考虑横向剪切变形的反对称角铺设层合板的弯曲

本文对考虑横向剪切变形的反对称角铺设复合材料层合板弯曲问题进行了理论分析,得到了简化分层理论的封闭形式解。在由位能变分原理得到一般方程的基础上引入合理假设,得到了适合本问题的求解方程。在用简化的分层理论对典型算例进行数值计算的同时,也用经典层合板理论和一阶剪切变形理论进行了计算,一并与相关文献的三维精确解加以比较,结果表明,简化分层理论可以有效地应用于反对称角铺设层合板的弯曲问题。      

应用广义虚载荷法求解反对称角铺设层合板的弯曲

本文应用广义虚载荷法结合富里叶级数,得到了各种边界条件下反对称角铺设层合板弯曲问题的富里叶级数解。同时给出了加快级数收敛的公式以及逐项微分富里叶级数任意次的方法。      

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.      

复合材料层合板非线性屈曲分析

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。     

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。     

基于新修正偶应力理论的斜交铺设层合Kirchhoff板模型与尺度效应

基于新修正偶应力理论, 建立了只含有1个尺度参数的复合材料斜交铺设层合Kirchhoff板模型, 并分析了铺设角对尺度效应的影响。采用虚功原理推导了任意铺设角的层合Kirchhoff板的弯曲方程和边界条件。通过新模型给出了四边简支反对称角铺设微尺度层合Kirchhoff板的解析解。结果表明:细观尺度各向异性层合板的尺度效应并不仅仅受其几何尺寸的影响, 还受铺设角的影响;铺设角对尺度效应可能产生非常显著的影响。      

双轴受压反对称角铺设复合材料层合板在固支边界下的后屈曲和模态跃迁

为有效分析双轴受压反对称角铺设复合材料层压板在固支边界下的后屈曲性能, 由渐近修正几何非线性理论推导其双耦合四阶偏微分方程(即应变协调方程和稳定性控制方程), 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。对四层固支边界复合层合板的数值模拟结果表明: 该解析法与有限元方法在主后屈曲区域的线性屈曲荷载计算结果吻合良好; 有限元方法在解靠近二次分岔点时失去收敛性, 而解析方法可深入后屈曲区域, 准确捕捉模态跃迁现象; 对于反对称角铺设层合板, 可仅用纯对称模态来定性预测主后屈曲分支、二次分岔荷载及远程跃迁路径。      

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。      

各向异性反对称角铺设层合板的非线性弯曲强迫振动分析

笔者以具有代表性的各向异性复合材料反对称角铺设层合板为例,对其在简谐激振力作用下的非线性弯曲强迫振动问题做了包括算例在内的全解析过程分析.得到各向异性反对称角铺设层合板在各种级别荷载作用下的幅-频关系,以及层合板结构铺设层数的变化对非线性弯曲强迫振动幅-频关系的影响,所求得的解析形式的结果保证了结果的可靠性以及由此所推得的结论的代表性.本文工作无疑是复合材料层合板非线性动力问题的一个有意义的尝试,它们对于以后探讨各向异性层合板其它方面的非线性动力问题具有一定的意义.      

复合材料角铺设层合板非线性振动特性研究

本文运用渐进摄动法得到复合材料角铺设层合板系统的平均方程在此基础上研究了四边简支碳纤维增强复合材料角铺设层合板在外激励作用下的非线性振动和混沌运动。指出由于复合材料角铺设层合板的强耦合作用而引起该板系统运动控制方程的复杂性,系统平面的振动方程不仅与横向振动方程相耦合而且与中面法线的转角有关。考虑了复合材料角铺设层合板系统在1:1内共振和基本参数共振的情况下的动力学特性,数值模拟得到了复合材料角铺设层合板在参数激励和横向激励联合作用下的复杂周期和混沌运动。     

Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading

A two-dimensional global higher-order deformation theory is presented for the free vibration and stability problems of angle-ply laminated composite and sandwich plates subjected to thermal loading. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through Hamilton’s principle. Several sets of truncated Mth order approximate theories are applied to solve the eigenvalue problems of a simply supported angle-ply multilayered plate. Natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading are obtained. Critical temperatures are obtained by increasing the temperature until the natural frequency vanishes. The effects of prebuckling displacements on the natural frequencies and critical temperatures are taken into account. Modal displacement distributions through the transverse direction of the laminates are plotted for the specific temperature parameter. Numerical results are compared with those of the published existing theories. The present global higher-order approximate theories can predict the natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading accurately within small number of unknowns.     

Effect of transverse cracks on the elastic properties of high temperature angle-ply laminated composites

The development of transverse cracks can be detrimental to the stiffness and dimensional stability of composite laminates. In this investigation, a modified shear lag analysis, taking into account the concept of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in high temperature angle-ply laminated composites. The results present well the effect of high temperature and the fibre orientation of the outer layers on the degradation of mechanical properties of the angle-ply polymer composite laminates.     

Elastic constants identification of symmetric angle-ply laminates via a two-level optimization approach

A two-level optimization method for elastic constants identification of symmetric angle-ply laminates is presented. Measured axial and lateral strains of two symmetric angle-ply laminates with different fiber angles are used in the proposed method to identify four elastic constants of the composite laminates. In the first-level optimization process, the theoretically and experimentally predicted axial and lateral strains of a [(45°/−45°)₂]_s laminate are used to construct the error function which is a measure of the differences between the experimental and theoretical predictions of the axial and lateral strains. The identification of the material constants is then formulated as a constrained minimization problem in which the best estimates of the shear modulus and Poisson’s ratio of the laminate are determined by making the error function a global minimum. The problem of this level of optimization is then solved using a multi-start global minimization algorithm. In the second-level optimization process, the shear modulus and Poisson’s ratio determined in the previous level of optimization are kept constant while the Young’s moduli of the second angle-ply laminate with fiber angles other than 45° are identified using the same minimization technique that has been used in the previous level. The accuracy of the proposed method are studied by means of a number of numerical examples on the material constants identification of symmetric angle-ply laminates made of different composite materials. Finally, static tensile tests of [(45°/−45°)₂]_s and [(30°/−30°)₂]_s laminates made of Gr/ep composite material are performed to measure the strains of the laminates. The experimental data are then used to identify the elastic constants of the laminates. The excellent results obtained in the experimental investigation have demonstrated the feasibility and applications of the proposed method.     

A further study on thermal buckling of simply supported antisymmetric angle-ply laminates in a uniform-temperature field

This paper examines carefully the thermal-buckling temperatures of simply supported composite antisymmetric angle-ply laminates subjected to a uniform-temperature field rise, predicted by various displacement fields and stress/strain/temperature relationships. It can be concluded that, if an appropriate stress/strain/temperature relationship is used, the buckling temperatures predicted by the first-order transverse-shear-deformation-plate theory are virtually the same as those predicted by other higher-order transverse-shear and transverse-normal-deformation-plate theories.     

Experimental study on mechanical behavior of laminates at low temperature

A series of tensile tests were conducted to research the mechanical behavior of the glass fiber and the carbon fiber reinforced epoxy laminates at low temperature (77 K). The specimens of laminates contained various stacking sequences (angle-ply) and notch geometry (central and edge notch). The curves of loading vs displacement of cross-head were recorded and the curves of stress-strain were got. The strengths of the various laminates were given too. Using a microscope-CCD imaging system, the growth of damage area was imaged. The concept of the energy dissipation density of laminates was presented and the data of the energy dissipation density for some laminates were got. The results showed that the strength and the energy dissipation density of laminates at 77 K are higher than those at 296 K.     

An accurate stress analysis model for angle-ply laminates with weakly bonded layers

Summary This paper presents a shear slip model suitable for the analysis of angle-ply composite laminated plates with weakly bonded layers. Being an extension of a relevant model that deals with perfectly bonded laminates, this study accounts further for the effects of shear slip by introducing appropriate interfacial bonding conditions. Accordingly, the model is based on a general five-degrees-of-freedom displacement field which includes certain general shape functions of the transverse co-ordinate. These are determined by means of appropriate three-dimensional elasticity considerations and include information relevant to the interfacial constitutive relations that account for weak bonding between layers. In dealing with weakly bonded angle-ply laminated plates in cylindrical bending, a closed form solution which is independent of the imposed boundary edge conditions is obtained. As a special case, the corresponding cross-ply laminated, weakly bonded plates solution is obtained by letting all the lamination angles involved to take 0° or 90° values. The high accuracy of the present model is shown by means of numerical comparisons with corresponding results based on an exact elasticity solution obtained for simply supported laminates. The effects of shear slip on the response of angle- and cross-ply laminated plates subjected to different edge boundary conditions are finally studied by means of corresponding numerical results that are obtained, presented and discussed.     

Finite element analysis of free edge stresses in non-linear viscoelastic composites under uniaxial extension,bending and twisting loadings

A finite element procedure for the analysis of time-dependent interlaminar stresses in non-linear viscoelastic laminated composites subjected to arbitrary combinations of axial extension, bending and/or twisting loads has been developed based on Schapery's non-linear constitutive relations and Pipes and Pagano's displacement field for laminates under a generalized plane deformation state. Parametric studies are presented to demonstrate the accuracy of the numerical procedures. As illustrative examples, time-dependent non-linear interlaminar stresses for cross-ply and angle-ply laminates subjected to bending and twisting are present. Other layup orientations can be conveniently analysed using the presently developed numerical procedure. © 1997 John Wiley & Sons, Ltd.     

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0]₆, [±30]₅ and [±45]₅ laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.     

Analysis of laminated composite beams using layerwise displacement theories

Within the displacement field of a layerwise theory, two laminated beam theories for beams with general lamination are developed. In the first theory, an existing layerwise laminated plate theory is adapted to laminated beams. The procedure used in the second theory is simple and straightforward and similar to the one used in the development of plate and shell theories. These theories can also be used in developing simpler theories such as classical, first, and higher-order shear deformation laminated beam theories. Equations of motions are obtained by using Hamilton’s principle. For the assessment of the accuracy of these theories, analytical solutions for static bending and free vibration are developed and compared with those of an existing three-dimensional elasticity solution of cross-ply laminates in cylindrical bending and with the three-dimensional finite element analysis for angle-ply laminates.