应力状态进行了分析。推导了压电材料埋入梁结构时其埋入深度和压电材料本身厚度的优化目标函数。根据优化目标函数，绘制出了在给定的基体材料和压电材料弹性模量比之下，压电材料的驱动力矩随埋入深度和压电材料厚度变化的三维曲面和等高线图，直观地表示出了埋入型压电材料智能结构获得最佳驱动力矩的配置方案。同时也分析了结构和压电材料两者的弹性模量之比对其结果的影响。结果表明，压电材料对于结构的作动力矩与其埋入基体材料的深度、本身厚度以及基体材料和压电材料的弹性模量之比都有着密切的联系。同时将结果也推广到了压电板结构，此时压电材料和基体材料的泊松比时其结果也有一定的影响。

Optimization of Thickness and Depth of Embedded Piezoelectri Patch in Composite Beam and Plate Structures

Using classical beam and plate theory and considering the piezoelectric effect of piezoelectric material, the objective function for finding the optimal thickness and depth of embedded piezoelectric material is set up. Optimizing the objective function, a three-dimensional plots and contour maps are presented with different modulus ratio between the basis material and piezoelectric material, which can be used to show the best configurations for the smart beams and plates when piezoelectric materials were embedded inside. The results show that both the thickness and deepness of embedded piezoelectric materials as well as modulus ratio (the Poisson ratio in the plate case) between the basis material and piezoelectric material have great influence on the actuating moment.