新型厚薄通用的压电层合板三角形CDST-S6E单元

基于压电复合材料层合板一阶剪切变形理论及叠层理论,构造了一种新型三角形三节点压电层合板单元,简记为CDST-S6E单元.该单元采用压电耦合的运动方程求解位移场及电势场,层合板主体结构用一阶剪切变形理论模拟,其剪应变场及单元转角场由结点包含有两个剪切自由度的DST-S6单元理论确定,电势作为附加自由度,应用叠层理论对压电层合板的电势场沿厚度方向进行线性插值.该CDST-S6E单元不需要借助减缩积分、假设应力或应变等辅助数学手段,也不会产生对稳定性带来影响的附加零能模式,可较好避免厚薄板单元的剪切闭锬问题且具有简洁的表达形式.数值算例表明,CDST-S6E单元具有较高的精度,可以较为精确地预测压电层合板的变形及电势场,是一种厚薄通用的优质压电层合板单元.     

具损伤压电智能层合板的动力分析

基于应变能等效原理、高阶剪切变形理论和Hamilton变分原理,考虑复合材料铺设层内的损伤效应,建立了具损伤压电智能层合板的运动控制方程,并运用Galerkin方法进行求解.数值算例中,讨论了损伤效应、厚跨比及压电层厚度与层合板总厚度之比对四边简支压电智能层合板自由振动频率的影响和外部控制电压对其动力响应的影响.     

层合结构压电器件的机电耦合响应

压电传感嚣和致动器都可以看成是由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构,推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而,又推导出了两类(一类为单层压电-弹性层。另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中,包括了两个压电常数d211和d222。最后。通过比较解析解、实验值以及有限元计算结果,发现它们吻合得很好。     

压电复合材料梁和板的变形控制问题

由于具有良好的结构、力学性能,复合材料层合板在现代飞行器上大量应用;而压电复合材料,作为一种新兴的智能材料,由于其独特的力电耦合性能得到了人们更多的关注。本文研究含有压电片的复合材料梁和板在电场作用下的变形控制问题。基于经典的梁理论和层合板理论,分别研究了下列问题:(1)双压电片布置的悬臂梁的变形;(2)含有压电层的层合板变形控制问题;(3)含有一对压电片的层合板的变形控制问题。针对上述问题,分别给出了理论解和数值解,并进行了相关讨论分析。结果表明压电材料可对结构进行精确控制,因此本文的结果可对复合材料梁和板在电场作用下的变形控制问题提供工程参考。     

层合结构压电器件的机电耦合效应

压电传感器和致动器都可以看成是一种复合材料层合板结构，由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构，我们推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而，又推导出了两类(一类为单层压电-弹性层，另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中，包括了两个压电常数d211和d222。此外，还建立了含压电材料的有限元算式，进行了实验测量。最后，通过比较解析解(包括考虑了d222参数的理论值和没有考虑d222参数的理论值)，实验值以及有限元计算结果，发现它们吻合得很好，而且考虑d222是十分必要的。     

不同边界条件正交各向异性中厚板的振动与稳定分析

本文采用高阶剪切变形理论对正交各向异性中厚矩形板进行振动与稳定分析,数值计算采用样条有限点法,得出了六种不同边界条件矩形板的自振频率和屈曲载荷,并与相应的经典板理论的结果进行比较.结果说明横向剪切变形对复合材料层合板的影响与板的各向异性程度、板的宽厚比(b/h)、层合板的层数和板的支承条件有关,它随着层合板各向异性程度的增加而增加,随着层合板宽厚比的增加而逐渐消失.     

热环境下贴压电层的功能梯度材料板的自由振动和动力响应

基于Reddy高阶剪切变形理论和广义Kármán型方程,用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解,分析中考虑了材料热物参数对温度变化的依赖性,讨论了环境温度和控制电压对固有频率及动力响应的影响。     

层合板六参量几何非线性高阶剪切理论

提出了层合板六参量的高阶剪切变形理论的位移场假定,以考虑在大变形条件下层合板法向变形和厚度的变化。同时对ｖｏｎ Ｋａｒｍａｎ应变位移简化假设进行补充修改,考虑某些有限变形条件下被忽略小量的影响,建立了对应于该文六参量模型和更加适凳大变形分析的层合板几何非线性关系,平衡方程和边界条件。利用该文模型分析了橡胶复合材料简支板的大变形弯曲行为,并对比Ｒｅｄｄｙ五参量几何非线性简单高阶剪切变形层合理论解和弹     

基于高阶剪切变形理论的四边形求积元板单元及其应用

近年来由各类新型复合材料或功能梯度材料构成的板结构在工程领域得到了广泛应用,其显著特点是材料性能沿板厚变化.为合理考虑横向剪切应变,许多学者基于Reddy高阶剪切变形理论,构建了不同的有限元单元对该类板结构进行分析,但其中满足$C^{1}$连续条件的单元相对较少.本文基于Reddy高阶剪切变形理论,采用求积元方法,建立了$C^{1}$连续的四边形板单元.利用该单元对均质材料、复合材料、功能梯度材料构成的等厚度矩形板、变厚度矩形板及等厚度斜板的线弹性弯曲和自由振动问题进行了计算分析,并与现有文献中的相应计算结果进行了对比.研究表明:基于高阶剪切变形理论的四边形求积元板单元具有较高的计算效率和良好的适应性,文中各类材料构成的等变厚度矩形板及等厚度斜板均只需1个单元即可得到理想的计算结果.对于等/变厚度矩形板,可仅使用9$\times$9个积分点,而对于等厚度斜板,随着斜角的增大,所需积分点的数目逐渐增多至15$\times $15.该四边形求积元板单元可进一步用于新型复合材料板的非线性分析.      

计入横向剪切变形时层合板位移差分解法

在考虑横向剪切变形对层合板弹性解的影响时，本文提出一种数值计算方法。由边界条件给出边界结点位移的表达式，根据薄板的经典理论和一阶横向剪切变形理论导出位移增量所满足的平衡微分方程，引用经典理论计算的横向剪力修正了荷载列阵。致使在较粗的网格划分时、宽广的层合板长厚比范围内，仍能得到与解析解颇为一致的数值解。     

压电智能复合材料层合梁的力电耦合模型及层间应力分析

由于非凡的物理性能,石墨烯纳米片(GPL)被认为是最有吸引力的复合材料增强材料之一.GPL增强材料可以明显提高聚偏氟乙烯(PVDF)压电性能和力学性能.在力电载荷作用下,对含均匀石墨烯薄片增强(GSR)智能压电复合材料层合梁层间应力预测至关重要.若对受到力电耦合作用且层与层之间材料性能突变的压电层合梁层间剪切变形预测有误,则其层间应力过大可能导致层间失效.因此,论文提出一种适于分析此类问题且满足层与层之间相容性条件的有效力电耦合模型,用于含GSR致动器的复合材料层合梁层间应力分析.应用Reissner混合变分原理(RMVT),可以提高考虑力电耦合效应的横向剪应力预测精度.三维(3D)弹性理论和所选模型计算结果将用于评估所提梁模型性能.此外,还从力电载荷、压电层厚度、石墨烯体积分数和长厚比等方面对含GSR致动器复合材料层合梁力学响应特性进行了系统的研究.     

板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点，从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同，层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭，并在层间结合面处发生强不连续，呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用，不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出，现有各种考虑剪切变形影响的计算模型虽然有了很大的发展，但在全面和准确性上仍然存在一定的不足，难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型，同时可适用于各种薄板与厚板的分析，对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化，与三维弹性理论的标准解高度吻合。数值算例进一步表明，随着层间纤维走向的变化，板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此，本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers

Free vibration of functionally graded(FG) annular sector plates embedded with two piezoelectric layers is studied with a generalized differential quadrature(GDQ)method. Based on the first-order shear deformation(FSD) plate theory and Hamilton's principle with parameters satisfying Maxwell's electrostatics equation in the piezoelectric layers, governing equations of motion are developed. Both open and closed circuit(shortly connected) boundary conditions on the piezoelectric surfaces, which are respective conditions for sensors and actuators, are accounted for. It is observed that the open circuit condition gives higher natural frequencies than a shortly connected condition. For the simulation of the potential electric function in piezoelectric layers, a sinusoidal function in the transverse direction is considered. It is assumed that properties of the FG material(FGM) change continuously through the thickness according to a power distribution law.The fast rate convergence and accuracy of the GDQ method with a small number of grid points are demonstrated through some numerical examples. With various combinations of free, clamped, and simply supported boundary conditions, the effects of the thicknesses of piezoelectric layers and host plate, power law index of FGMs, and plate geometrical parameters(e.g., angle and radii of annular sector) on the in-plane and out-of-plane natural frequencies for different FG and piezoelectric materials are also studied. Results can be used to predict the behaviors of FG and piezoelectric materials in mechanical systems.     

A theoretical analysis of piezoelectric/composite anisotropic laminate with larger-amplitude deflection effect,Part I: Fundamental equations

Considering the effects of both the different material properties of composite layers and the poling directions of piezoelectric layers, we utilized the assumption of the simple-higher-order shear deformation theory to model and analyze the laminated composite plate integrated with the random poled piezoelectric layers. Further, the generalized Hamilton’s variation principle for electro-elasticity was employed to deduce the fundamental equations of piezoelectric/composite anisotropic laminate, i.e. the governing equations and boundary conditions. For the special requirement of the larger-amplitude deflection of smart structures, the Von Karman strains were used to account for the geometric nonlinear effect of the practical larger-amplitude deflection on the electro-elastic behavior of smart composite structures. Moreover, the sensor equations were also carried out with considering the large-amplitude deflection effect of smart composite structures.     

A new simple third-order shear deformation theory of plates

An improved simple third-order shear deformation theory for the analysis of shear flexible plates is presented in this paper. This new plate theory is composed of three parts: the simple third-order kinematics of displacements reduced from the higher-order displacement field derived previously by the author; a system of 10th-order differential equilibrium equations in terms of the three generalized displacements of bending plates; five boundary conditions at each edge of plate boundaries. Although the resulting displacement field is the same as that proposed by Murthy, the variational consistent governing equations and the associated proper boundary conditions are derived and identified in this work for the first time in the literature. The applications and accuracy of the present shear deformation theory of plates are demonstrated by analytically solving the differential governing equations of a twisting plate, a bending beam and two bending plates to which the 3-D elasticity solutions are available, and excellent agreements are achieved even for the torsion of a plate with square cross-section as well the local effects of stresses at plate boundaries can be characterized accurately. These analytical solutions clearly show that the simple third-order shear deformation theory developed in this work indeed gives better results than the first-order shear deformation theories and other simple higher-order shear deformation theories, since the present third-order shear flexible theory is based on a more rigorous kinematics of displacements and consists of not only a system of variational consistent differential equations, but also a group of consistent boundary conditions associated with the differential equations. The present simple third-order shear deformation theory can easily be applied to the static and dynamic finite element analysis of laminated plates just like the applications of other popular shear flexible plate theories, and improved results could be obtained from the present simple third-order shear deformable theories of plates.     

Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection

Considering mass and stiffness of piezoelectric layers and damage effects of composite layers, nonlinear dynamic equations of damaged piezoelectric smart laminated plates are derived. The derivation is based on the Hamilton＇s principle, the higher- order shear deformation plate theory, von Karman type geometrically nonlinear straindisplacement relations, and the strain energy equivalence theory. A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection with a closed control loop. Simply supported rectangular laminated plates with immovable edges are used in numerical computation. Influence of the piezoelectric layers＇ location on the vibration control is in- vestigated. In addition, effects of the degree and location of damage on the sensor output voltage are discussed. A method for damage detection is introduced.     

Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings

A postbuckling analysis is presented for a simply supported, shear deformable functionally graded plate with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads. The temperature field considered is assumed to be of uniform distribution over the plate surface and through the plate thickness and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A two step perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FGM plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, volume fraction distribution, applied voltage, the character of in-plane boundary conditions, as well as initial geometric imperfections are studied.     

Analytical solution for the cylindrical bending vibration of piezoelectric composite plates

An analytical solution for the cylindrical bending vibrations of linear piezoelectric laminated plates is obtained by extending the Stroh formalism to the generalized plane strain vibrations of piezoelectric materials. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thickness and width. Fourier basis functions for the mechanical displacements and electric potential that identically satisfy the equations of motion and the charge equation of electrostatics are used to solve boundary value problems via the superposition principle. The coefficients in the infinite series solution are determined from the boundary conditions at the edges and continuity conditions at the interfaces between laminae, which are satisfied in the sense of Fourier series. The formulation admits different boundary conditions at the edges of the laminated piezoelectric composite plate. Results for laminated elastic plates with either distributed or segmented piezoelectric actuators are presented for different sets of boundary conditions at the edges.     

复合材料层合板壳非线性力学的研究进展

复合材料层合板壳是由多种组分材料组合而成.与单一材料的板壳结构相比,它无明确的材料主方向,各层间材料间断和不连续,具有明显的几何非线性和材料非线性等新的特点.其失效模式也远比单一材料的情况复杂,具有如基体开裂、脱胶、分层、分层裂纹偏转、多分层以及分层传播等多种模式.各国学者基于不同的考虑,提出了多种方法研究复合材料层合板壳的失效.首先,在简要介绍了层合板壳线性力学基本理论的基础上,重点回顾了层合板壳结构非线性力学几种基本理论发展的过程,主要阐述了经典大挠度非线性理论、一阶剪切变形理论、高阶剪切变形理论、锯齿理论、广义分层理论的理论体系及基本公式,并对几种理论之间的联系和差异进行了总结;其次,介绍了当前层合结构非线性领域的研究进展,综述了典型复合材料板壳结构的失效机理及优化设计、复合材料板壳结构在复杂环境下的破坏机理、复合材料板壳结构的物理非线性、含脱层纤维增强复合材料板壳结构的破坏机理等各研究热点的最新研究成果;最后,对该领域未来的研究方向进行了展望.