压电复合材料层合板的混沌动力学研究

压电复合材料具有独特的机电耦合性、比强度高、比刚度大和抗疲劳性能好等优点,越来越广泛地被应用于航空航天等工程领域中。根据Reddy的三阶剪切变形层合板理论,研究了受面内横向外激励力、面内纵向参数激励和面外参数激励以及压电参数激励联合作用下四边简支矩形复合材料层合板在1:2:4内共振情况下的六维平均方程。考虑平均方程存在一对双零特征值和两对纯虚特征值的情况,利用规范形理论进行化简,得到与原方程拓扑等价的最简规范形,然后在此基础上利用能量相位法从理论上分析得到系统会产生同宿的多脉冲跳跃现象;同时,基于平均方程,通过数值仿真,发现系统会产生混沌运动,具有跳跃现象。     

冰雹冲击复合材料层合板失效模式分析与数值模拟

针对复合材料层合板结构,建立了冰雹冲击复合材料层合板的有限元模型,在充分考虑冲击过程中冰雹的流体特性下,给出了冰雹和复合材料层合板的材料模型和损伤准则,利用显式有限元分析工具LS-DYNA研究了不同冰雹冲击速度下复合材料层合板的临界破坏速度和破坏形式。结果表明,文中给出的冰雹、复合材料层合板的材料模型和损伤准则能够合理地再现冰雹冲击复合材料板的过程;复合材料层合板(AS4/8552)在冰雹高速冲击下首先发生的是基体开裂,当冰雹速度到达125m/s时,层合板上表面纤维发生断裂,但在整个冰雹冲击过程中层合板没有发生压缩失效     

冰雹冲击复合材料层合板仿真研究

针对飞机空中受冰雹撞击会造成复合材料结构分层或损伤问题,用有限元软件ANSYS/LS-DYNA对复合材料的抗冰雹冲击行为进行分析。采用光滑质点流体动力学方法(Smooth Particle Hydrodynamic,SPH)模拟冰雹冲击刚性平板的高度非线性力学行为。通过对比模拟结果与实验数据知两者吻合较好,验证冰雹模型的准确性。将该模型引入冰雹冲击复合材料结构模型,采用粘聚区模型(Cohesive Zone Model,CZM)预测复合材料结构的分层损伤,获得合理计算结果;并分析冰雹撞击层合板损伤情况及不同参数对层合板损伤影响。     

复合材料层合板非线性热屈曲分析

本文基于高阶变形理论和修正型Hahn-Tsai非线性本构模型,提出一种复合材料层合板非线性热屈曲分析方法.针对四边简支反对称角铺设复合材料层合板,导出了非线性热屈曲临界温度封闭解.数值结果表明:材料非线性能显著降低层合板临界温度.      

基于二维等效FE-SEA混合方法的复合材料层合板传声损失分析

为研究湍流脉动噪声激励下复合材料层合板的传声特性,首先基于一般层合板理论将复合材料层合板等效为单层各向异性板,进而采用FE-SEA混合方法研究其传声损失。同时开展复合材料层合板传声损失试验,并将FE-SEA结果和统计能量法(SEA)结果以及实验值进行对比分析。研究结果表明:FE-SEA结果和实验值整体上分布趋势一致,而且误差也相对较小,其中3 000 Hz～10 000 Hz误差在2 dB以内,但由于刚度等效导致2 000 Hz附近结果误差相对较大。相较于SEA方法, FE-SEA混合方法综合考虑了复合材料层合板边界条件和详细得几何特征,不仅可以准确地计算复合材料层合板的固有特性,而且使得传声损失结果在全频带内与试验值吻合得更好。因此建立的二维等效FE-SEA混合模型可以准确预示复合材料层合板在湍流脉动噪声激励下的传声损失。     

含分层损伤复合材料层合板非线性动力稳定性

采用Reddy 的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型, 推导了考虑几何非线性和阻尼效应的Methieu 方程, 给出了该方程的解析解表达式; 研究了参数振动解的稳定性; 然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响; 研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响, 以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知, 随着复合材料层合板分层损伤的扩大, 其动力稳定性能逐渐减弱, 特别是损伤接近层合板的中面时, 分层损伤对其动力稳定性能的影响最大。      

对称层合板复合材料的屈曲变形解析

提出了如何利用2 元多项式位移函数来分析层合板复合材料的屈曲问题。在解析中同时 考虑到层合板的面外剪切变形。解析表明屈曲载荷在多项式项数大于20 以上时趋于稳定, 可得到 高精度的解。本文并对对称角铺设层合板进行了系统地数值解析, 明确了在各种边界拘束条件下 材料的工程弹性系数, 层合板长宽比, 铺层数, 层合角对屈曲载荷的影响, 从而以达到优化设计。同 时, 验证了本解析法对任意边界条件下的层合板的屈曲解析是非常有效的。      

基于NASTRAN的复合材料层合板层间应力分析

基于MSC.PATRAN/NASTRAN软件,采用一种准三维混合有限元模型,计算了复合材料层合板的层间应力,得到了层间应力对层合板面内应力分布的影响规律,为合理设计层合板,优化层间剪切强度,扩大层合板的应用范围,提供了分析手段和理论依据;这种准三维混合模型的有限元计算方法,提高了复合材料层合板的分析效率和分析精度,也为其他复合材料结构分析提供了新的分析思路和途径.     

反对称角铺设复合材料层合板热后屈曲和模态跃迁分析

为有效分析反对称角铺设复合材料层压板热后屈曲性能,由渐近修正几何非线性理论推导双耦合四阶偏微分方程（即协调方程和动态控制方程）,通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程,从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题,研究了模态跃迁前后不同复杂程度的后屈曲模式。通过四边简支、面内不可移边界下复合层合板的数值计算表明：该解析法与有限元方法在主后屈曲区域的计算结果有很好的吻合性;有限元方法在解靠近二次分岔点时失去收敛性,而解析法仍具有深入探索后屈曲区域和准确捕捉模态跃迁现象的能力。     

复合材料悬臂板系统的多脉冲同宿轨道

针对复合材料悬臂板系统的非线性动力学行为进行了分析。模型考虑高阶横向剪切效应、几何大变形和横向阻尼的影响,基于Reddy的高阶剪切变形理von Karman的大变形理论,利用Hamilton原理,Galerkin离散和多尺度法得到系统横向位移的平均方程。应用广义Melnikov方法研究了复合材料悬臂板的非线性混沌动力学行为。分析了在共振带附近,复合材料悬臂板系统存在的Shilnikov类型多脉冲跳跃同宿轨道。最后结合数值模拟,进一步揭示系统存在多脉冲跳跃现象。     

大变形复合材料薄板多体系统动力学建模

本文对大变形复合材料薄板的多体系统动力学建模方法进行研究。基于Kirchhoff假设,法线与中面保持垂直,从格林应变的表达式出发,建立了面内应变和曲率与绝对位置坐标和斜率的关系,在此基础上推导了广义弹性力阵和弹性力阵对广义坐标的导数阵,用绝对节点坐标方法建立了大变形复合材料薄板多体系统的动力学方程,用广义法和和牛顿迭代法求解微分-代数混合方程。对外载荷作用下的复合材料薄板进行数值仿真,通过与ANSYS的仿真结果进行对比,验证了本文建模方法的准确性和快速收敛性。最后,将建模方法应用于复合材料太阳帆板展开机构的数值仿真,分析了不同铺层情况下驱动力和约束力的振动特性。     

Dynamic investigation of laminated composite beams with shear and rotary inertia effect subjected to the moving oscillators using FEM

An algorithm based on the finite element method (FEM) has been developed to study the dynamic response of composite laminated beams subjected to the moving oscillator. The first order shear deformation theory (FSDT) is assumed for the beam model. The algorithm accounts for the complete dynamic interaction between the components of system. The proposed method can also be applied to the general moving mass and the simplified moving force problems. After deriving the governing equations of motion of beam and oscillator, the corresponding equations of motion are integrated by applying the Newmark’s time integration procedures to obtain the system responses in each time step. The numerical results of free vibration and moving force problems analysis of isotropic and composite laminated beams are presented and, whenever possible, compared to the available analytical solution and other numerical results in order to demonstrate the accuracy of the present method. In addition, parametric analysis is carried out over a wide range of velocities and mass, frequency and damping ratios of system components.     

Thermal buckling behavior of composite laminated plates

Thermal buckling behavior of composite laminated plates was studied by making the use of finite element method. The thermal buckling mode shapes of cross-ply and angle-ply laminates with various E₁/E₂ ratios, aspect ratios, fiber angle, stacking sequence and boundary condition were studied in detail. The results indicate that the high E₁/E₂ and α₂/α₁ ratios of AS4/3501-6 and T 300/5208 laminates produce higher bending rigidity along the fiber direction and higher in-plane compressive force in a direction perpendicular to the fiber direction. Therefore, the higher thermal buckling mode shapes are formed. The thermal buckling mode that composite laminated plate will buckle into is mainly dependent on the E₁/E₂ ratio, α₂/α₁ ratio, fiber orientation and aspect ratio of the plate.     

A model of composite laminated Reddy plate based on new modified couple stress theory

Based on new modified couple stress theory a model for composite laminated Reddy plate is developed in first time. In this theory a new curvature tensor is defined for establishing the constitutive relations of laminated plate. The characterization of anisotropy is incorporated into higher-order laminated plate theories based on the modified couple stress theory by Yang et al. in 2002. The form of new curvature tensor is asymmetric, however it can result in same as the symmetric curvature tensor in the isotropic elasticity. The present model of thick plate can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model for cross-ply composite laminated Reddy plate of couple stress theory with one material’s length constant is used to demonstrate the scale effects. Numerical results show that the present plate model can capture the scale effects of microstructure. Additionally, the present model of thick plate model can be degenerated to the model of composite cross-ply laminated Kirchhoff plate and Mindlin plate of couple stress theory.     

Stiffened plate bending analysis in terms of refined triangular laminated plate element

Based on the higher-order global–local theories, a finite element model is proposed to study the bending behavior of stiffened laminated plates. The proposed model treats the embedded stiffeners as the part of laminated plate, so that the compatibility of displacements and stresses between the plate and the stiffeners can be automatically satisfied. Distributions of the displacements and stresses through the thickness of laminates were also given for the first time, which can serve as references for future investigations as such information is lacking in the published literature. In addition, the impact of the stiffeners on the bending response of the stiffened laminated plates is also studied in terms of the quantity, the collocation and the geometry of stiffeners. Numerical results showed that the higher-order global–local theories are more suitable for predicting the bending response of thick and moderately thick stiffened laminated plates compared to the first order theory commonly used in engineering. By varying the quantity, the collocation and the geometry of stiffeners, the stiffness and the strength of stiffened laminated plates can be remarkably improved.     

Finite volume analysis of laminated composite plates

A numerical procedure for analysis of general laminated plates under transverse load is developed utilizing the Mindlin plate theory, the finite volume discretization, and a segregated solution algorithm. The force and moment balance equations with the laminate constitutive relations are written in the form of a generic transport equation. In order to obtain discrete counterparts of the governing equations, the plate is subdivided into N control volumes by a Cartesian numerical mesh. As a result, five sets of N linear equations with N unknowns are obtained and solved using the conjugate gradient method with preconditioning. For the method validation, a number of test cases are designed to cover thick and thin laminated plates with aspect ratio (width to thickness) from 4 to 100. Simply supported orthotropic, symmetric cross‐ply, and angle‐ply laminated plates under uniform and sinusoidal pressure loads are solved, and results are compared with available analytical solutions. The shear correction factor of 5/6 is utilized throughout the procedure, which is consistent with test cases used in the reviewed literature. Comparisons of the finite volume method results for maximum deflections at the center of the plate and the Navier solutions obtained for aspect ratios 10, 20, and 100 shows a very good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

General higher-order layer-wise theory for free vibrations of doubly-curved laminated composite shells and panels

ABSTRACT

The present article illustrates a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels. The theoretical framework relates to the dynamic analysis of shell structures by using a general displacement field based on the Carrera Unified Formulation (CUF), including the stretching effect for each layer. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order layer-wise formulation is to propose a kinematic assumption, with an arbitrary number of degrees of freedom. The main aim of this work is to determine the explicit fundamental operators that can be used for the layer-wise (LW) approach. These fundamental operators are obtained for the first time by the author and are related to motion equations of doubly-curved shells described in an orthogonal curvilinear co-ordinate system. The free vibration shell and panel problems are computationally solved using the generalized differential quadrature (GDQ) and generalized integral quadrature (GIQ) techniques. The numerical results are compared with recent papers in the literature and commercial finite element codes.