绝对节点坐标法中压电层合板的大变形研究  

Large deformation of piezoelectric laminated plate based on absolute nodal coordinate formulation

作　　者：郭永彬[1] 孙靖尧 黎亮[1] 章定国[1] GUO Yong-bin;SUN Jing-yao;LI Liang;ZHANG Ding-guo(School of Science,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学理学院,江苏南京210094

出　　处：《振动工程学报》2022年第6期1355-1363,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(12072159,12232012);中央高校基本科研业务费专项资金资助项目(30922010314)。

摘　　要：压电层合板可以通过对作动器施加电压变形为各种形态,在智能可折叠结构领域具有潜在的应用前景。理解这种结构的大变形作动机理是软体智能结构设计的基础。利用等效单层模型,基于绝对节点坐标法(ANCF),建立了一种柔性压电层合薄板单元。引入了压电材料的本构方程来推导弹性力和压电力,建立了压电层合薄板单元的动力学方程,并对比了在大变形范围内三种曲率表达形式的收敛效果。通过与ABAQUS有限元软件求得的结果进行比较,验证了压电层合薄板单元的正确性,并给出了一些大变形算例。结果表明,在压电材料全覆盖、部分覆盖、多段覆盖等情形下,该单元均能得到较为稳定的结果,表明此单元可以与单层线弹性单元进行耦合。此外还研究了压电层合板受集中力状态下的动态响应。该研究有助于理解受智能压电材料驱动的柔性或软体结构的复杂耦合非线性力学行为。Piezoelectric laminated plates can be deformed into many patterns and have potential application prospect in the field of smart foldable structures.Knowing the large deformation actuation mechanism of such structures is the basis in the soft machine design.In this paper,using the equivalent single-layer model,a flexible piezoelectric laminated thin plate element based on the absolute nodal coordinate formulation(ANCF)is established.This plate element contains three layers,in which the base layer is made of linear elastic material,and the top and bottom layers are both made of piezoelectric materials.The constitutive equation of the piezoelectric material is introduced to derive the elastic force and the piezoelectric force,and the kinetic equations of the piezoelectric laminated thin plate are obtained.Three different forms of the curvature are introduced and the convergence of the results are analyzed.The correctness of the piezoelectric laminated thin plate element proposed in this paper are validated by comparing with the commercial finite element software ABAQUS,and a group of simulations are provided.Results show that when various voltages are applied to the piezoelectric actuators that located in arbitrary positions of the base layer,the flexible beam can achieve the desired shape smoothly.Stable results can be obtained under the conditions of fully covered,partially covered and multiple covered plate with piezoelectric materials,which means this plate element can be coupled with the one-layer linear elastic element.What’s more,dynamic responses of a plate with concentrated force are also investigated.Research in this work can be helpful to the understanding of complicated coupled nonlinear mechanics of flexible or soft structures driven by smart piezoelectric materials.

关 键 词：非线性振动 绝对节点坐标法 层合板 压电材料 智能结构 大变形 

分 类 号：O322[理学—一般力学与力学基础] O313.7[理学—力学]