Optimum design of composite laminates

A new procedure for the optimum layup design of composite laminates is described in this paper. In this method the global optimum search and local relaxing constraints are adequately combined together. The design variables are divided and applied in separate processes. A 16-node hybrid semi-Loof element model is used in the global structure analysis. The iterative complex method is adopted in the optimization. The method is suitable for the minimum weight design of a laminate subjected to the strength and stiffness constraints under multiple loading. The numerical results demonstrate the high efficiency and reliability of the present method.The project was supported by National Natural Science Foundation of China     

基于铺层参数的铺层方式与纤维分布协同优化的层合板最大刚度设计

纤维增强复合材料层合板的弹性性质依赖于单层板的纤维含量(体分比)以及铺层方式(总层数、各单层的厚度与铺设方向)。本文研究在给定材料用量条件下层合板的最大刚度设计问题,采用铺层参数作为铺层方式的描述参数、以铺层参数和单层板纤维含量体分比在层合板面内的分布的描述参数为设计变量,以层合板的柔顺性最小为目标,建立了铺层方式和纤维分布协同优化的层合板最大刚度设计问题的提法和求解方法,给出了具有最大刚度的层合板最优铺层方式和纤维含量的分布规律的设计实例。     

Deterministic and stochastic motion of a ball between retainers

International Applied Mechanics -     

On refined theories of composite laminates

Summary A review of the developments in the displacement-based theories of plates is presented. It is shown that many of the third-order theories reported in the literature are based on the same or equivalent displacement field, and are thus lead to the same results. A strain-consistent third-order theory is presented, which contains most existing third-order plate theories as special cases. The layer-wise laminate plate theory proposed by the author is also reviewed. The accuracy of the theories is evaluated by comparing the numerical solutions with those of the three-dimensional elasticity theory.

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Sommario Si passano in rassegna varie teorie delle piastre basate sugli spostamenti. Viene mostrato che molte delle teorie del terzo ordine che compaiono nella letteratura sono basate sullo stesso (o un equivalente) campo di spostamenti, e quindi conducono agli stessi risultati. Viene quindi presentata una teoria del terzo ordine coerente nelle deformazioni, che contiene come casi particolari la maggior parte delle esistenti teorie del terzo ordine. Viene anche rivista la teoria delle piastre a strati già proposta dall'autore. L'accuratezza delle teorie è valutata paragonando le soluzioni numeriche con quelle della teoria tri-dimensionale dell'elasticità.

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Invited Lecture presented at New Developments in Structural Mechanics, International Meeting in memory of Professor Manfredi Romano; Catania, Italy, 4–6 July 1990.     

Snap-through of unsymmetric fiber-reinforced composite laminates

An approximate theory based on assumed strain and displacement fields, the Rayleigh–Ritz technique, and virtual work is used to predict the snap-through forces and moments for three families of unsymmetric fiber-reinforced composite laminates. Unsymmetric laminates generally have two stable equilibrium configurations when cooled from their elevated cure temperature, and it is the moment required to snap the laminate from one stable configuration to the other that is the subject of this paper. A simple force-controlled experiment is described which is used to measure the snap-through moment and the characteristics of the configuration change, by way of strains, in four laminates. The correlation between predicted results and experimental measurements is quite good, both in terms of moment levels and in terms of strain response.     

Exact solutions for magneto-electro-elastic laminates in cylindrical bending

Analytical solutions are derived for the cylindrical bending of multilayered, linear, and anisotropic magneto-electro-elastic plates under simple-supported edge conditions. We construct the general solution in terms of a simple formalism for any homogeneous layer, from which any physical quantities can be solved for the given boundary conditions. For multilayered plates, we derive the solution in terms of the propagator matrices. A special feature of cylindrical bending, which distinguishes itself from the three-dimensional plate problem, is that the associated eigenvalues for any homogeneous layer are independent of the sinusoidal mode, and thus need to be solved only once. Typical numerical examples are also presented for a piezomagnetic plate, a two-layered piezoelectric/piezomagnetic plate, and a four layered piezoelectric/piezomagnetic plate, with different span-to-thickness ratios. In particular, the piezoelectric and piezomagnetic fields show certain interesting features, which give guidance on the development of piezoelectric/piezomagnetic thin-plate theories. Furthermore, it is shown that the variations of the elastic, electric, and magnetic quantities with thickness depend strongly upon the material property and layering, which could be useful in the analysis and design of smart composite structures with sensors/actuators.     

Fracture of composite laminates by three-point bend

An experimental investigation has been carried out on the fracture behavior of T300/5208 graphite/epoxy laminates using three-point bend and tension tests. One laminate, a [0/±45/90] _ns orientation, was used withn=1 for tension specimens andn=4 and 8 for bend specimens. The crack-growth-resistance curve was constructed by compliance matching from crack-opening displacement and load data obtained from three-point bend tests. The value of effective crack length and corresponding crack resistance at onset of instability was nearly constant and independent of the initial crack length and laminate thickness. Experimental data from both bend and tension tests correlated reasonably well to the average-stress-failure criterion. Data were also compared with results found in the literature.     

Mixed-mode failure of composite laminates with cracks

The behavior of quasi-isotropic graphite/epoxy laminates with cracks subjected to various biaxial-stress fields was studied experimentally. This was accomplished by uniaxial tensile loading of specimens with cracks of various orientations with the loading axis. It was found that the critical stress-intensity factor, based on a projected crack length increased by a characteristic damage dimension, is nearly constant with stress biaxiality and initial crack length. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

SMA-induced snap-through of unsymmetric fiber-reinforced composite laminates

A theory is developed and experiments designed to study the concept of using shape memory alloy (SMA) wires to effect the snap-through of unsymmetric composite laminates. The concept is presented in the context of structural morphing, that is, a structure changing shape to adjust to changing conditions or to change operating characteristics. While the specific problem studied is a simplification, the overall concept is to potentially take advantage of structures which have multiple equilibrium configurations and expend power only to change the structure from one configuration to another rather than to continuously expend power to hold the structure in the changed configuration. The unsymmetric laminate could be the structure itself, or simply part of a structure. Specifically, a theory is presented which allows for the prediction of the moment levels needed to effect the snap-through event. The moment is generated by a force and support arrangement attached to the laminate. A heated SMA wire attached to the supports provides the force. The necessary SMA constitutive behavior and laminate mechanics are presented. To avoid dealing with the heat transfer aspects of the SMA wire, the theory is used to predict snap-through as a function of SMA wire temperature, which can be measured directly. The geometry and force level considerations of the experiment are discussed, and the results of testing four unsymmetric laminates are compared with predictions. Laminate strain levels vs. temperature and the snap-through temperatures are measured for the these laminates. Repeatability of the experimental results is generally good, and the predictions are in reasonable agreement with the measurements.     

Fracture process zone concept and delamination of composite laminates

Delaminations occur at the free edges of composite laminates because of high interlaminar stresses, which develop due to a mismatch in elastic properties between adjacent plies and the limited toughness of the matrix. The process of delamination is modelled using the concept of a fracture process zone. A finite element analysis that can be used with a constant or linear stress-displacement relationship within the fracture process zone is presented. It is found that the simple constant stress model gives an accurate prediction of the delamination on the free edge of a tensile specimen.     

复合材料层板的抗贯穿机理与模拟研究

为了研究树脂基纤维增强复合材料层板的抗侵彻贯穿机理和动态力学行为与抗侵彻毁伤的关系, 通过球形破片模拟弹贯穿实验表征了复合材料层板抗高速侵彻的吸能特性;通过高速摄影技术分析了层板 贯穿过程的瞬态变形失效特点;采用CT扫描成像及SEM 电镜分析等手段研究了复合材料层板的抗贯穿破 坏耗能模式。实验结果显示,高速冲击下层板抗贯穿吸能与入射速度成正比;高速侵彻过程是复合材料层板 高应变率变形的动态过程,高应变率动态力学行为对复合层板抗贯穿吸能特性影响显著;冲击波在层板中的 传播特性决定了不同破坏模式阶段的划分以及损伤区域的范围。基于复合层板高速贯穿下的动力学瞬态分 析,建立了复合层板抗高速侵彻吸能的两阶段动态破坏模型,模型计算值与实验值符合良好。研究结果表明, 应变率效应与惯性效应在复合材料层板抗侵彻性能分析中是不可忽视的2个关键因素。     

Finite element modeling of consolidation of composite laminates

Advanced fiber reinforced polymer composites have been increasingly applied to various structural components. One of the important processes to fabricate high performance laminated composites is an autoclave assisted prepreg lay-up. Since the quality of laminated composites is largely affected by the cure cycle, selection of an appropriate cure cycle for each application is important and must be optimized. Thus, some fundamental model of the consolidation and cure processes is necessary for selecting suitable parameters for a specific application. This article is concerned with the ``flow-compaction' model during the autoclave processing of composite materials. By using a weighted residual method, two-dimensional finite element formulation for the consolidation process of thick thermosetting composites is presented and the corresponding finite element code is developed. Numerical examples, including comparison of the present numerical results with one-dimensional and two-dimensional analytical solutions, are given to illustrate the accuracy and effectiveness of the proposed finite element formulation. In addition, a consolidation simulation of AS4/3501-6 graphite/epoxy laminate is carried out and compared with the experimental results available in the literature. The project supported by the National Natural Science Foundation of China (10272037) The English text was polished by Yunming Chen.     

Wave propagation in transversely impacted composite laminates

An experimental investigation was conducted to determine wave-propagation characteristics, transient-strain distributions and residual properties for unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicon-rubber projectiles at velocities up to 250 ms^?1 (820 ft/s). Tests were conducted at normal and 45-deg oblique impact. Strain signals obtained from surface and embedded strain gages were recorded and analyzed to determine the types of waves, propagation velocities, peak strains, strain rates and attenuation characteristics. The predominant wave is a flexural on propagating at different velocities in different directions. The flexural wave velocity is higher in the higher-modulus direction. In general, measured wave velocities were higher than theoretically predicted. The amplitude of the in-plane wave is less than ten percent of that of the flexural wave. Peak strains and strain rates in the transverse to the (outer) fiber direction are much higher than those in the direction of the fibers. Strain rates up to 640 s^?1 were measured. Under oblique 45-deg impact, the flexural wave is still the predominant one. Peak strains under this oblique impact range between 36 and 56 percent of those under normal impact of the same velocity. Residual elastic properties and strength were measured around the point of impact. The most significant result was a reduction in the transverse strength of the unidirectional laminates. The dynamics of impact were also studied with high-speed photography. The projectile is completely flattened within 50–70 μs and the total contact time is of the order of 300 μs.     

Multipatch discontinuous Galerkin isogeometric analysis of composite laminates

This paper is concerned with the isogeometric analysis (IGA) of composite laminates under cylindrical bending. Non-uniform rational B-splines (NURBS) are employed as basis functions for both geometric and computational implementations. In order to account for multiple domains, each lamina is modeled as a single NURBS patch. This multipatch representation corresponds to decomposition of the computational domain (composite laminate) into non-overlapping subdomains. As NURBS patches are discontinuous across their boundaries, a standard FEA-like procedure does not work for multipatch IGA; an additional numerical technique is required for coupling NURBS patches. Therefore, in this paper, one of the discontinuous Galerkin (DG) methods, namely symmetric interior penalty Galerkin formulation, is employed to allow for discontinuities. For numerical calculations, a composite laminate with stacking sequences $$0^{\circ }{/}90^{\circ }$$ and $$0^{\circ }{/}90^{\circ }{/}0^{\circ }$$, respectively, is adopted. The stresses are calculated along the thickness of the composite laminate, subjected to a sinusoidal load, and they are compared with the analytical solutions. It is shown that DG–IGA gives a better approximation in comparison with the standard IGA.     

Experimental and analytical comparisons of failure in thermoplastic composite laminates

Failure characteristics of Gr/PEEK were studied, using an experimental investigation and a fully nonlinear ply-by-ply finite-element technique. The stacking sequence of the laminates (with centrally located holes) investigated were: 0, 90, ±45 deg, (0/45/90/−45 deg)_2s and (0±45/90 deg)_2s. The [0 deg] laminate failure was characterized by splitting at the extremities of the hole and along the fibers. The [90 deg] laminates failed in the transverse direction, whereas the [±45 deg] laminates exhibited considerable elongation to failure. In the case of the quasi-isotropic laminates, the failure progression appeared to be due dominantly to matrix cracking followed by fiber failure. Analytical predictions of the failure process showed reasonably good correlation with the experimentally determined data.     

Characterisation of pure and mixed mode fracture in composite laminates

The extensive use of advanced fibre composite materials for aircraft construction has necessitated the development of a damage tolerance methodology for aircraft components. Such a methodology would facilitate the design of more efficient and reliable composite structures and their maintenance in service. Therefore, it is necessary to characterize and understand the complex failure modes of fibre composites, including the influence of temperature, moisture and various defects arising from manufacture or service conditions.This paper briefly discusses the present status of some approaches to the experimental characterization of pure and mixed-mode fracture of composite laminates.     

Delamination buckling in composite laminates with interlaminar defects

Analyzed are the delamination buckling and growth in compressively loaded layered composite plates. Delamination is assumed to spread from an initial interlaminar defect. The method involves an analytical approach using fracture mechanics and a numerical analysis assuming that the adhesive layers can be modelled by elastic springs with finite tensile strength. Analytical and numerical results are compared and discussed.