Analysis of first ply failure in composite laminates

The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. It is found that cracks may propagate in two directions on planes which are parallel to the fiber axis and perpendicular to the midplane of the ply. In general, crack propagation in the direction of the fiber axis controls the strength of thin plies, while cracking in the direction perpendicular to the fiber axis determines the strength of thick plies. The theory relates ply thickness, crack geometry and ply toughness to ply strength. It predicts a significant increase in strength with decreasing ply thickness in constrained thin plies. The strength of thick plies is found to be constant, but it may be reduced by preexisting damage. Results are illustrated by comparison with experimental data.     

Nonlinear free vibration of a composite rectangular specially-orthotropic plate with variable fiber spacing

The geometrically nonlinear free vibration of a composite rectangular plate with variable fiber spacing is investigated. The investigation is limited to a single ply composite having straight and parallel fibers. The fibers are distributed more densely in the central region where high stiffness is needed than in other regions. The assumptions of von Karman’s nonlinear thin plate theory are made. The problem is solved numerically using the hierarchical finite element method. The nonlinear equations of free motion are mapped from the time domain to the frequency domain using the harmonic balance method. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained for simply supported and clamped composite square plates with three variable distributions of E-Glass, Graphite, and Boron fibers in Epoxy matrices. The efficiency of the hierarchical finite element procedure is demonstrated through convergence and comparison with published data. The variable fiber spacing, fiber volume fraction, type of fiber material, and boundary conditions are shown to influence the hardening behavior.     

Nonlinear analysis via global–local mixed finite element approach

A computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh–Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh–Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure. The potential of the global–local mixed approach and its advantages over global–local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.     

Experimental investigation into dynamic axial impact responses of double hat shaped CFRP tubes

This paper aims to explore the dynamic responses and crashing characteristics of double hat shaped tubes made of weave carbon fiber reinforced plastic (CFRP). Experimental investigations were carried out into three different thicknesses and lengths of the composite tubes fabricated by the bladder molding process. Three distinct failure modes, classified as progressive end crushing, mid-length collapse and overlap opening, were observed in the dynamic crushing tests. Unlike continuous splaying fronds observed in the quasi-static tests, dynamic tests exhibited a number of fragment segments in the progressive end crushing mode. It is shown that the ply number was a critical parameter affecting the failure mode and energy absorption capability. The increase in ply number led to increases in the peak load and specific energy absorption (SEA); whereas the tubal length seemed insensitive to energy absorption capability. Compared to the quasi-static cases, the dynamic impact tests resulted in the higher peak load (increased from 46 % to 125 %) and lower SEA (reduced from 21 % to 33 %) for the tested tubes.     

Wide‐Range Tunable Dynamic Property of Carbon‐Nanotube‐Based Fibers

A carbon nanotube (CNT) fiber is formed by assembling millions of individual tubes. The assembly feature provides the fiber with rich interface structures and thus various ways of energy dissipation, as reflected by the nonzero loss tangent (>0.028–0.045) at low vibration frequencies. A fiber containing entangled CNTs possesses higher loss tangents than a fiber spun from aligned CNTs. Liquid densification and polymer infiltration, the two common ways to increase the interfacial friction and thus the fiber's tensile strength and modulus, are found to efficiently reduce the damping coefficient. This is because the sliding tendency between CNT bundles can also be well suppressed by a high packing density and the formation of covalent polymer cross‐links within the fiber. The CNT/bismaleimide composite fiber exhibits the smallest loss tangent, nearly the same as that of carbon fibers. At a higher level of the assembly structure, namely a multi‐ply CNT yarn, the interfiber friction and sliding tendency obviously influence the yarn's damping performance, and the loss tangent can be tuned within a wide range, similar to carbon fibers, nylon yarns, or cotton yarns. The wide‐range tunable dynamic properties allow new applications ranging from high quality factor materials to dissipative systems.     

A NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF VEHICLES MOVING ON FLEXIBLE STRUCTURES HAVING GAPS

A numerical method is presented for the dynamic analysis of vehicles moving on flexible structures which contain gaps. The Lagrange multipliers associated with the kinematic constraints of the vehicle components and the contact forces between the rigid wheels of the vehicle and the flexible structures are simultaneously computed with the solutions of the equations of motion by using the iterative schemes. On the kinematic joints and on the possible contact points the velocity and acceleration constraints as well as the displacement constraints are satisfied by the monotone reductions of the corresponding error vectors. And a well-developed simple one-step time integration of ordinary differential equation is employed for the solution of the equations of motion. Convergences of the iterative schemes are analysed and numerical simulations are conducted. © 1997 by John Wiley & Sons, Ltd.     

Response of gradient-viscoelastic bar to static and dynamic axial load

Summary. The response of a bar to static or dynamic axial load is studied analytically on the basis of a simple linear theory of gradient viscoelasticity. The governing equations of axial equilibrium and motion are first obtained by combining the basic equations. They are also obtained by a variational statement, which provides in addition all possible boundary conditions. A correspondence principle between the gradient elastic and gradient viscoelastic formulation and solution is established. Thus, the Laplace transformed with respect to time viscoelastic solution is obtained from the corresponding elastic one by simply replacing the elastic modulus by its Laplace transform times the Laplace transform parameter. The time domain response is finally obtained by a numerical inversion of the transformed solution. Two boundary value problems, one quasi-static and one dynamic, are studied and the gradient viscoelasticity effect on the solutions is assessed.     

变截面复合材料薄壁转轴在不同约束下的振动与稳定性

该文针对复合材料变截面薄壁旋转轴在不同约束下的振动与稳定性问题,提出了一个动力学模型。基于变分渐进法和拉格朗日方程,推导了复合材料变截面薄壁转轴的自由振动方程。在转轴的结构模型中,综合考虑了扭转、拉伸和弯曲引起的截面翘曲的影响。采用伽辽金法,分析了截面按线性或者抛物线变化的变截面旋转轴的固有频率和临界转速,其中还考虑了一端固定一端自由和一端固定一端铰支两种边界条件以及复合材料铺层角的影响。此外,通过对比分析模型的计算结果与商用有限元软件ANSYS的结果,该文所提出的分析模型的有效性在一定程度上得到了验证。     

剪式可展机构非线性动力学分析的子系统方法

剪式可展机构由相互耦合的闭环子系统构成,针对这种拓扑结构的多体系统,给出了基于子系统模型的非线性动力学建模方法。将剪式可展机构分解为多个简单子系统,推导出子系统等效质量矩阵和等效力向量,通过子系统间的反向递推求解整个多体系统的等效质量矩阵和等效力向量,从而将大规模运动方程转化为简单运动方程,缩减了求解规模。所建立的子系统模型可以重复使用,且当子系统的结构或子系统个数发生变化时,便于整个剪式可展机构模型的修改,易于程式化建模。与传统方法的对比验证了该方法的正确性。     

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques based on the combined use of finite elements and the classical Bubnov–Galerkin approximation are presented for predicting nonlinear steady-state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees-of-freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global-temperature modes, or basis vectors. The Bubnov–Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global–temperature modes). The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal–temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem-adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations. The potential of the proposed reduction methods for the solution of large-scale, nonlinear steady-state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer. This study shows that the use of the uniform-temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large-scale, nonlinear thermal problems.     

横向流体激励下绳索的动力学分析

通过分析横向流体对绳索的作用力 ,建立了绳索的动力学方程。借助 Pilipchuk坐标变换 ,使具有零刚度的绳索动力学方程包含静刚度项 ,继而使用两变量摄动方法对绳索运动进行近似分析。然后 ,用数值方法考核了近似分析结果的可靠性 ,讨论了流体速度、绳索质量、重力和初始状态等对绳索运动行为的影响。     

Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM

In this paper, the nonlinear behavior of symmetric and antisymmetric cross ply, thin to moderately thick, elastic rectangular laminated plates resting on nonlinear elastic foundations are studied using differential quadrature method (DQM). The first-order shear deformation theory (FSDT) in conjunction with the Green’s strain and von Karman hypothesis are assumed for modeling the nonlinear behavior. Elastic foundation is modeled as shear deformable with cubic nonlinearity. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton–Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Comparisons are made and the convergence studies are performed to show the accuracy of the results even with a few number of grid points. The effects of thickness-to-length ratio, aspect ratio, number of plies, fiber orientation and staking sequence on the nonlinear behavior of cross ply laminated plates with different boundary conditions resting on elastic foundations are studied.     

A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters

The purpose of this paper is to propose an effective solution scheme of simultaneous optimization design of layup configuration and fiber distribution for maximum stiffness design of laminated plates. Firstly, a numerical analysis of the lamination parameters feasible region for a laminated plate consisting of various given number of ply groups (each ply group may have different thickness and all the fibers in one ply group are orientated in an identical direction) is carried out, and it is found that the feasible region based on only a few ply groups is very close to the overall one determined by infinite plies. Therefore, it is suggested that the feasible region of lamination parameters of a laminated plate could be approximately determined by the layup configuration of least ply groups. Secondly, a two-step simultaneous optimization scheme of layup configuration and fiber distribution for maximum stiffness design of laminated plates is proposed. Accordingly, by using ply thickness, fiber orientation angle and fiber volume fraction in a laminated plate of least ply groups as design variables, the optimal lamination parameters for maximum stiffness is obtained. Then, taking the optimal lamination parameters as the design objective, a detailed layup design optimization is implemented by considering some limitations on manufacturing, such as preset ply thickness, and specific fiber orientation angle and a limited maximum number of consecutive plies in the same fiber orientation. Numerical examples are also presented to validate the proposed two-step optimization scheme.     

复合材料变截面旋转薄壁悬臂梁自由振动分析

基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。     

振动平板夯周期运动的稳定性与分岔

建立振动平板夯的两自由度动力学模型,采用不同的微分方程对其工作历程进行分段描述。并通过四阶Runge-Kutta法,仿真分析了其周期运动的稳定性以及通过倍周期分岔进入混沌的过程。讨论了系统参数对振动平板夯周期运动和混沌的影响,为提高振动平板夯性能设计提供了依据。     

碳纤维增强树脂复合材料和铝合金温热自冲铆接工艺及接头力学性能

为研究传统自冲铆(SPR)工艺连接碳纤维增强树脂复合材料(CFRP)和铝合金的损伤问题,制备三种典型铺层结构的自冲铆接头,研究铺层结构对接头表面宏观损伤形貌的影响。在不同测试温度下对CFRP进行力学试验,研究温度对CFRP力学性能及失效的影响。基于CFRP的温热力学性能,以减小接头损伤为目的,创新性提出了CFRP和铝合金的温热自冲铆接(WSPR)工艺,对比了两种铆接工艺获得接头中CFRP的损伤差异。制备CFRP和铝合金的WSPR接头,研究铺层角度对接头力学性能和失效过程的影响。研究表明:常温下铆接时,钉头附近区域易出现宏观裂纹缺陷,主要以平行于纤维方向的基体裂纹和垂直于纤维方向的纤维裂纹形式存在。在树脂基体的玻璃化转变温度下,CFRP在横向和剪切方向的延展性大幅度提高,导致WSPR接头的CFRP表面无宏观裂纹,同时减小了分层损伤面积。铺层角度影响接头的拉剪力学性能及失效过程,[0/90/0]_s铺层接头的力学性能最优。      

克服纤维桥连对GIC影响的隔离层法

本文分析了纤维桥连产生的原因和它对Ⅰ型层间断裂韧性G_IC的影响,提出了一种克服纤维桥连的“隔离层”法,从试件铺层设计入手,力图将纤维嵌套的可能性减到最低.有限元计算结果表明,隔离层的引入并没有改变层间裂纹尖端的应力分布和应力集中,试件的弯曲刚度计算表明,当隔离层的铺层角取±10°～±20°时,可以使±θ隔离层带来的试件弯扭耦合效应降到最低.实验结果证明了这种方法的可行性.     

Optimum design of formable CFRP sheets by generic algorithm and FE analysis by homogenization of multilayered structure with macroscopic anisotropy

A new method for designing carbon-fiber-reinforced plastic (CFRP) sheets with a suitable ply structure for stamping is proposed. This method combines a generic algorithm with a three-dimensional finite element method (FEM) to reproduce a layered structure by homogenizing the fiber structure with elastic-plastic anisotropy of each layer. The maximum strain is used as a fracture index to evaluate the severity of sheet deformation under stamping. The ply structure of the CFRP is optimized for elliptic cup drawing, and the optimized ply structure is validated experimentally. Through the experimental validation, it is proven that the proposed method gives acceptable results for the optimization of the ply structure of thermosetting CFRP sheets for cold/warm stamping.     

Dynamic characterization of the thickness-tapered laminated plant fiber-reinforced polymer composite plates

Evolution of the laminated woven natural fiber fabric-reinforced polymer composite structures makes a way to the development of the non-uniform laminated composite structures in order to achieve the stiffness variation throughout the structure. An attempt is made in this work to carry out the experimental and numerical investigations on the dynamic characteristics of the thickness-tapered laminated woven jute/epoxy and woven aloe/epoxy composite plates. The governing differential equations of motion for the thickness-tapered laminated composite plate are developed using the h-p version FEM based on higher order shear deformation theory. The validation of the present finite element formulation is carried out by comparing the natural frequencies obtained using the finite element formulation with those natural frequencies determined experimentally. The developed model is further validated with the available literature works on tapered composite plate to confirm the efficiency of h-p version FEM. This work also explores the study of the vibrational characteristics of composite plates under the influence of plant fiber’s transverse isotropic material characteristics and porosity associated with plant fiber composites through the elastic constants evaluated in the author’s previous work. Also the influences of aspect ratios, ply orientations, and taper angles under various end conditions on the natural frequencies of the woven jute/epoxy composite plate are studied using the present finite element formulation. The forced vibration response of the thickness-tapered laminated woven jute/epoxy composite plate under the harmonic force excitation is carried out considering CFCF and CFFF end conditions.