Some studies on free vibration of composite laminates

Free vibration analysis is carried out to study the vibration characteristics of composite laminates using the modified shear deformation, layered, composite plate theory and employing the Rayleigh-Ritz energy approach. The analysis is presented in a unified form so as to incorporate all different combinations of laminate boundary conditions and with full coverage with regard to the various design parameters of a laminated plate. A parametric study is made using a beam characteristic function as the admissible function for the numerical calculations.The numerical results presented here are for an example case of fully clamped boundary conditions and are compared with previously published results. The effect of parameters, such as the aspect ratio of plates, ply-angle, number of layers and also the thickness ratios of plies in laminates on the frequencies of the laminate, is systematically studied. It is found that for anti-symmetric angle-ply or cross-ply laminates unique numerical values of the thickness ratios exist which improve the vibration characteristics of such laminates. Numerical values of the non-dimensional frequencies and nodal patterns, using the thickness ratio distribution of the plies, are then obtained for clamped laminates, fabricated out of various commonly used composite materials, and are presented in the form of the design curves.     

Vibration of shear-deformable rectangular plates using a spline-function Rayleigh-Ritz approach

The prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described, through the use of B-spline functions as trial functions in a Rayleigh-Ritz approach. Through-thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the spline-function Rayleigh-Ritz approach are described: in one of these the deflection and rotations are represented by functions of the same polynomial order, whilst in the other a lower-order representation is used for each rotation component in one of the co-ordinate directions. It is shown in a number of applications that the former version leads to shear-locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.     

OPTIMAL ROBUST DESIGN OF NOVEL MATERIALS: PROBLEMS OF STABILITY AND VIBRATIONS

A numerical method for the optimal design of thin anisotropic laminates is presented, layer thicknesses and lamination angles being the design variables. An optimal solution is pursued with respect to frequency domain objectives, e.g. fundamental frequency and Euler critical load. A special feature of the method is the semi-analytical second order design sensitivity that is computed with the aid of a Rayleigh-Ritz analysis approach. A modified sequential quadratic programming scheme is then introduced, where standard quasi-Newton approximations are avoided by an exact calculation of the Hessian matrix. Furthermore, the robustness of the method with respect to scatter in material properties such as mass density and elastic moduli is assessed. A stochastic extension of the Rayleigh-Ritz approach is developed on this purpose that allows the location of those regions in the design space that are most sensitive to physical parameter randomness. This allows the use of a modified objective function that penalizes sensitive solution.     

Non-linear bending of antisymmetric cross-ply plates

The bending of antisymmetric cross-ply plates, based on Von-Karman plate theory, is investigated in this paper with one term approximations for the in-plane and transverse displacements. Rayleigh-Ritz solutions are presented for the non-linear response of cross-ply laminates with various modular and aspect ratios and subjected to sinusoidal transverse loading.     

Post-buckling analysis of composite plates containing embedded delaminations with arbitrary shape by using higher order shear deformation theory

The compressive post-buckling behavior of composite laminates containing embedded delamination with arbitrary shape is investigated analytically. For modeling the embedded delamination, the laminate is divided into three smaller regions. The higher order shear deformation theory is implemented and the formulation is based on the Rayleigh-Ritz approximation technique by the application of the simple/complete polynomial series for each region. The nonlinear equilibrium equations, which are achieved through the application of the principle of Minimum Potential Energy, are solved by employing the Newton-Raphson iterative procedure. Some interesting results are obtained and compared with those achieved by the finite element method of analysis using ANSYS commercial software. A good agreement is seen to exist between the results. This is while for a given level of accuracy in the results, ANSYS requires a markedly larger number of degrees of freedom compared to that needed by the developed method. Moreover, a considerable reduction in the load carrying capacity of laminate is noticed due to the presence of delamination.     

The vibration and stability of symmetrically-laminated composite rectangular plates subjected to in-plane stresses

Consideration is given to the twin problems of the elastic buckling of rectangular, symmetrically-laminated composite plates and of the vibration in the presence of applied in-plane stress of such laminates. First-order shear deformation plate theory provides the mathematical model of plate behaviour and the Rayleigh-Ritz and finite strip methods are used to generate numerical results for laminates of thin and moderately thick geometry, with various combinations of standard plate edge conditions. The applied stresses include uniform shear stress as well as direct stresses, and anisotropic material properties can be included. The presented results demonstrate the accuracy of the numerical methods and highlight the very significant influence that transverse shear and related thickness effects can have in the subject problems.     

Local buckling loads of sandwich panels made with laminated faces

The paper is devoted to assessing the optimal arrangements of hybrid laminated faces of sandwich panels in order to maximize local buckling loads corresponding to the wrinkling of compressed faces. The analysis is carried out by modelling compressed faces as thin unsymmetric laminates resting on elastic two-parameter foundations. The First-order Shear Deformation Theory, in conjunction with the Rayleigh-Ritz method, has been used to evaluate buckling loads of simply supported flat laminates subjected to in-plane biaxial compression and shear forces. A numerical investigation is intended to support evidence for the influence of laminate parameters (fibre orientation, geometrical dimensions) and foundation parameters (modulus of subgrade reaction and shear modulus); obtained results are reported and discussed in the paper.     

T型耦合板结构振动特性研究

本文以T型耦合板为研究对象,在同时考虑面内振动和面外振动条件下采用改进傅立叶级数方法（Improved Fourier Series Method,IFSM）对其自由振动特性进行了计算分析。板结构的面内振动和面外振动位移函数表示为改进傅立叶级数形式,并引入正弦傅立叶级数以解决边界的不连续或跳跃现象。将位移函数的级数展开系数作为广义坐标,采用Rayleigh-Ritz方法对其进行求解。通过对不同边界条件及耦合连接情况下T型板自由振动特性进行计算,并将之与有限元法结果相比较,验证了本文方法的正确性和有效性,为耦合板结构的振动控制提供可靠的理论依据。     

含任意分层缝纫正交层合板压缩屈曲分析

建立了分析含任意形状分层的缝纫增强复合材料层合板压缩屈曲问题的连续分析模型。该模型允许缝纫层合板含有一个或多个形状不同的分层。分析结果表明,缝纫针脚在分层区域的分布、缝纫密度和缝线的等效刚度系数对分层子板的压缩屈曲应变均有较大影响。      

An efficient meshfree method for vibration analysis of laminated composite plates

A detailed analysis of natural frequencies of laminated composite plates using the meshfree moving Kriging interpolation method is presented. The present formulation is based on the classical plate theory while the moving Kriging interpolation satisfying the delta property is employed to construct the shape functions. Since the advantage of the interpolation functions, the method is more convenient and no special techniques are needed in enforcing the essential boundary conditions. Numerical examples with different shapes of plates are presented and the achieved results are compared with reference solutions available in the literature. Several aspects of the model involving relevant parameters, fiber orientations, lay-up number, length-to-length, stiffness ratios, etc. affected on frequency are analyzed numerically in details. The convergence of the method on the natural frequency is also given. As a consequence, the applicability and the effectiveness of the present method for accurately computing natural frequencies of generally shaped laminates are demonstrated.     

复杂边界条件圆柱壳自由振动特性分析

提出一种半解析法来分析圆柱壳结构自由振动特性。将圆柱壳壳结构在轴向方向分解为若干壳段,用沿轴向的Jacobi多项式和沿周向的Fourie r级数来表示各个壳段的位移函数,并采用罚参数法对圆柱壳结构的边界条件和壳段间的连续性条件进行模拟;最后,基于Rayleigh-Ritz法求得圆柱壳结构的自由振动频率。研究表明,该方法具有较好的收敛性,与公开发表文献一致性较高,研究成果可为复杂边界条件下圆柱壳结构自由振动特性分析提供数据积累和方法依据。     

Large Deflection Compressional Analysis of Unsymmetric Delaminated Composite Plates with Consideration of Contact Phenomenon

In this study, an efficient method is developed to investigate the compressive large deflection behavior of unsymmetric composite laminates with multiple through-the-width delaminations. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique by the implementation of the simple and complete polynomial series. The method can handle both local deflection of the delaminated sublaminate and global deflection of the whole plate. Also, the contact among sublaminates is investigated. The three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model.     

混杂薄膜天线层的双稳态复合材料层板力电性能

给出了既有双稳态特性又具有天线功能的多功能复合材料层板设计与分析方法。基于非线性层板理论和Rayleigh-Ritz法,建立了双稳态混杂层板构型预报理论模型,并通过有限元计算和实验进行了验证。研究了薄膜天线混杂非对称双稳态复合材料层板的临界载荷及电磁性能,分析了铺层方式对双稳态混杂层板稳定构型、临界载荷和电磁性能的影响。结果表明：双稳态混杂层板通过转变其稳定构型实现天线主辐射方向在俯仰面内偏转30°,实现方向图可重构,扩大天线波束的扫描范围。铺层方式对层板构型和反射系数影响较大,当天线辐射层铺设在层板表面且聚酰亚胺薄膜厚度大于0.2 mm时,其双稳态特性消失,没有出现分叉现象,且其中心频率会左移大约0.2 GHz。     

Reduction method for the non-linear analysis of symmetric anisotropic panels

Reduction method and computational procedures are presented for reducing the size of the analysis model and the number of degrees of freedom used in predicting the non-linear response of symmetric anisotropic panels. The two key elements of the method are (a) operator splitting, or decomposition of the characteristic arrays of the finite element model into sums of orthotropic and non-orthotropic contributions, (b) application of a reduction method through the successive use of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate a small number of global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the classical Rayleigh-Ritz technique. The global approximation vectors are selected to be those commonly used in single (or multiple) parameter perturbation techniques, namely a non-linear solution corresponding to zero non-orthotropic arrays and a number of its derivatives with respect to an anisotropic tracing parameter (and possibly, to a load or arc-length parameter in the solution space). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed reduction method is demonstrated by means of a numerical example, and its potential for solving quasi-symmetric non-linear problems of anisotropic panels is discussed.     

矩形Mindlin板振动分析的DSC方法

提出了一种离散奇异卷积（DSC：Discrete Singular Convolution）方法来对基于Mindlin剪切变形理论的矩形厚板进行自由振动分析。此方法采用了Gauss delta序列核作为基函数并结合pb-2Rayleigh-Ritz方法（pb-2指的是atwo-dimensional polynomial function（p-2）and a boundary function（b））的边界函数得到了一种新型的Ritz方法。数值结果表明此方法相当精确有效。     

Stress and failure analysis of laminated composites based on layerwise B-spline finite strip method

A layerwise B_k,k−1-spline finite strip method is developed for stress and failure analysis in fibre reinforced composite laminates. The composite laminates are divided into a number of numerical layers in the thickness direction. A linear variation of in-plane displacements are assumed across the thickness of each numerical layer to represent the sectional warping which can have significant effects on through thickness shear stresses. The development of B_k,k−1-spline finite strip method is presented. Material failure criteria and material degradation models for progressive failure are discussed and integrated in a progressive failure analysis for composite laminates. Numerical applications include a progressive failure analysis example are presented to verify the layerwise B-spline finite strip method developed for stress and failure analysis in composite laminates. Whenever possible the present predictions are compared with the existing analytical and numerical results.     

用样条有限点法分析正交各向异性层合板的振动与稳定问题

本文采用样条有限点法,对多种边界条件下正交各向异性层合板的振动与稳定问题,进行了系统的分析,编制了通用程度。计算结果表明:样条有限点法在分析计算正交各向异性层合板的振动与稳定问题时,具有自由度少、收敛快、精度高、计算格式简便,易于在微机上计算等优点。     

频率相关自由阻尼层复合材料加筋板动力分析

采用子空间迭代法和精细积分对敷设粘弹性阻尼层的含损伤复合材料加筋板结构进行了频率和动力响应分析。分析中对层合板和层合梁采用了Adams应变能法与Raleigh阻尼模型相结合的阻尼矩阵构造方法;对表面粘弹性阻尼材料则考虑了材料性质和耗散系数对激振频率与温度的依赖性,建立了频率相关粘弹性材料阻尼矩阵的计算方法。通过有限元分析,分别研究了敷设自由阻尼层无损伤和含分层损伤复合材料加筋板的自振频率和模态特征,并根据幅频曲线讨论了阻尼材料模量、耗散系数和阻尼层厚度等因素对结构响应的影响,提出的计算方法对通过合理选择阻尼层材料与几何参数来有效地控制加筋板结构的振动特性,具有一定的参考价值。     

正交层板弯曲问题的一种半解析法

本文提出了一个完全满足对称正交层合板弯曲基本方程的挠度级数表达式,并导出了相应的位移、变形及内力的显表达式。边界条件则用离散型最小二乘法近似满足。由于所用级数较简单且具备完备性,因而推导与计算都较简单,对于各种边界条件下的单连通板,它都能逼近其精确解。文中的例子表明,本方法往往用较少的待定系数及配点,就可获得相当好的结果。      

基于细化单胞模型的复合材料层合板强度预报方法

通用单胞模型常被应用于复合材料细观力学分析。但原始的通用单胞模型存在求解量大、计算效率低的问题。本文中对其改进, 建立了以子胞界面细观应力为未知量的细化单胞模型。该模型可以充分考虑纤维、基体和界面相等细观组分, 并实现单向板的宏-细观多尺度力学分析。通过将组分材料失效判据引入到模型中, 再与经典层合理论相结合, 提出了一种基于细化单胞模型的复合材料层合板强度预报方法, 并给出了基于试验数据的强度谱定量评测方法。通过与世界失效分析习题的失效理论和试验数据进行对比, 证明本文的预报方法具有很高的计算精度和广泛的普适性。