复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥壳非线性稳定性的基本方程中增加横向转动惯量项并引入三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

径向冲击下复合材料层合圆柱壳的动力屈曲

采用Lagrange方程导出包含横向剪切变形和转动惯量的复合材料层合圆柱壳径向脉冲屈曲控制方程;用四阶Runge-Kuta方法对方程数值求解,寻找占优屈曲模态数及对应于允许初缺陷放大值时的临界冲击速度;通过计算碳/环氧材料角铺设层合圆柱壳,讨论了横向剪切变形、壳体几何尺寸、铺层角度等因素对层合圆柱壳动力屈曲的影响.     

复合材料层合开顶扁球壳在集中冲击下的非线性动力屈曲

研究了具有刚性中心的复合材料层合开顶扁球壳在中心集中冲击载荷作用下的非线性动力屈曲问题。通过增加横向转动惯量项得到中心集中冲击下复合材料层合开顶扁球壳非线性稳定性的控制方程，采用Galerkin方法得到以刚性中心位移表达的冲击动力响应方程，并用Runge-Kutta方法进行数值求解，应用Budiansky-Roth准则（简称B—R准则）确定冲击屈曲的临界荷载；讨论了壳体几何尺寸对复合材料层合开顶扁球壳冲击屈曲的影响。     

玻璃/环氧圆柱壳的冲击响应与稳定性分析

应用Love的壳体理论得到了非轴对称变形的复合材料圆柱壳的控制方程。对扰动状态的非轴对称变形,位移函数采用复Fourier级数形式,得到了Mathieu形的扰动方程,由此给出了静态临界载荷和固有频率。本文中对层合壳在轴向冲击载荷下的动态稳定性研究考虑了几何非线性,这是以往在该问题的研究中所未涉及的问题。研究表明,考虑几何非线性得到的临界载荷较线性几何关系计算结果要高5 %左右。因此,考虑几何非线性是必要的。      

纤维增强复合材料迭层圆柱壳的几何非线性分析

本文从非线性弹性理论出发,在小应变、中等小转动的前提下,全面考虑了变形对于平衡方程的影响,导出了和传统理论不同的壳体非线性理论;并用摄动法和伽略金法分别求解了四边不可动固支正交各向异性复合材料迭层园桂壳块以及考虑横向剪切的四边可动简支园桂形扁壳的非线性弯曲问题。计算表明:变形较大时,变形对所有平衡方程的影响都是值得注意的。      

一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元

基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。      

变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

层合中厚浅球壳受撞击时的非线性动力响应分析

建立了正交铺设层合中厚浅球壳在任一位置受撞击载荷作用的非线性运动微分方程,根据Hertzian定律,考虑撞击物与浅球壳之间的弹性接触效应,确定了壳体在其接触处所承受的冲击力。对此非线性动力问题,采用有限差分法与时间增量法求解。算例中,讨论了撞击物的速度、壳体中曲面曲率半径及接触点位置对壳体所受冲击载荷及其位移响应的影响。     

绝对节点坐标法中压电层合板的大变形研究

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。     

热载荷下轴对称回转复合材料层合壳体的边界效应

本文采用有限单元法研究轴对称回转复合材料层合壳体在热荷载作用下壳体内的温度场和热应力场的分布, 并以算例讨论了温度场的分布、铺层次序、壳厚对层合壳体热应力(包括层间应力)的影响。      

Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells

A thermal buckling analysis is presented for laminated cylindrical shells with surface mounted piezoelectric actuators under combined action of thermal and electrical loads. Derivations of the equations are based on the classical laminated shell theory, using the Sanders nonlinear kinematic relations. The analysis uses the Galerkin method to obtain closed form solutions for the buckling loads of shallow and nonshallow piezolaminated cylindrical shells. Temperature dependency of material properties is taken into account. Illustrative examples are presented to verify the accuracy of the proposed formulation. The effects of the various design parameters on thermal buckling loads are investigated.     

Nonlinear dynamic stability of laminated composite shells integrated with piezoelectric layers in thermal environment

This paper reports the nonlinear dynamic stability characteristics of laminated composite cylindrical (CYL) and spherical (SPH) shells integrated with piezoelectric layers using the finite element method. The shells are subjected to a thermal environment in addition to the in-plane periodic load and the electric load. The theoretical formulation considers Sanders?? approximation for doubly curved shells, and von Kármán type nonlinear strains are incorporated into the first-order shear deformation theory (FSDT). The formulation includes the effects of transverse shear, in-plane and rotatory inertia. The in-plane periodic load is taken as the parametric excitation in the governing equation. The nonlinear matrix amplitude equation is obtained by employing Galerkin??s method. The correctness of the formulation is established by comparing the authors?? results with those available in the published literature. Detailed parametric studies are carried out to investigate the effects of different parameters on the dynamic stability characteristics of laminated composite shells.     

粘弹性圆柱壳在轴向恒压下的动力稳定性

基于Timoshenko-Mindlin假设,得到考虑粘弹性的各向同性圆柱壳及纤维增强正交铺设层合圆柱壳在轴向恒压下的动力学方程。文中对两端简支的圆柱壳进行了分析,依Laplace变换,导出动力稳定的特征方程,由Routh-Hurwitz判据建立动力稳定性条件,对两类圆柱壳讨论了横向剪切变形的影响。     

Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings

Based on the first-order shear deformation theory (FSDT), approximate solution for FG (functionally graded) laminated piezoelectric cylindrical shells under thermal shock and moving mechanical loads is given utilizing Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the functionally graded layer are acted as distributed sensor and actuator to control dynamic characteristics of the FG laminated cylindrical shells. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of FG laminated cylindrical shells. Constant-gain negative velocity feedback approach is used for active vibration control. The active vibration control to a single moving concentrated loading, thermal shock loading and a continuous stream of moving concentrated loadings is, respectively, investigated. Results indicate that the control gain and velocity of moving loadings have significant effects on the dynamic response and resonance of the system.     

Computational approach of piezoelectric shells by the GDQ method

A piezoelectric laminated cylindrical shell with shear rotations effect under the electromechanical loads and four sides simply supported boundary condition was studied by using the two-dimensional generalized differential quadrature (GDQ) computational method. The typical hybrid composite shells with 3-layered cross-ply [90°/0°/90°] graphite–epoxy laminate and bounded PVDF layers are considered under the sinusoidal pressure loads and electric potentials on the shell. The governing partial differential equation with first-order shear deformation theory in terms of mid-surface displacements and shear rotations can be expressed in series equations by the GDQ formulation. Thus we obtain the GDQ numerical solutions of non-dimensional displacement and stresses at center position of laminated piezoelectric shells. Displacement is generally affected by the thickness of laminated piezoelectric shells under the action of mechanical load. Stresses are generally affected by the thickness and the length of laminated piezoelectric shells under the actions of mechanical load and electric potential.     

基于有限元法的周期压电智能梁滤波特性分析

周期结构具有通频和禁频特性,使其在动态载荷的滤波器、具有主动控制功能的结构研究中得到了重要应用。基于Timoshenko梁理论,考虑基梁和压电片的转动惯量和剪切效应,采用有限元法和传递矩阵法推导了波在周期性地粘贴压电片的Timoshenko梁中的传播模型,分析了几何尺寸和材料特性对其频带性质的影响,并与Bernoulli-Euler梁理论得到的结果进行了对比。研究表明,当基梁与压电层厚度比达到40时,禁带带宽减小了54%,因此对于周期结构中的深梁,应舍弃Bernoulli-Euler梁理论而采用Timoshenko梁理论建立的模型;对于不同尺寸和材料特性的压电周期结构,频带性质会有很大不同,可以通过调整结构的参数来改变其频带性质,从而改变波动在结构中的传播特性。     

Postbuckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical shell with piezoelectric actuators subjected to lateral or hydrostatic pressure combined with electric loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction 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 theory with a von Kármán–Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling is extended to the case of FGM hybrid laminated cylindrical shells of finite length. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of pressure-loaded, perfect and imperfect, FGM cylindrical shells with fully covered piezoelectric actuators under different sets of thermal and electric loading conditions. The results reveal that temperature dependency, temperature change and volume fraction distribution have a significant effect on the buckling pressure and postbuckling behavior of FGM hybrid cylindrical shells. In contrast, the control voltage only has a very small effect on the buckling pressure and postbuckling behavior of FGM hybrid cylindrical shells.     

Active control of functionally graded laminated cylindrical shells

An analytical method on active vibration control of smart FG laminated cylindrical shells with thin piezoelectric layers is presented based on Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the smart FG laminated cylindrical shell act as distributed sensor and actuator, which are used to control vibration of the smart FG laminated cylindrical shell under thermal and mechanical loads. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of the smart FG laminated cylindrical shell with thin piezoelectric layers. Constant-gain negative velocity feedback approach is used for active vibration control with the structures subjected to impact, step and harmonic excitations. The influences of different piezoelectric materials (PZT-4, BaTiO₃ and PZT-5A) and various loading forms on the active vibration control are described in the numerical results.     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. The non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths of FRC laminated cylindrical shells.