Bezier曲线变角度层合板设计及屈曲特性分析

基于二次Bezier曲线法,开展纤维变角度层合板的屈曲特性研究。首先,对原始的二次Bezier曲线进行了扩展,提出了分段式二次Bezier曲线变化方法,重新定义了纤维变角度铺放参考路径,确定了变角度层合板的表示形式。其次,以[0±20(β)65]_(2s)和[90±20(β)65]_(2s)为例对变角度层合板的屈曲特性进行了有限元分析,并与定角度层合板对比。最后,研究了不同终止角α和连接点参数β对层合板屈曲性能的影响,结果表明:连接点参数β的增大使得两种变刚度层合板的线性屈曲载荷先增大后减小,终止角大于起始角时,层合板的一阶屈曲载荷逐渐增大,铺放角度的增大有利于层合板屈曲载荷的提高。     

丝束变角度层合板屈曲性能的参数化研究

通过选择合适的纤维轨迹,丝束变角度(VAT)层合板相对于直纤维层合板能拥有更好的抗屈曲特性。为研究纤维轨迹特征长度和定向坐标系偏角对VAT层合板屈曲性能的影响,首先对原始的纤维角度线性变化方法进行改进,提出了一种纤维角度分段线性变化方法,拓展了纤维轨迹的设计空间;其次,采用改进后的纤维轨迹定义方法构建了一系列变刚度层合板;最后,基于有限元方法,从内力分布角度对变刚度层合板不同承载情况下的屈曲性能进行研究和探讨。数值结果表明:单向轴压工况下,采用半边长的特征长度和90°偏角的纤维轨迹,能使层合板的稳定性最好;双向轴压工况下,应将特征长度和定向坐标系偏角作为额外的设计变量,并通过优化获得最优的纤维轨迹。     

面内线性变化载荷作用复合材料层合板的振动与屈曲优化

采用广义微分求积（GDQ）法开展了不同边界条件下承受面内线性变化载荷作用复合材料层合板振动与屈曲的分析与优化。针对GDQ法求解面内线性变化载荷工况复合材料层合板屈曲问题存在计算振荡、不收敛现象,提出载荷扰动策略实现了GDQ法对复合材料层合板屈曲问题的稳定高效求解。基于基础圆频率和临界屈曲载荷系数的归一化指标,分析了铺层角度对复合材料层合板综合性能的影响,并结合直接搜索模拟退火算法开展了复合材料层合板的铺层顺序优化。结果表明:铺层角度变化对屈曲性能的影响明显强于频率特性;面内线性变化载荷中,以弯曲载荷作用下复合材料层合板的优化综合性能受边界条件变化的影响最小,而优化铺层角度受边界条件变化的影响最大。研究结果为复杂载荷作用下复合材料层合板的设计提供了参考。      

纤维角度对变角度层合板减振性能的影响

自动铺丝技术可以实现复杂曲率曲线铺放,可极大提高角度设计的自由度。本文以改善复合材料层合板动态特性为目的,对变角度层合板的减振性能进行了研究分析。首先对不同角度变化变角度层合板进行自由衰减试验,研究了纤维角度变化与变角度层合板阻尼比的关系。然后对含相应角度变角度夹层板进行随机试验,研究了层合板随机激励条件下的振动响应,并采用共振峰处传递函数(Transition function,TF)和拾振点加速度总均方根(Root mean square,RMS)两种指标评价减振效果。结果表明:层合板阻尼比在纤维变化角度为±<45|60>时最大,纤维变化角度为±<73|88>时最小。基于RMS减振评价指标,±<45|60>夹层板较传统直线板减振性能提高27.13%;基于共振峰TF减振评价指标,纤维角度变化对不同共振峰减振效果规律差异明显。研究表明,变角度层合板减振性能明显优于传统直线层合板,相关实验结果将对变角度层合板减振设计及优化提供一定的参考意义。      

复合材料层合板在非保守力作用下的动力稳定性

利用弹性非保守系统自激振动的拟固有频率变分原理,推导出复合材料矩形板受非保守随从力作用的变分方程,进而导出此问题的有限元基本方程及求解临界力和固有频率的特征方程。用载荷增量法计算了在多种边界条件下不同边长比的复合材料矩形板在面内受随从力作用的临界载荷,分析了不同角铺设方向及两种材料组合板的临界载荷。计算结果表明,边界条件对层合板的动力稳定性有较大影响,复合材料层合板的角铺设方向对临界载荷有较大影响。     

多分层对复合材料层合板自振特性的影响

基于Mindlin一阶剪切理论分项等参插值的有限元法, 建立了含多个分层损伤复合材料层合板自由振动分析的有限元模型和分析方法, 并采用线性接触模型模拟分层区域上、 下子板的相互作用。通过典型数值算例, 讨论了分层位置、 数目及板的边界条件诸参数对其振动特性的影响。结果表明: 分层位置沿板长方向变化时, 中间分层的频率变化范围较大, 表面分层变化较小, 但变化趋势基本相同; 沿层合板厚度方向, 多分层中最长分层的位置越靠近层合板中面, 则其对振动特性的影响越大; 多个分层位置较靠近层合板表面, 且板边界条件约束较弱时, 多分层与单分层对振动特性影响的差别不大, 此时, 可将多分层损伤层合板简化为单分层损伤层合板来进行振动分析。      

复合材料层合板自由振动的谱切比雪夫解法EI北大核心CSCD

采用二维谱切比雪夫法(2D-ST),对一般边界条件下复合材料层合板的自由振动进行了分析。基于一阶剪切变形理论(FSDT),采用边界弹簧技术模拟任意边界条件,推导了复合材料层合板的能量方程表达式。利用二维谱切比雪夫法求解能量方程,得到了任意边界条件下复合材料层合板的自由振动特征方程。在数值算例中,通过与其它方法的计算结果进行对比,验证了所提出方法的收敛性和准确性,并在此基础上研究了弹性模量比和铺设角对复合材料层合板振动特性的影响。     

层合板分析的无网格局部Petrov-Galerkin方法

基于Kirchhoff均匀各向异性板控制方程的等效积分弱形式和对挠度函数采用移动最小二乘近似函数进行插值, 进一步研究无网格局部Petrov-Galerkin方法在纤维增强对称层合板弯曲问题中的应用。该方法不需要任何形式的网格划分, 所有的积分都在规则形状的子域及其边界上进行,其问题的本质边界条件采用罚因子法来施加。通过数值算例和与其他方法的结果比较, 表明无网格局部Petrov-Galerkin法求解层合薄板弯曲问题具有解的精度高、收敛性好等一系列优点。      

基于细观力学的大开孔层合板缝合补强力学性能计算的新方法基于细观力学的大开孔层合板缝合补强力学性能计算的新方法

从细观力学的角度出发,考虑了面内纤维弯曲及富树脂缺陷,建立了大开孔层合板缝合补强孔边针脚损伤的单胞模型。建立了纤维弯曲函数,推导了纤维弯曲区域的纤维体积分数及纤维弯曲角度。基于复合材料力学分析方法,计算得出了单胞的材料弹性常数。研究表明:缝合导致单胞面内纤维最大弯曲角不超过20°,单层板纵向杨氏模量减小,横向杨氏模量、剪切模量及泊松比均增大,变化幅度均在-8%~20%之间;且对于大开孔层合板缝合补强而言,针距变化引起的材料性能变化相对边距大许多。由上述计算结果,建立了一种缝合补强大开孔层合板力学性能计算的新方法,同时引入针孔模拟针脚处的应力集中现象,结果表明:缝合会造成层合板面内力学性能降低,并且对面内的压缩性能影响大于对面内拉伸性能的影响。      

各向异性复合材料对称角铺设层合板非线性弯曲强迫振动

笔者曾经研究讨论了各向异性复合材料反对称角铺设层合板的非线性弯曲强迫振动问题[1]。本文是这一研究领域的继续和扩展。在这里,笔者详细研究了各向异性复合材料对称角铺设层合板在简谐激振力作用下的非线性弯曲强迫振动问题,做了包括算例的全解析过程分析,得到了各向异性对称角铺设层合板在各种量级载荷作用下的幅一频关系,分析了对称角铺设层合板结构的铺设方向角对非线性弯曲强迫振动的幅一频关系影响,所求得的解析形式结果保证了结果的可靠性。本文无疑是对复合材料层合板非线性强迫振动问题研究的一个有意义的深入扩展,它们对于探讨其它复合材料结构的非线性动力问题具有一定的意义。      

考虑纤维面外起伏的变刚度层合板优化策略研究

针对变刚度层合板在自动铺放制造过程中因间隙/重叠缺陷产生大量纤维面外起伏缺陷的问题,提出采用铺层偏移法与断送纱策略两种铺层优化策略来进行变刚度层合板的铺层设计,在研究过程中同时引入考虑间隙/重叠缺陷建模的方法。根据变刚度层合板铺层的特点提出缺陷重复单元的概念,通过对缺陷重复单元的分析来反映纤维面外起伏的影响,并提出通过纤维面外系数来表征变刚度层合板的纤维面外起伏尺度,最后对不同优化策略的变刚度层合板的屈曲性能进行分析。研究表明:基准设计方案、铺层偏移法与断送纱策略所对应的纤维面外起伏系数为0.83、0.95、0.93,所提出的优化策略对变刚度层合板的纤维面外起伏尺度有着明显的抑制作用。铺层偏移法优化后的[±<50/65>]_6s变刚度层合板最大厚度超差为33%,所对应的屈曲载荷为9117.1 N,屈曲载荷提升17.6%;断送纱策略优化后的[±<50/65>]_6s变刚度层合板最大厚度超差为50%,所对应的屈曲载荷为9716.3N,屈曲载荷提升25.3%。      

Optimal design of variable fiber spacing composites for morphing aircraft skins

Morphing aircraft concepts aim to enhance the aircraft performance over multiple missions by designing time variant wing configurations. The morphing concepts require wing skins that are flexible enough to allow large in-plane stretching and high bending stiffness to resist the aerodynamic loads. In this study, an optimization problem is formed to enhance the in-plane flexibility and bending stiffness of wing skins made of composite laminate. Initially, the optimal fiber and elastomer materials for highly flexible fiber reinforced elastomer laminates are studied using materials available in the literature. The minor Poisson’s ratio of the laminate is almost zero for all the fiber and elastomer combinations. In the next stage, the effects of boundary conditions and aspect ratio on the out-of-plane deflection of the laminate are studied. Finally, an optimization is performed to minimize the in-plane stiffness and maximize the bending stiffness by spatially varying the volume fraction of fibers of a laminate. The optimization results show that the in-plane flexibility and bending stiffness of the laminate with a variable fiber distribution is 30–40% higher than for the uniform fiber distribution.     

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。      

Surrogate-based multi-objective optimization of a composite laminate with curvilinear fibers

A variable stiffness design can increase the structural performance of a composite plate and provides flexibility for trade-offs between structural properties. In this paper, we examine the simultaneous optimization of stiffness and buckling load of a composite laminate plate with curvilinear fiber paths. The problem, which falls in the area of multi-objective optimization, is formulated and solved through a surrogate-based optimization algorithm capable of finding the set of optimum Pareto solutions. We integrate surrogate modeling into an evolutionary algorithm to reduce the high computational cost required to solve the optimization process. The results show that a curvilinear fiber path can increase both buckling load and stiffness simultaneously over the quasi-isotropic laminate. Furthermore, the optimum direction for varying the fiber angle is dependent on the loading direction and boundary conditions. The results for a plate under uniform compression with free transverse edges shows that varying the fiber orientation perpendicular to the loading direction can increase the buckling load by 116% with respect to that of a quasi-isotropic laminate.     

Influence of the prebuckling stress-field on the critical loads of inhomogeneous composite laminates

The paper studies the uniaxial buckling behavior of composite laminates in which preselected variations of fiber spacing in the constituent laminae are adopted. Such laminates are referred to as inhomogeneous laminates because of the variable elastic stiffness along the coordinate axes. A non-uniform prebuckling stress state observed even under constant uniaxial compression has a pronounced influence on the buckling behaviour of an inhomogeneous laminate. A procedure is summarized for computing the critical load of a laminate using the Ritz method which exploits an analogy between the bending and stretching formulations and utilizes Gram-Schmidt orthogonal polynomials. The paper illustrates that the variation in fiber spacing is an innovative way of increasing the critical load for a prescribed amount of fiber and highlights its remarkable sensitivity to the nature of fiber spacing, in-plane and out-of-plane boundary conditions, fiber type and the aspect ratio of the laminate.     

Off-axis transformation of the composite laminate stiffness properties

Most composite structures are orthotropic with respect to the major structural loading direction, i.e. the 0 ° fibres are along the principal bending axes of an aircraft wing (the spar line). The laminate stiffness properties are given with the laminate orthotropic axes aligned with the structural axes. If the orthotropic axes are not aligned to the structural axes, then the laminate stiffness properties are generated from classical laminated plate theory with individual ply angles rotated through the appropriae angle of transformation. In this discussion, the transformation of a laminate's stiffness from the on-axis position to an off-axis position is accomplished in one step. Two typical examples are shown to illustrate where and why such a transformation is used.     

Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers

In this paper, natural frequencies and vibrational mode shapes of variable stiffness composite laminate (VSCL) plates with curvilinear fibers are studied. In each ply of this rectangular VSCL, the fiber-orientation angle changes linearly with respect to the horizontal coordinate. To define the modes of vibration of the laminates, a new p-version finite element, which follows third-order shear deformation theory (TSDT), is employed. The convergence properties of this new element are investigated. Taking manufacturing restrictions regarding the fiber curvatures into account, maps of natural frequencies as functions of tow-orientation angles are determined in demonstrative examples. It is verified that the use of curvilinear fibers instead of the traditional straight fibers introduces a greater degree of flexibility, which can be used to adjust frequencies and mode shapes.     

Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.     

Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates

The advent of advanced fiber placement technology has made it possible, through the use of fiber steering, to exploit the anisotropic properties of composite materials to a larger extent than was previously possible. Spatial variation of stiffness can be induced by steering composite fibers in curvilinear paths to give beneficial load and stiffness distribution patterns. Buckling of composite panels is one area where fiber steering has been proven to be very effective. Fiber angles and predefined fiber angle variations are used in most of the research on fiber steered composites reported in the literature, however, from an optimization point of view it is attractive to design such variable stiffness (VS) structures in terms of lamination parameters (LPs). This results in a two-step design approach. In the first step a VS composite is designed in terms of LPs, and in the second step the LPs are converted into fiber angle distributions for each layer in the laminate. A methodology is proposed to convert a known LP distribution for a VS composite laminate into a realistic design in terms of fiber angles, with minimum loss of structural performance, whilst satisfying a constraint on in-plane fiber angle curvature. The proposed conversion process is formulated as an optimization problem and can be used for any number of equi-thickness plies. The methodology was tested by converting a known optimal LP design for a sample structure, a square plate under bi-axial compression into a fiber angle design. The effect of the in-plane curvature constraint, the number of layers in the laminate, and the choice of objective function for the conversion process were studied for a balanced symmetric lay-up.