A DYNAMIC RESPONSE PREDICTION MODEL OF FIBER-METAL HYBRID LAMINATED PLATES EMBEDDED WITH VISCOELASTIC DAMPING CORE UNDER LOW-VELOCITY IMPACT EXCITATION 1)

本文首次从解析角度建立了低速冲击激励下嵌入黏弹性阻尼芯层的纤维金属混杂层合板动态响应预测模型. 首先,结合经典层合板理论和冯$\cdot$卡门假设,建立了嵌入黏弹性芯层的纤维金属混杂层合板弹性损伤本构关系. 然后,将层合板受冲击时的变形分成接触和拉伸两个区域,在接触区域内,对金属层采用 Von Mises 失效准则,纤维层采用 Tsai-Hill 失效准则和对黏弹性层采用指数 Drucker-Prager 失效准则判断层合板损伤情况. 考虑不同材料层对冲击动态响应的贡献来修正两个变形区域的位移公式,进而计算结构因弹性变形产生的应变能,以及接触区域因塑性变形消耗的能量,实现每次失效事件发生后各层材料的能量、位移和冲击接触力的理论求解,并给出了结构动态响应分析的具体流程图. 最后,以嵌入 Zn33 黏弹性芯层的 TA2 钛合金混杂 T300 碳纤维/树脂层合板为研究对象,开展落锤冲击实验. 验证结果表明,理论预测与测试获得的冲击接触力、位移响应以及冲击载荷-位移曲线吻合较好,且关注的峰值点计算误差最大不超过 9%,进而验证了所提出的理论模型的有效性.     

纤维/金属网增强层板低速冲击损伤机理和演化

本文首先通过落锤低速冲击实验测试了纯玻璃纤维增强环氧树脂复合材料和304不锈钢丝网(SSWM)/玻璃纤维混杂复合材料的力学性能，探究了SSWM嵌入数量对混杂复合材料抗冲击性能的影响．随后采用Abaqus有限元软件建立了混杂复合材料的低速冲击模型，分别采用三维Hashin失效准则和Jason-Cook破坏准则模拟了纤维/基体和SSWM的损伤；建立了基于表面接触的内聚力模型来模拟界面分层；编写了VUMAT用户子程序定义混杂复合材料层合板的渐进失效过程．结果表明：相较于纯玻璃纤维增强环氧树脂层合板，SSWM/玻璃纤维混杂增强环氧树脂层合板的抗冲击性能更优，其中铺层形式为铺层III的混杂复合材料抗冲击性能最佳．通过对比发现有限元仿真结果与实验结果吻合良好，表明建立的模型适用于SSWM/玻璃纤维混杂增强环氧树脂复合材料低速冲击损伤的评估．通过分析仿真结果发现混杂复合材料的低速冲击损伤主要是冲击区域的纤维断裂、基体破坏和层间分层；SSWM通过吸收和传递冲击能量从而提升了混杂复合材料的抗冲击性能．     

编织Kevlar/Epoxy复合材料层合板在冲击荷载下的动态响应

通过编织Kevlar/Epoxy复合材料层合板的平头弹冲击实验，分析了结构在不同冲量下的变形失效模式以及结构的抗冲击性能。实验表明复合板的变形失效模式主要表现为:(1)弹性变形；(2)复合板表面嵌入失效及整体塑性大变形；(3)背面纤维拉伸断裂及分层失效。基于实验研究，运用LS-DYNA 971有限元程序对铺层数不同的复合板在冲击载荷作用下的动态响应过程进行了数值模拟，模拟结果与实验吻合较好，子弹作用区域边缘处首先发生近似圆形的嵌入失效，而在板背面发生近似正方形的破坏区域；计算中重点分析了铺层数对结构动力响应的影响，在一定冲量范围内，通过对铺层数的优化，能够有效地减小后面板挠度，提高结构的能量吸收效率，增强结构的抗冲击性能。     

含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应

研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite, FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场. 基于Hamilton 能量变分原理, 推导了动力学控制方程组. 通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态. 随后, 结合四阶龙格库塔法,拓展了两步摄动-伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明, 接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.      

玻璃纤维增强铝合金层合板低速冲击响应分析

基于ABAQUS/Explicit建立了GLARE的有限元模型,分析了其在低速冲击载荷作用下的动态响应,讨论了低速冲击过程中冲头与层合板之间的接触力随冲头位移的变化过程,并进一步分析了低速过程中结构的破坏过程及能量平衡。研究发现:冲头承受的载荷在冲击过程中会发生剧烈变化,且在击穿GLARE前,载荷受冲击速度影响很小;冲头的动能损失基本转化成了层合板结构增加的内能,主要包括铝合金板的塑性变形能、整体材料应变能、因损伤破坏吸收的能量;其中铝合金板的塑性变形能占比最高,可通过进一步设计铝合金板来提高GLARE的抗冲击性能。本文为GLARE层合板在结构冲击防护中的设计及应用提供了重要的参考依据。     

复合材料层压板低速冲击响应与损伤参数关系研究

论文针对复合材料标准冲击试样,用落锤试验手段研究了三种不同铺层层压板的低速冲击特性.分析了冲击响应接触力和能量的基本特性及变化规律,发现冲击能量相对于层压板阻抗水平的不同会导致接触力-时间曲线形状的差异.从冲击总能量、吸收能量和损伤耗散能量的角度阐释了能量和接触力与层压板分层损伤、凹坑变形的关系.发现损伤直接取决于吸收能量,与冲击总能量有较好的正相关关系.最大接触力是表征层压板损伤阻抗性能的一个门槛值.在一定能量条件下进行冲击,峰值接触力若达到层压板的接触力门槛值,则峰值接触力不再随损伤程度而增加,不能继续作为损伤的表征参数.同时,进行了冲击过程动态有限元模拟,得到的冲击响应参数曲线和损伤结果与试验结果有较好的对应关系.     

含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应

研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite,FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场.基于Hamilton能量变分原理,推导了动力学控制方程组.通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态.随后,结合四阶龙格库塔法,拓展了两步摄动-伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明,接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.     

复合材料层合板静压痕接触的等效弹性模量

在复合材料层合板静压痕接触问题中,由于层合板接触区域的纤维走向发生了变化,导致沿厚度方向的弹性模量产生变化并随着凹坑深度的增加而增大。本文建立压头压入后的力学分析模型,得到了与凹坑深度相关的沿厚度方向的等效弹性模量;将等效弹性模量代入目前被广泛接受的修正Hertz接触理论,建立了新的接触力与凹坑深度的关系式。通过与静压痕试验中接触力和凹坑深度的关系进行比较,结果表明该接触关系式能较好地描述接触力和凹坑深度的关系。与文献修正理论相比,在压痕较小时,本文的修正结果较好。     

短纤维增强复合材料层合板的高速冲击性能优化

本文以冲击体最大损失动能为目标函数,以纤维的方向角为设计变量,根据Hashin破坏准则并考虑四种损伤能量耗散对短纤维增强复合材料层合板的高速冲击性能进行优化.用ABAQUS有限元程序对短纤维增强复合材料层合板的高速冲击问题进行数值模拟,并采用遗传优化算法获得最优纤维方向角的布置.数值模拟及优化设计的结果表明:与传统的直线纤维增强复合材料层合板相比,合理的短纤维角度布置能有效提高复合材料层合板的抗冲击能力.研究结果可为短纤维复合材料抗冲击设计提供一定的帮助.     

高速冲击载荷下梯度金属泡沫夹芯梁的动态响应与失效

采用泡沫弹冲击加载实验对梯度金属泡沫夹芯梁结构开展了不同冲击强度下的动态响应和失效研究，分析了由三种不同密度泡沫铝组成的等面密度的五种不同梯度的夹芯结构在夹支边界条件下的抗高速冲击性能，结合三点弯曲实验，研究梯度效应对夹芯结构抗冲击性能的影响。研究表明：密度梯度对结构的失效过程和失效模式有着明显的影响，且夹芯梁结构的初始失效模式对结构整体响应和主要的能量吸收机制起着主导作用；当冲击条件不足以使得均质芯材发生压缩时，均质及负梯度夹芯结构初始失效模式为整体弯曲变形，低强度芯层位于前两层的梯度结构随着冲击强度的变化出现不同程度的局部芯层压缩；当冲击强度较低时，梯度结构通过丰富的局部失效表现出明显优于均质结构的抗冲击变形能力；当冲击强度大于临界值时，均质结构具有更好的抗冲击变形能力。通过合理地设计密度梯度实现逐层压缩吸能，能够有效的提升防护结构的抗冲击性能。     

APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange＇s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data, the results show：both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.

     

复合材料层压板低速冲击响应尺度效应数值模拟研究

为了研究尺度效应对于复合材料层压板在低速冲击作用下的动态响应和冲击损伤的影响,基于相似理论,建立了三种不同尺寸的层压板受冲击的三维有限元模型。在该模型中,针对层压板的面内损伤,采用改进的Chang-Chang准则进行预测;针对层压板内层间分层损伤,则使用Cohesive界面单元进行模拟。一旦复合材料层压板在低速冲击作用下产生损伤,则对出现损伤的区域进行材料参数退化。采用该模型对三种不同尺寸的层压板的冲击过程进行有限元分析,并将不同冲击速度下的冲击响应进行比较,得出了如下结论：在层压板内未发生冲击损伤时,冲击产生的挠度和冲击力与相似理论解十分吻合,一旦出现冲击损伤,则冲击力的变化与相似理论解有所差别;如果两个缩放模型的冲击速度之比等于缩放比例的平方根,则两个模型中的相对分层尺寸基本是相同的,这个结果与已有的实验结果吻合;而对冲击后面内损伤的分析表明,其损伤尺寸不符合这一相似规律。     

Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory

In a recent paper, Cho and Kim [Journal of Applied Mechanics] proposed a higher-order cubic zigzag theory of laminated composites with multiple delaminations. The proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. In this work, we investigate the dynamic behavior of laminated composite plates with multiple delaminations. A four-node finite element based on the efficient higher-order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response. Through the dynamic version of the variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method. To prevent penetration violation at the delamination interfaces, unilateral contact constraints by Lagrange multiplier method are applied in the time response analysis. The present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations.     

Optimum design of laminated composite foam-filled sandwich plates subjected to strength constraint

Optimum design of laminated composite sandwich plates with both continuous (core thickness) and discrete (layer group fiber angles and thicknesses) design variables subjected to strength constraint is studied via a two-level optimization technique. The strength of a sandwich plate is determined in a failure analysis using the Tsai–Wu failure criterion and the finite element method which is formulated on the basis of the layerwise linear displacement theory. In the first level optimization of the design process, the discrete design variables are temporarily treated as continuous variables and the corresponding minimum weight of the sandwich plate is evaluated subject to the strength constraint using a constrained multi-start global optimization method. In the second level optimization, the optimal solution obtained in the first level optimization is used in the branch and bound method for solving a discrete optimization problem to determine the optimal design parameters and the final weight of the plate. Failure test of laminated composite foam-filled sandwich plates with different lamination arrangements are performed to validate the proposed optimal design method. A number of examples of the design of laminated composite foam-filled sandwich plates are given to demonstrate the feasibility and applications of the proposed method.     

Influence of rotatory inertia on dynamic stability of the viscoelastic symmetric cross-ply laminated plates

The dynamic stability problem of the symmetrically laminated cross-ply plates made of the viscoelastic Voigt–Kelvin material, compressed by time-dependent stochastic membrane forces, is investigated. The effect of rotatory inertia is included in the present formulation. It is assumed that all elastic moduli have the same retardation times. By using the direct Liapunov method, bounds of the almost sure stability of cross-ply plates as a function of viscous damping coefficient, retardation time, variances of the stochastic forces, ratio of the principal lamina stiffnesses, number of layers, plate aspect ratio, cross-ply ratio and intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as an harmonic process with random phase.     

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.     

考虑面内破坏过程的含分层损伤复合材料加筋层合板的动力响应

基于复合材料层合板一阶剪切理论，推导了复合材料层合板单元的刚度阵和质量阵列式；同时采用了Adams应交能法与Rayleigh阻尼模型相结合的方法，构造了相应的阻尼阵列式；为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象，建立了含分层损伤复合材料加筋层合板动力分析的分层分析模型和虚拟界面联接模型。在上述模型和理论基础上，采用了Tsai提出的刚度退化准则和动力响应分析的精细积分法，对含分层损伤复合材料加筋层合板结构进行了动力响应和破坏分析。通过算例，分别讨论了外载频率、分层位置，以及破坏过程的刚度退化对含损伤复合材料加筋层合板动力响应特征的影响，得到了一些具有理论和工程价值的结论。