基于三阶剪切变形理论的压电功能梯度板静力学等几何分析

针对压电功能梯度板的静力学问题,建立了一种基于三阶剪切变形理论的等几何分析求解方法.其中,定义功能梯度板的材料属性为板厚方向的幂函数分布,并假设压电功能梯度板中的机械位移场与电势场相互独立.利用压电材料的第二类本构方程以及哈密顿变分原理,推导出压电功能梯度板的相关等几何有限元方程.在压电功能梯度板的自由振动分析中,研究...

Static iso-geometric analysis of piezoelectric functionally graded plate based on third-order shear deformation theory

Aiming at the static problem of a piezoelectric functionally graded plate(PFGP),an iso-geometric analysis method based on the third order shear deformation theory was proposed.The material properties of PFGP were assumed to be a power function distribution along plate thickness,and its mechanical displacement field and electric potential field were assumed to be independent of each other.Firstly,using the second type constitutive equation of piezoelectric materials and Hamilton principle,the iso-geometric finite element equations of a PFGP were derived.Secondly,in its free vibration analysis,convergence and accuracy of the proposed method for PFGP’s various mechanical boundary conditions were studied,and the effects of electrical boundary conditions,functional gradient index n,width to thickness ratio of functional gradient layer,and thickness ratio of functional gradient layer to piezoelectric layer on PFGP’s natural frequencies were analyzed.Finally,static bending behaviors of PFGP under mechanical load,electrical load and electro-mechanical coupling condition were analyzed,respectively and a displacement feedback control law was used to realize a close-loop deformation control of PFGP.Several examples’results obtained with the proposed method were compared with those published in relevant literatures to demonstrate the reliability and accuracy of the proposed method.