夹在两个柔性层中薄膜的正弦模态界面屈曲分析

当一层比较硬的薄膜被封闭在上下两层柔性层中,组成了三层材料结构.在压应力的作用下,这层薄膜可能会发生屈曲失稳.由可弯曲电路封装在柔性层中组成的三层材料系统能进一步提高其弯曲性能的事实得到启发,不同于广泛研究的双层材料结构表面屈曲问题,从理论上分析三层材料结构在压应力作用下的刚硬薄膜的正弦模态屈曲问题.柔性层和刚硬薄膜材料假定皆为各向同性.由于薄膜厚度远远小于柔性层厚度,柔性层在理论分析中认为是无穷厚的.刚硬薄膜可以用非线性薄板模拟,其变形为小应变但是允许有限转动,用于描述屈曲时的状态.利用线性扰动分析,得到了屈曲临界薄膜应力,波数和平衡状态下的波幅的解析表达式.结果表明,针对不同的刚硬薄膜和柔性层的弹性模量,当刚硬薄膜相对于上下柔性层越硬,就越容易发生界面屈曲.     

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。     

多亚层柔性节点模型及其在双材料4ENF试件界面分析中的应用

提出了多亚层柔性节点模型用于分析双材料裂纹尖端的应力和变形。该模型考虑了胶层的变形,各亚层视为独立的剪切变形梁,采用两个界面柔度系数考虑界面应力对各亚层界面变形的影响,界面变形包括双材料界面和胶层的变形。通过对FRP-混凝土末端切口四点弯试件(Four-point bending end-notched flexure specimen,简称4ENF)进行界面分析,并与其他模型和有限元分析对比表明:刚性节点模型忽略了裂纹尖端的应力和变形集中,只能粗略地估计构件的整体变形和界面应力;半刚性节点容许裂纹尖端的转动,对裂纹尖端的变形估计优于刚性节点模型,但精度依然不高;多亚层柔性节点模型反映了裂纹尖端的应力和变形集中,与数值分析结果吻合很好,该研究对进行双材料结构的工程设计具有理论指导和参考价值。     

基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性梁进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性梁刚-柔耦合动力学方程.从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程.通过引入准静态概念,把其结构动力学方程转化为准静态方程.对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项.并对此非惯性系下作大范围运动柔性梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.     

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.     

复合材料的多层、夹层和加筋圆柱曲板的稳定和振动

本文在文献〔1,2〕的基础上,考虑了沿壳体厚度方向的剪切变形,探讨周边简支的纤维增强复合材料的正交各向异性的多层、夹层和加筋矩形圆柱曲板(与圆柱壳),在轴压、侧压和剪切(扭矩)作用下的临界载荷和横向振动固有频率的计算问题。在编成计算程序后,用一些算例将用文献〔1〕中的扁壳方程(Donnell壳体理论) 和文献〔3〕中的非扁壳方程(Love的壳体一阶近似理论) 算得的结果作了比较;将轴压下轴对称失稳和非轴对称失稳的临界载荷作了比较;将在轴压和侧压作用下失稳时外加筋曲板和内加筋曲板的临界载荷作了比较;将有薄膜力N_x~0和N_y~0同时和分别作用时与没有薄膜力作用时的横向振动固有频率作了比较;将按壳体的剪切变形理论和经典理论算得的临界载荷作了比较;将铺层情况对临界载荷的影响作了比较。     

刚-柔-热耦合多体系统的动力学分析

本文研究了柔性多体系统刚-柔-热耦合动力学特性。以哈勃天文望远镜(HST)为研究对象,基于柔性多体系统动力学理论,考虑了柔性附件弹性变形引起的热辐射边界条件的变化,建立了中心刚体和太阳能毯柔性附件多体系统的刚-柔-热耦合的动力学方程。通过对热载荷作用下哈勃天文望远镜多体系统的数值仿真研究了热辐射角、阻尼系数、比热容、支撑梁、太阳能毯之间的轴向力等参数对于柔性附件热颤振的影响;并提出增加结构阻尼、减小支撑梁和太阳能毯之间的轴向力、选择阻尼系数和比热容均较大的支撑梁材料、采用柔度较大的主体桶材料等改善热颤振的措施。     

一种新型介电弹性体仿生可调焦透镜的变焦分析

介电弹性体 (dielectric elastomer) 是电活性聚合物智能材料的一种,在外加电场作用下,可产生多种形式的响应.在驱动柔性透镜的变焦方面,相对于传统的机械操控变焦方法 显示出独特的优势.针对一款在电压激励下可高效调节焦距的介电弹性体仿人眼变焦透镜,该透镜由上下两层介电弹性薄膜和固定框架构成,并在封闭腔内充入盐水,上层薄膜涂覆环形柔性电极.在电压激励下,上层膜发生变形,由于盐水的体积保持恒定,引 起下层膜随之变形,使得透镜的焦距发生改变.采用 neo-Hookean 模型,利用变分原理导出了该透镜的控制方程、边界条件和连 续条件.利用打靶法求解了该非线性问题并高效地处理了非线性问题的界面连续条件. 理论分析结果与实验结果相吻合. 利用此模型开展了广泛的参数分析,研究表明,透镜的几何形状、初始焦距、介电弹性体薄膜的预拉伸率、涂覆的电极面积、材料的剪切模量等对透镜焦距的调节性能都有重要的影响.所建立的理论分析模型可为柔性仿生透镜的设计和参数优化提供有效的分析方法.      

温度场下岛-桥结构屈曲薄膜的动力学分析

基于岛-桥结构的柔性电子器件已被用于健康监测和皮肤电子等领域。但是柔性电子器件在工作中极易受工作温度变化等激励产生振动,进而影响器件的灵敏度与可靠性。因此本文研究在温度场作用下岛-桥结构屈曲薄膜的动力学问题。首先,基于Euler-Bernoulli梁理论,建立温度场作用下岛-桥结构屈曲薄膜的动力学控制方程。其次,通过引入新变量,将原动力学方程引入Hamilton体系中,得到相应的Hamilton正则方程。随后,采用辛Runge-Kutta方法求解该Hamilton正则方程,并与经典Runge-Kutta方法对比,数值结果显示了辛算法在求解非线性动力学方程时高精度、高数值稳定性的优势,进一步讨论了温度变化量、预应变、阻尼系数等对屈曲薄膜动力学响应的影响。本文研究为柔性电子器件动力学设计提供了理论参考。     

柔性梁刚柔耦合碰撞动力学及变形传播研究

运用柔性多体系统刚柔耦合动力学理论,研究了作大范围回转运动柔性梁的碰撞动力学问题.考虑柔性梁的横向变形,以及横向变形引起的纵向缩短项即非线性耦合变形项.采用基于Hertz接触理论及非线性阻尼理论的非线性弹簧阻尼模型来求解碰撞过程中产生的碰撞力,运用第二类拉格朗日方程建立了系统的刚柔耦合碰撞动力学方程.编制仿真软件进行动力学仿真计算,得到了碰撞力和系统动力学响应,对比分析了不同动力学模型对系统动力学响应的影响.同时研究了碰撞导致的柔性梁横向变形传播的波动特性.     

功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论，导出了热/机载荷作用下，位移形式的功能梯度 中厚圆/环板轴对称弯曲问题的控制方程，获得了问题的位移和内力的一般解析解. 作为特 例，分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板，给出了它们的 解，并分析了热/机载荷作用下解的形态，讨论了横向剪切变形、材料梯度常数和边界条件， 对板的轴对称弯曲行为的影响.     

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.     

脱层梁屈曲的高阶剪切理论

脱层的存在将会大大降低层合结构的屈曲载荷。该文将含任意位置脱层的两端固支梁分成多段子层,用厚度的三次多项式模拟脱层梁屈曲时子层的轴向位移,利用变分原理和欧拉方程导出了脱层梁的屈曲方程和定解条件,并用状态空间方法进行求解。通过与一阶剪切理论和经典理论的比较,指出了它们各自的适用范围;考虑了脱层梁三种不同的屈曲模态。分析了脱层长度、深度、位置和材料的铺层方向对脱层梁屈曲载荷的影响;最后给出了多处简单脱层的屈曲分析。     

基于物理中面FGM中厚板自由振动的有限元分析

基于物理中面和一阶剪切变形板理论,研究了不同边界条件下功能梯度材料(FGM)中厚板的自由振动问题．假设功能梯度板的材料性质沿厚度方向按幂函数规律连续变化．根据哈密顿原理建立了FGM板有限元形式的自由振动方程,利用MATLAB软件编写程序进行了计算．通过数值算例,讨论了不同边界条件下FGM中厚板的无量纲频率随材料梯度指数和厚宽比的变化情况,并与经典板理论下的频率进行了比较．     

Mechanical buckling and free vibration of thick functionally graded plates resting on elastic foundation using the higher order B-spline finite strip method

In this study, the mechanical buckling and free vibration of thick rectangular plates made of functionally graded materials (FGMs) resting on elastic foundation subjected to in-plane loading is considered. The third order shear deformation theory (TSDT) is employed to derive the governing equations. It is assumed that the material properties of FGM plates vary smoothly by distribution of power law across the plate thickness. The elastic foundation is modeled by the Winkler and two-parameter Pasternak type of elastic foundation. Based on the spline finite strip method, the fundamental equations for functionally graded plates are obtained by discretizing the plate into some finite strips. The results are achieved by the minimization of the total potential energy and solving the corresponding eigenvalue problem. The governing equations are solved for FGM plates buckling analysis and free vibration, separately. In addition, numerical results for FGM plates with different boundary conditions have been verified by comparing to the analytical solutions in the literature. Furthermore, the effects of different values of the foundation stiffness parameters on the response of the FGM plates are determined and discussed.     

Flexoelectric vibration analysis of nanocomposite sandwich plates

Abstract

In the present study, free vibration of sandwich flexoelectric plates resting on Pasternak foundation is investigated. The top and bottom layers are under applied voltage based on flexoelectricity considerations and core is a nanocomposite plate where reinforced by carbon nanotubes. Based on first-order shear deformation theory, flexoelectricity considerations and Hamilton’s principle, the governing equations are derived for the first time. Navier’s method is used to solve the governing equations analytically in the case of simply supported sandwich plate. Finally, the effects of different parameters are discussed in details. It is found when thickness of flexoelectric face sheets increase, the frequency of nano-sandwich plate decrease. The results of this study can be useful in design and manufacturing of flexoelectric systems as sensor and actuator.     

基于修正偶应力和高阶剪切变形理论的变截面微梁的自由振动

基于修正偶应力和高阶剪切理论建立了仅含有一个尺度参数的Reddy变截面微梁的自由振动模型,研究了变截面微梁自由振动问题的尺度效应和横向剪切变形对自振频率计算的影响。基于哈密顿原理推导了动力学方程与边界条件,并采用微分求积法求解了各种边界条件下的自振频率。算例结果表明,基于偶应力理论预测的变截面微梁的自振频率均大于经典梁理论的预测结果,即捕捉到了尺度效应。另外,梁的几何尺寸与尺度参数越接近,尺度效应就越明显,而梁的长细比越小,横向剪切变形对自振频率的影响就越明显。     

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams.     

Stability and vibration of shear deformable plates––first order and higher order analyses

This work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions. The Reissener–Mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of Reddy have been applied to the plate’s analysis. The governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the vibration and stability analysis of compressed members, which provides for the derivation of the exact dynamic stiffness matrix including the effect of in-plane and inertia forces. The large number of numerical examples demonstrates the applicability and versatility of the present method. The results obtained by both shear deformation theories are compared with those obtained by the classical thin plate’s theory and with published results. Many new results are given too.     

剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。