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.     

Strain and Fracture of Glass-Fiber Laminate Containing Metal Layers

This paper describes an experimental study on strain and fracture of plane samples made of glass-fiber laminate and fabric-based laminate with surface and inner aluminum layers. It is shown that the presence of these layers reduces the strength of glass-fiber laminate under static and low-cycle loading. This can be explained by the fact that the stretching of a hybrid composite along the layers is accompanied by the formation of localized tensile regions of glass-fiber laminate across the layers. As a result, both the hybrid composite and its glass-fiber laminate component are stratified.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

ROBUST OPTIMUM DESIGN OF LAMINATED COMPOSITE PLATES

A last-ply failure (LPF) analysis method for laminated composite plates is incorpo- rated into the ?nite element code-ANSYS, and a robust optimum design method is presented. The composite structure is analyzed by considering both in-plane and out-…     

Electro-elastic analysis of fiber-reinforced multilayered cylindrical composites with integrated piezoelectric actuators

Based on the electro-mechanical coupling theory and the laminate elasticity theory, an electro-elastic solution is obtained for the fiber-reinforced cylindrical composites with integrated piezoelectric actuators when subjected to mechanical and electrical loadings. The hybrid composite is composed of three parts: internal piezoelectric actuator, fiber-reinforced laminated interlayer, and external piezoelectric actuator. The general solution in each piezoelectric smart layer is obtained by introducing three undetermined constants, and the general solutions in the fiber-reinforced laminated interlayer are obtained by means of the state-space method. The mechanical behaviors of the hybrid fiber-reinforced cylindrical composites are investigated. The illustrative examples show that the fiber’s angle, the stacking sequence as well as the applied electric loading strongly affect the physical fields in the fiber-reinforced multilayered cylindrical composites.     

变角度纤维复合材料环扇形层合板的自由振动分析

与传统的直线纤维增强复合材料相比,变角度纤维复合材料具有更强的可设计性,为改善结构性能提供了更大的可能．鉴于此,本文将研究纤维的变角度铺设对复合材料环扇形层合板的自振频率及振动模态的影响．假设纤维的方向角沿环扇形板的径向线性变化,基于经典的层合板理论,采用微分求积法获得了环扇形层合板自由振动问题的数值解．通过与现有文献及ABAQUS有限元结果的比较验证了本文模型及方法的正确性和收敛性,并详细分析了纤维起始角和终止角的变化对层合板的自振频率及振动模态的影响．研究结果表明：与常刚度层合板相比,变角度纤维复合材料层合板的基频具有更大的调整空间,通过合理选择纤维起始角和终止角可有效提高层合板的基频．研究结果可为该种新型复合材料结构的优化设计提供一定的参考．     

Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells

This study introduces a non-linear finite element analysis approach to the procedure of modeling hybrid laminate composite shells with embedded shape memory alloy (SMA) wire subjected to coupled structural and thermal loading. Numerical analyses of SMA wire reinforced composite laminates were carried out by synergizing the non-linear laminate shell element with Brison's model of the SMA constitutive law. To verify the proposed procedure, the present illustrative applications involve rectangular laminated panels clamped along one side. Analysis results were compared with corresponding experimental results from a prior study. Several test cases that depend on the volume fraction of SMA, temperature, and ply angles are presented to illustrate the highly entangled thermo-mechanical behavior of shape memory alloy hybrid composites (SMAHCs). The results of the numerical analysis show the ability of the suggested procedure to compute the thermo-mechanical behavior of a SMAHC in accordance with the SMA's internal phase transformations induced by stress and temperature variation and demonstrate very good agreement with experimental results.     

含圆孔复合材料层板在拉伸载荷下损伤破坏过程的模拟

本文应用有限元法模拟受拉含孔夏合材料层板损伤起始、累积直至破坏的过程。在模拟中引入了作者早些时建立的包含基体开裂层非对称约束影响的损伤本构关系，以及裂纹密度与损伤区应力关系函数等。本文给出损伤累积模拟方法并编制了程序，用该程序可以获得层板加载过程中各层的损伤状态、计算其刚度衰减和应力重分布以及最终破坏载荷。给出了数值模拟算例并与现有研究结果进行了比较。     

Stress-resultant plasticity theories for composite laminated plates

Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.     

板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点,从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同,层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭,并在层间结合面处发生强不连续,呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用,不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出,现有各种考虑剪切变形影响的计算模型虽然有了很大的发展,但在全面和准确性上仍然存在一定的不足,难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型,同时可适用于各种薄板与厚板的分析,对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化,与三维弹性理论的标准解高度吻合。数值算例进一步表明,随着层间纤维走向的变化,板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此,本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

含孔平面编织混杂铺层层合板压缩破坏仿真

对ANSYS软件平台进行了二次开发,建立了平面编织混杂铺层层合板损伤累积有限元模 型,对含孔平面编织混杂铺层层合板的压缩破坏行为进行了仿真计算. 研究结果表明,所建 模型能够较好地仿真含孔平面编织层合板的损伤破坏过程,并能准确预测层合板的 损伤类型、损伤扩展以及破坏强度;同时提出并验证了适合该类型层合板的损伤判 据和衰减准则. 该模型所给结果形象直观,适合工程应用.     

Stiffened Composite Panels with a Stress Concentrator Under in-Plane Compression

The in-plane compressive strength of a stiffened thin-skinned composite panel with a stress concentrator is examined. Two possible in-plane failure mechanisms are investigated. The first one is near-surface instability at the edge of the cutout, where high stress gradients are expected because of the stress concentration and the thickness heterogeneity of the laminated skin. Analytical 3D formulas allowing simple parametrical investigation of the phenomenon under consideration are derived. The second failure mechanism is fiber microbuckling in 0°-plies. An equivalent crack model is used to predict the compressive strength of a multidirectional composite laminate. How a stiffener affects the compressive strength of the thin-skinned panel with a hole is studied for both mechanisms. Experimental and predicted values of the critical load are in good agreement.     

Reliability analysis of FRP laminated plates with consideration of both initial imperfection and failure sequence

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability. Project supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry, and the Research Foundation of Huazhong University of Science and Technology.     

Assessment of composite failure and ultimate strength without experiment on composite

This paper attempts to estimate the ultimate strength of a laminated composite only based on its con- stituent properties measured independently. Three important issues involved have been systematically addressed, i.e., stress calculation for the constituent fiber and matrix materials, failure detection for the lamina and laminate upon the internal stresses in their constituents, and input data determination of the constituents from monolithic measurements. There are three important factors to influence the accuracy of the strength prediction. One is the stress concentration factor （SCF） in the matrix. Another is matrix plasticity. The third is thermal residual stresses in the constituents. It is these three factors, however, that have not been sufficiently well realized in the composite community. One can easily find out the elastic and strength parameters of a great many laminae and laminates in the current literature. Unfortunately, necessary information to determine the SCF, the matrix plasticity, and the thermal residual stresses of the composites is rare or incomplete. A useful design methodology is demonstrated in the paper.     

考虑内部损伤影响的层合板最终强度预测

层合板强度分析若只考虑面内失效而忽略自由边界处的分层失效,往往会高估强度值,得不到合理的预测结果.该文提出了一种层合板强度的数值分析方法,综合考虑了层合板的面内失效(基体失效和纤维断裂)以及层间分层失效.采用有限元方法对层合板进行结构分析得到板的应力响应,结合面内失效判据和分层失效判据对层合板各个单层进行失效判断,采用刚度退化和逐步失效方法求得层合板的最终失效强度.与以往方法相比,该文模型和方法考虑的因素更全面.数值算例表明该方法预测得到的最终失效载荷和分层起始载荷和已有文献实验结果一致.     

Nonlinear buckling optimization of composite structures considering “worst” shape imperfections

Nonlinear buckling optimization is introduced as a method for doing laminate optimization on generalized composite shell structures exhibiting nonlinear behaviour where the objective is to maximize the buckling load. The method is based on geometrically nonlinear analyses and uses gradient information of the nonlinear buckling load in combination with mathematical programming to solve the problem. Thin-walled optimal laminated structures may have risk of a relatively high sensitivity to geometric imperfections. This is investigated by the concepts of “worst” imperfections and an optimization method to determine the “worst” shape imperfections is presented where the objective is to minimize the buckling load subject to imperfection amplitude constraints. The ability of the nonlinear buckling optimization formulation to solve the laminate problem and determine the “worst” shape imperfections is illustrated by several numerical examples of composite laminated structures and the application of both formulations gives useful insight into the interaction between laminate design and geometric imperfections.     

Stability of parametric vibrations of hybrid composite plates

In this paper, the dynamic stability of laminated hybrid composite plates subjected to periodic uniaxial stress and bending stress is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. Based on Bolotin's method the regions of dynamic instability of laminated hybrid composite plates are determined by solving the eigenvalue problems. The effects of layer thickness ratio, layer number, core material and load parameter on the dynamic instability of laminated hybrid composite plates are investigated and discussed.     

纤维增强复合材料强度理论的研究现状与发展趋势——"破坏分析奥运会"评估综述

复合材料强度涉及许多力学问题,计算分析复杂. 由于分析问题的角度和解决问题的方法不同, 迄今为止已经产生了许许多多不同的强度理论. 那么, 究竟这些理论的效果如何?为此,在英国的工程与自然科学研究委员会和机械工程师协会支持下, 一个堪称为复合材料``破坏分析奥运会'的评估于1991年启动并在2004年完成. 本文根据参赛理论和评比结果, 对复合材料破坏与强度理论的研究现状进行了简要综述, 并指出了今后发展所需解决的一些问题.      

Closure effects in delaminated graphite epoxy laminate under compression

Flaws in composite laminates may result in a severe loss of static and dynamic strength. Such flaws may be inherent or gained by misadventure. The extent of this loss can be influenced by several factors including loading, laminate stacking sequence, lamina properties, flaw size and damage type.In this study, the free-edge delamination of a laminated composite under compression loading is investigated. Computational, analytical and experimental tests are performed on a graphite/epoxy laminate AS4/3501-6 containing near surface edge defects and the crack opening behaviour is investigated.The computational analysis consists of a three dimensional finite element model where the plies can be catered for individually and interply delamination modelled. In the experimental investigations, a delamination is simulated by inserting teflon film at appropriate locations during the lay-up process.     

Reliability assessment of post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression

A method for reliability assessment of the post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression is presented in the paper. The prediction of the post-buckling compressive strength is performed by a progressive failure analysis which was developed based on a progressive stiffness degradation model and a nonlinear finite element analysis with a new explicit through-thickness integration scheme. A method coupled with the finite element analysis is proposed for reliability assessment where a finite difference method combined with an improved first-order reliability algorithm that omits the non-important random variables but retains sufficient accuracy was developed for reliability estimation. Two numerical examples are described demonstrating the capabilities of the method developed.