Numerical analysis of edge effect in laminated composite structures

In order to further study free edge effect in composite laminates, a new method is developed. This method is based on the perturbation and modified method of least square. In this paper, we emphatically discuss the solution within the boundary layer region, the socalled inner solution. As an example, we will discuss structures composed of two and four symmetric laminates. Project Supported by the Science Fund of the Chinese Academy of Science.     

Micromechanics-based constitutive modeling for unidirectional laminated composites

A micromechanics-based constitutive model is developed to predict the effective mechanical behavior of unidirectional laminated composites. A newly developed Eshelby’s tensor for an infinite circular cylindrical inclusion [Cheng, Z.Q., Batra, R.C., 1999. Exact Eshelby tensor for a dynamic circular cylindrical inclusion. J. Appl. Mech. 66, 563–565] is adopted to model the unidirectional fibers and is incorporated into the micromechanical framework. The progressive loss of strength resulting from the partial fiber debonding and the nucleation of microcracks is incorporated into the constitutive model. To validate the proposed model, the predicted effective stiffness of transversely isotropic composites under far field loading conditions is compared with analytical solutions. The constitutive model incorporating the damage models is then implemented into a finite element code to numerically characterize the elastic behavior of laminated composites. Finally, the present predictions on the stress–strain behavior of laminated composite plate containing an open hole is compared with experimental data to verify the predictive capability of the model.     

STAGS computational procedure for progressive failure analysis of laminated composite structures

Non-linear analyses are difficult simulations to perform and place increased demands not only on the computational systems but also on the analyst. The number of possible problems and/or difficulties increases significantly compared to those for linear elastic analyses. Combined material and geometric non-linearities challenge the analyst and the solution algorithms. Progressive failure and damage propagation for composite structures result in even more complexities due to the discrete, abrupt changes in local material stiffness. Analysts need to interrogate the computed solutions carefully based on their understanding of structural mechanics, material behavior, computational procedures and non-linear phenomena to distill correct physics from such simulations. This paper describes the computational strategy incorporated into the STAGS non-linear finite element analysis code with special emphasis on progressive failure analysis of laminated composite structures. Results for selected laminated composite structures are used to demonstrate the PFA capability.     

Multicriteria optimization of laminated composite material structures

The search for the optimum design of a given structure is a basic aspect of structural analysis. In recent years there has been a renewed interest in structural optimization, particularly in the field of composite material structures. The aim is often to obtain the best solution that is able to respect both the technical and the economic requirements. In this paper, the optimization process is pursued as the determination of the Pareto-optimal curves for composite material structures. The problem has been tackled by means of an analytical optimization methodology (trade-off method) appropriately transformed into a design procedure. A sensitivity analysis is also performed, in order to try out the measure in which the optimal solutions are affected by the variation of the design variables. Two examples are presented, concerning a hemispherical shell and a cylindrical shell.

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Sommario Molti problemi della ricerca dell'ottimo progettuale presentano la difficoltà di coinvolgere nella soluzione più obiettivi da considerare simultaneamente. Il problema risulta piuttosto complesso (in particolare nel caso di strutture in materiale composito) quando gli obiettivi, spesso contrastanti, hanno natura diversa e quindi risultano non facilmente combinabili fra loro. Tale problema si pone spesso quando si vuole da un lato aumentare l'affidabilità strutturale e dall'altro diminuire i costi della struttura. Nel presente articolo, vengono affrontati alcuni aspetti dell'ottimizzazione di strutture in materiale composito: a tale scopo viene presentata una procedura di ottimizzazione per problemi multi-obiettivo che, avvalendosi del Trade-off method, è in grado di determinare la curva degli ottimi di Pareto. Successivamente viene effettuata un analisi di sensitività allo scopo di valutare la sensibilità delle soluzioni ottimali nei confronti della aleatorietà delle variabili di progetto. Vengono presentati in tal senso due esempi relativi a strutture in materiale composito.

     

飞机复合材料层压板结构中的广义强度准则

通过对经典复合材料结构强度理论和准则在层压板上的适用性计算和试验对比研究,指出了在层压板上采用经典强度理论所得计算结果与试验结果的差异。并分析了产生这种差异的原因,主要是经典强度准则表达武中采用的无拉剪耦合假设和层与层之间理想粘接假设,只适用于单层板或正交各向异性板。本文提出了一种广义强度准则的思想,其核心是放松正交各向异性约束条件和通过试验测定强度参数,而在实际飞机结构中的准正交各向异性层压板结构设计上仍可使用经典层压板强度准则。     

Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity

This work presents a new multi-layer laminated composite structure model to predict the mechanical behaviour of multi-layered laminated composite structures. As a case study, the mechanical behaviour of laminated composite beam (90°/0°/0°/90°) is examined from both a static and dynamic point of view. The results are compared with the model “Sinus” and finite element method studied by Abou Harb. Results show that this new model is more precise than older ones as compared to the results by the finite element method (Abaqus). To introduce continuity on the interfaces of each layer, the kinematics defined by Ossadzow was used. The equilibrium equations and natural boundary conditions are derived by the principle of virtual power. To validate the new proposed model, different cases in bending, buckling and free vibration have been considered.     

NONLINEAR THREE-DIMENSIONAL ANALYSIS OF COMPOSITELAMINATED PLATES

ＮＯＮＬＩＮＥＡＲＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＡＮＡＬＹＳＩＳＯＦＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＤＰＬＡＴＥＳ￥(江晓禹，张相周，陈百屏)ＪｉａｎｇＸｉａｏｙｕ；（ＳｏｕｔｈｗｅｓｔｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ６...     

超声速复合材料层合壁板结构的颤振特性分析

对超声速复合材料壁板结构的气动弹性颠振特性进行了分析研究.采用Hamilton原理和假设模态法建立结构的运动方程,采用活塞理论模拟超声速非定常气动力,通过求解本征值问题,得到结构的固有频率和阻尼比等物理量.数值计算了结构无量纲固有频率随气动压力的变化曲线,确定颤振临界气动压力(或颤振速度),并计算了结构的受迫振动时间响应历程曲线,分析比较了不同纤维铺设方式和不同铺设角度对超声速复合材料壁板结构气动弹性稳定性的影响.本文研究结果对超声速飞行器壁板结构的气动弹性稳定性分析和设计具有理论参考价值.     

复合材料层合圆柱壳的有限元分析

本文根据Reissner-Mindlin型的全局位移场(一阶和三阶)，应用有限元预测一修正法，数值计算和分析了机械载荷作用下复合材料层合圆柱壳的挠度和横向剪应力。首先按照一般的有限元分析过程(没有引入剪切修正系数)计算出层合圆柱壳的挠度预测值；然后利用Lagrange插值构造横向剪应力的一般形式，使得满足层间连续和表面上为零的条件，通过最小二乘法拟合三维应力平衡方程获得横向剪应力；最后在单元上计算和引入剪切修正系数，再经过有限元分析计算出层合圆柱壳的挠度修正值。数值计算结果与三维线弹性解的比较表明，挠度修正值和横向剪应力的精度是十分满意的。     

Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.     

An extended stress-based method for orientation angle optimization of laminated composite structures

Orientation optimization plays an important role in the lay-up design of composite structures.Earlier orientation optimization methods face the main problem of huge number of design variables.Recently,a patch concept is proposed to reduce the number of design variables.However,the traditional stress-based method can not deal with patch orientation optimization of composite structures.In this paper,we propose an extended stress-based method to deal with such problems.The considered problems are to minimize the mean compliance under multiple load cases or to maximize the eigenvalues of a composite structure.Four numerical examples are solved to demonstrate the efficiency of the new method.It is shown that the new method has the ability to deal with constraints on orientation angle,such as symmetric,antisymmetric and discrete orientation angle constraints.The iteration is less time-consuming because no sensitivity analysis is needed and a quick convergence rate can be achieved.     

Vibration analysis of a stepped laminated composite Timoshenko beam

The goal of this study is to investigate the vibration characteristics of a stepped laminated composite Timoshenko beam. Based on the first order shear deformation theory, flexural rigidity and transverse shearing rigidity of a laminated beam are determined. In order to account for the effect of shear deformation and rotary inertia of the stepped beam, Timoshenko beam theory is then used to deduce the frequency function. Graphs of the natural frequencies and mode shapes of a T300/970 laminated stepped beam are given, in order to illustrate the influence of step location parameter exerts on the dynamic behavior of the beam.     

Problem of the dynamics and stability of laminated composite structures with interphase delamination

International Applied Mechanics -     

Stress and strain analysis in elastic laminated composite beams

A detailed theoretical analysis of stress and strain in fiber-reinforced, laminated composite beams is presented within the framework of three-dimensional theory of thermo-elastodynamics. Each of reinforcing and matrix layers is made of different anisotropic material and is of different constant thickness. By the use of a variational theorem, the fully non-linear governing equations are consistently obtained for the case when the displacement components of each layer are taken to vary linearly over the cross-section of the layer. Then the linear version of the resulting equations, including the uniqueness of its solution is given, and the general results are briefly discussed.

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Zusammenfassung In der vorliegenden Abhandlung wird eine detaillierte Spannungs-und Verzerrungsuntersuchung von faserverstärkten laminierten Balken innerhalb der dreidimensionalen thermo-elastodynamischen Theorie durchgeführt. Für jede Verstärkungs-und Bindeschicht wird unterschiedliches anisotropes Verhalten und unterschiedliche Schichtstärke vorausgesetzt. Unter Annahme eines linearen Verlaufs der im Querschnitt liegenden Verformungskomponenten über jede einzelne Schicht werden mit Hilfe eines Satzes der Variationsrechnung die vollständigen nichtlinearen Grundgleichungen abgeleitet. Damit ist auch die linearisierte Form der Gleichungen mit eindeutiger Lösung bestimmt. Eine kurze Untersuchung der Ergebnisse in ihrer allgemeinen Form ist angeschlossen.

     

复合材料层合板壳的非线性热动态响应分析

本文基于高阶剪切变形理论，考虑同天应变和横向剪切应变的影响，对受热复合材料层合板壳的非线性热动态响应进行分析，计及了转动惯量的影响，给出了通用性较好的Ｃ＾０类有限元公式，文中数值算同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性，文中还就层合板的边界条件、纵厚比及铺设角度对非线性热动态响应的影响进行了分析。     

Numerical analysis of delamination growth for stiffened composite laminated plates

A study of postbuckling and delamination propagation behavior in delaminated stiffened composite plates was presented. A methodology was proposed for simulating the multi-failure responses, such as initial and postbuckling, delamination onset and propagation, etc. A finite element analysis was conducted on the basis of the Mindlin first order shear effect theory and the von-K6rm~n nonlinear deformation assumption. The total energy release rate used as the criteria of delamination growth was estimated with virtual crack closure technique (VCCT). A self-adaptive grid moving technology was adopted to model the delamination growth process. Moreover, the contact effect along delamination front was also considered during the numerical simulation process. By some numerical examples, the influence of distribution and location of stiffener, configuration and size of the delamination, boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated. The method and numerical conclusion provided should be of great value to engineers dealing with composite structures.     

Analysis of composite laminated plates

In the static and dynamic analysis of composite laminates, a theory for the laminated plates is presented in this paper. Because the deflection W_b which is caused by the classical bending deformation and the deflection W₅ which is caused by the shear deformation are divided from the total deflection W in the theory, this makes it easy to solve the governing equations. In addition, this theory is convenient for the discussion and analysis of the effects of transverse shear deformations on bendings, vibrations and stabilities of laminated plates.