Stacking sequence optimization of laminated plates

Optimum fiber orientations of laminated composite plates for the maximum strength are found under multiple inplane loading conditions. Tsai-Wu failure criterion is taken as objective function. Based on the state space method, effective optimal design formulation is developed and solution procedure is described with the emphasis on the method of calculations of the design sensitivities. Numerical results are presented for the several test problems.     

Biaxial testing of high strength carbon fiber composite cylinders for pulsed magnet reinforcement

A methodology is introduced to test carbon-fiber-reinforced, hoop-wound composite cylinders for their biaxial mechanical properties under axial compression and hoop tension. The understanding of the behavior of these composites under biaxial loads is extremely important in the design of pulsed magnets. These composites are used as reinforcements for both the inner conducting layers and as an overall exterior reinforcement. Testing of actual pulsed magnets to ascertain design change effects of composite reinforcement schemes on the maximum attainable field can be expensive; hence, a standard biaxial testing method is desirable which is relevant to the design of pulsed magnets. In this investigation, an attempt was made to produce a standard testing procedure aimed at measuring the biaxial mechanical properties (elastic, plastic, and failure envelope) of composite materials. This methodology was applied to two different carbon/epoxy based composites. The results of these tests (elastic properties and failure points) are compared with theoretical predictions, specifically those due to Tsai-Wu.     

Optimum head design of filament wound composite pressure vessels using a hybrid model of FE analysis and inertia weight PSO algorithm

Filament wound composite pressure vessels are widely used in industrial applications. Determination of the optimal head profile has been recognized as one of the most important design issues. This paper presents the optimum design of head contours for a filament wound composite pressure vessel using a hybrid model of finite element analysis and inertia weight particle swarm algorithm. Geometrical limitations, winding conditions and the Tsai-Wu failure criterion have been used as optimization constraints. The objective is to maximize the shape factor using present optimization technique. An actual design example taken from available literature is used as a case study. Results indicate that the dome contours using the suggested method shows stronger structure and greater internal volume. This confirms that the proposed model can efficiently define the optimal dome shape.     

Ply level uncertainty effects on failure curves and optimal design of laminated composites using directional bat algorithm

The present study investigates the effect of both ply level material uncertainty and ply angle uncertainty on the failure envelope, strength characteristics and design of laminated composite. Multiple failure envelopes and distributions of the strength parameters are obtained for Tsai-Wu and maximum stress criteria using Monte Carlo simulation. A newly developed directional bat algorithm (dBA) is then used to perform the constrained design optimization of laminated composite for the first time while considering uncertainty effects. The effect of ply level uncertainty on failure envelopes and the corresponding optimal design of laminated composite structures is thus quantified.     

Dome Shape Optimization of Composite Pressure Vessels Based on Rational B-Spline Curve and Genetic Algorithm

This paper presents an algorithm for shape optimization of composite pressure vessels head. The shape factor which is defined as the ratio of internal volume to weight of the vessel is used as an objective function. Design constrains consist of the geometrical limitations, winding conditions, and Tsai-Wu failure criterion. The geometry of dome shape is defined by a B-spline rational curve. By altering the weights of control points, depth of dome, and winding angle, the dome shape is changed. The proposed algorithm uses genetic algorithm and finite element analysis to optimize the design parameters. The algorithm is applied on a CNG pressure vessel and the results show that the proposed algorithm can efficiently define the optimal dome shape. This algorithm is general and can be used for general shape optimization.     

Prediction of reliability analysis of composite tubular structure under hygro-thermo-mechanical loading

The present paper focuses on reliability prediction of composite structure under hygro-thermo-mechanical loading, conditioned by Tsai-Wu failure criterion, where the Monte–Carlo method is used to estimate the failure probability(Pf). This model was developed in two steps: first, the development of a deterministic model, based on an analytical and numerical approach, and then, a probabilistic computation. Using the hoop stress for each ply, a sensitivity analysis was performed for random design variables, such as materials properties, geometry, manufacturing, and loading, on composite cylindrical structure reliability. The probabilistic results show the very high increase of failure probability when all parameters are considered.     

Mechanical bending behaviour of composite T-beams

A study of the design and mechanical behaviour of co-cured T-beams subjected to very high loading is presented. The T-beams were made by press moulding from pre-pregs of uni-directional glass or carbon fibre and glass fabric reinforced high performant epoxy matrix. Each type of beam was instrumented with strain gauges in the web and flange in order to carry out experimental four point bending tests. Analytical and numerical studies were also performed to compare experimental versus numerical and analytical results and to establish the suitability of a simplified bending theory for statically determinate composite beams constructed from laminated composite panels. The maximum carrying loads in the beam layers were evaluated experimentally and analytically using the Tsai-Wu failure criterion. Results showing the suitability of the simplified beam theory are presented and discussed.     

Design optimization of composites using genetic algorithms and failure mechanism based failure criterion

In this paper, minimum weight design of composite laminates is presented using the failure mechanism based (FMB), maximum stress and Tsai–Wu failure criteria. The objective is to demonstrate the effectiveness of the newly proposed FMB failure criterion (FMBFC) in composite design. The FMBFC considers different failure mechanisms such as fiber breaks, matrix cracks, fiber compressive failure, and matrix crushing which are relevant for different loading conditions. A genetic algorithm is used for the optimization study. The Tsai–Wu failure criterion over predicts the weight of the laminate by up to 86% in the third quadrant of the failure envelope compared to FMB and maximum stress failure criteria, when the laminate is subjected to compressive–compressive loading. It is found that the FMB and maximum stress failure criteria give comparable weight estimates. The FMBFC can be considered for use in the strength design of composite structures.     

基于可靠性的复合材料定向管优化设计

基于Tsai-Wu失效准则和一次二阶矩法,建立了复合材料定向管强度可靠性分析的方法。应用Python语言实现了ABAQUS 的二次开发,编程将有限元计算程序与可靠性分析方法相结合,并采用多岛遗传算法和序列二次规划算法相结合优化策略,建立了基于可靠性的定向管铺层参数动态优化模型。优化算例表明:在满足强度可靠度条件下,复合材料定向管重量减小了22.5%。     

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

Reliability-based optimization of fibrous laminated composites

This paper is concerned with the optimum design of multiaxial fiber reinforced laminate systems under probabilistic conditions of loads and material properties. A multiaxially laminated composite is treated as a structural system with each ply contained in the composite as one element. The Tsai-Wu failure criterion is adopted as the limit state function of a unidirectional ply. It is assumed that the system failure occurs when any one of the plies in a laminate system fails. The multiple-check-point method is successfully applied to evaluate the system reliabilities of multiaxial laminates under probabilistic in-plane stresses. An optimization problem is defined to find the optimal number of fiber orientation axes, optimum orientation angles, and optimum ply ratios which yield the highest system reliability.     

Circumferential stiffness tailoring of general cross section cylinders for maximum buckling load with strength constraints

Stiffness tailoring of laminated composite structures using steered fibre tows is a design method that maximally uses the directional properties of composite materials. Cylindrical structures usually have circular cross sections while some application, geometric or aerodynamic requirements can necessitate other cross sections, e.g. elliptical. Circumferential tailoring can increase the buckling load of thin cylinders by compensating for non-uniform sectional loading such as bending and/or varying radius of curvature in general cylinders. Here, strength constraints are considered in maximum buckling load design, to ensure that the failure load is greater than the buckling load. A two-step optimisation framework is used to separate the theoretical and manufacturing issues in design. A computationally cheap semi-analytical finite difference method is used to solve the linear static and buckling problems. Conservative failure envelopes based on Tsai-Wu failure criterion are used for strength evaluation. To avoid repetitive analyses, successive convex approximation method is used. For demonstration, circumferential tailoring framework is applied to a circular cylinder under bending and an elliptical cylinder under axial compression. The improvements in buckling capacity of variable over constant stiffness designs are shown and verified using nonlinear buckling analysis in the commercial FEM software Abaqus^TM, and the mechanisms of improvements are investigated.     

Optimal weaving for 2.5D interlocks

This paper deals with optimizing the representative volume element (RVE) of 2.5D interlock composites for enhanced damage resistance and elastic stiffness. The elastic moduli of the composite are determined as a volume average of the moduli of the matrix and fiber, while the overall resistance to failure is obtained through incremental use of the 3D Tsai-Wu failure criterion. The variables considered for the optimization problem are the volume fractions of the fibers, their proportions in each direction and the weaving step of the vertical reinforcement. The optimization is carried out using a sequential quadratic programming approach (SQP) and the results are validated against experimental data obtained for 2.5D interlocks with carbon reinforcements.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Failure load prediction of laminates repaired with a scarf-bonded patch using the damage zone method

The damage zone method (DZM) is an efficient way to predict the failure of composite structures with a minimum of real testing. Particularly, it is useful when the failure mechanism is too complicated to be accurately analyzed by a merely numerical method. The aim of this study was to use the damage zone model to predict the failure load of repaired laminates, in which scarf-bonded joints were used for repair. The model uses a test-based critical damage zone and stress-based failure criteria. A total of 45 carbon-epoxy composite (USN) laminate scarf-repaired specimens were first tested with two different defect sizes, four scarf angles, and three overlap layer sizes. The Tsai-Wu and Tsai-Hill criteria were used for the laminate, and the maximum shear stress criterion for the adhesive was adopted to predict failure onset. The predicted failure loads were compared to test results and a good agreement was obtained with a 9.2% maximum deviation for almost all parameters with the exception of a case with an unrealistically large scarf angle. To verify the feasibility of the DZM for different material, additional 30 repair specimens using other unidirectional carbon-epoxy laminate were then also tested and the predictions were confirmed by the results of the experiment.     

Damage and its growth in laminated composite circular/rectangular plates undergoing large deformations

A nonlinear finite element static analysis is used to predict the damage in rectangular/circular plates due to large deformation simulating low-velocity impact. The impact due to the ball impactor is modelled by an equivalent static load and load distribution is taken according to Hertzian law. Tsai-Wu criterion is used to predict the failure of each ply at Gauss points. The failure mode (fibre breakage or matrix cracking) is identified using maximum stress criterion. The material properties at each failed Gauss point is degraded appropriately and the stress analysis is carried out again. This iterative process is repeated until no further damage condition occurs. Numerical examples for both circular and rectangular composite plates are presented.     

一种新型刚度退化模型及复合材料结构渐进损伤分析的通用方法实现

针对复合材料结构的强度设计与分析方法问题,基于Tsai-Wu强度准则,该文提出了一种新型刚度退化模型,建立了一套层合/实体型复合材料结构渐进损伤分析的通用方法,并开发ABAQUS用户材料子程序用于层合型和实体型复合材料典型结构的渐进损伤数值仿真与试验验证,结果表明:该文提出的模型和算法,在保证层合型复合材料结构损伤分析能力和精度不低于已有方法基础上,对C/C实体型复合材料结构极限承载能力的数值模拟相对误差精度也达到20%量值水平。     

基于宏微观分析的碳纤维增强高分子复合材料强度性能表征

微观力学强度理论(MMF)是一种新型的基于物理失效模式的复合材料强度理论。通过对碳纤维/树脂(UTS50/E51)复合材料单向层合板进行纵向、横向静载拉伸、压缩和弯曲试验, 得到层合板的基本力学性能和宏观强度指标。建立了碳纤维增强树脂基复合材料微观力学模型, 获取树脂基体和纤维不同位置的机械载荷应力放大系数和热载荷应力放大系数。结合获取的应力放大系数及试验测得的单向层合板宏观强度, 计算出层合板组分的MMF强度特征值。绘制了基于MMF强度理论的层合板破坏包络线, 并与Tsai-Wu失效准则预测结果进行对比。实现了对UTS50/E51层合板MMF强度特征值的表征。     

Post Buckling Progressive Failure Analysis of Composite Laminated Stiffened Panels

The present work deals with the numerical prediction of the post buckling progressive and final failure response of stiffened composite panels based on structural nonlinear finite element methods. For this purpose, a progressive failure model (PFM) is developed and applied to predict the behaviour of an experimentally tested blade-stiffened panel found in the literature. Failure initiation and propagation is calculated, owing to the accumulation of the intralaminar failure modes induced in fibre reinforced composite materials. Hashin failure criteria have been employed in order to address the fiber and matrix failure modes in compression and tension. On the other hand, the Tsai-Wu failure criterion has been utilized for addressing shear failure. Failure detection is followed with the introduction of corresponding material degradation rules depending on the individual failure mechanisms. Failure initiation and failure propagation as well as the post buckling ultimate attained load have been numerically evaluated. Final failure behaviour of the simulated stiffened panel is due to sudden global failure, as concluded from comparisons between numerical and experimental results being in good agreement.