Multi-step blended stacking sequence design of panel assemblies with buckling constraints

In this paper, we propose a multi-step framework for design of composite panel assemblies and subsequent blending of the designs to ensure laminate continuity across multi-panel configurations. Multilevel optimisation is frequently used for solving complex optimisation problems. In composite design this approach leads to stacking sequence mismatch among adjacent structural components which is generally referred to as blending problem. To overcome stacking sequence mismatch, a guide-based genetic algorithm (GA) is used which in essence forces the design to be completely blended at any step in the design process. A serious drawback of guide based approach is that it necessitates repeated analysis of the entire structure within the GA iterations. A multi-step framework is proposed where the structure is first optimised using panel thickness and lamination parameters as continuous design variables. The continuous optimisation is performed using a successive convex approximation scheme. In the second step, discrete blended stacking sequences are obtained using a guide-based genetic algorithm. The fitness function in the guide-based GA is evaluated using convex approximations of the response. In this fashion, the cost of evaluating structural response within the GA optimisation is eliminated. The proposed framework is demonstrated via design of an eighteen panel horseshoe configuration, where each panel is optimised individually subject to a local buckling constraint. Numerical results indicate that the present algorithm is capable of producing near-optimal fully blended designs at a small fraction of the computational cost of traditional blending algorithms.     

考虑屈曲的复合材料加筋壁板铺层顺序优化

提出了一种考虑屈曲的复合材料加筋壁板铺层顺序优化方法。基于复合材料加筋壁板屈曲载荷求解的能量法,系统推导了轴压载荷作用下复合材料加筋壁板蒙皮、筋条局部屈曲载荷的显示表达式,考虑了加筋壁板各板元之间的弹性支持作用及筋条下缘条的影响,引入工程法求解了加筋壁板整体屈曲载荷。基于国产自主结构分析软件HAJIF中的复合材料铺层工程数据库,以铺层参数为中间变量,利用本文提出的复合材料加筋壁板屈曲载荷求解方法,构建了考虑屈曲的复合材料加筋壁板铺层顺序优化设计流程并完成程序实现,将最小二乘法用于最优铺层顺序与工程铺层数据库的匹配。相比于传统有限元计算方法,本文提出的复合材料加筋壁板屈曲载荷求解方法具备较好的求解精度及求解效率。复合材料加筋壁板优化算例表明,采用本文提出的加筋壁板屈曲载荷分析及其优化方法,在结构重量不变的前提下,屈曲载荷提高约17%,且铺层顺序优化结果可直接从铺层工程数据库中提取并用于工程实际。      

Design analysis of three-layered structural composites based on post-consumer recycled plastics and wood residues

Three-layered structural composites were produced from municipal plastic wastes and wood flour residues to investigate the effects of design parameters on their flexural and impact performance. The studied parameters include wood content, thickness of individual composite layers, as well as stacking sequence and configuration (symmetric and asymmetric structures). The results indicate that the core layer has a lower influence on the flexural properties of structural beams in comparison with the skins. But depending on beam configuration (stacking sequence), different flexural characteristics can be obtained using the same composite layers. The classical beam theory was used to predict the flexural modulus with high precision. In addition, performance of the beams under impact tests was shown to be independent from their stacking sequences and layer thicknesses for each configuration.     

Stacking sequence optimization to maximize the buckling load of blade-stiffened panels with strength constraints using the iterative fractal branch and bound method

Laminated carbon fiber reinforced polymer (CFRP) composites have widespread applications in aerospace structures, and thus optimization of the stacking sequences in these composites is indispensable. Here, a fractal branch and bound method (FBB) is proposed for optimizing the stacking sequences. This method requires only low computational costs, and an optimal result can be obtained rapidly by means of the deterministic process. For practical stacking sequence optimizations, more than two laminates have to be optimized, because a practical aerospace structural component usually comprises a panel and stiffeners made from composite laminates. Since the stacking sequences of the skin panel and stiffeners affect the buckling load of the stiffened panel, the optimization of both laminates must be performed simultaneously. In the present study, a new method to implement a strength constraint for the FBB method is proposed for the simultaneous optimization of more than two laminates (such as a panel and stiffeners). Moreover, a quadratic polynomial objective function, which includes lamination parameter variables of the two laminates: the stiffeners and the panel, is adopted. The strength constraint is implemented by means of a response surface. The new method is applied to the buckling load maximization of a blade-stiffened composite panel, in which the strength constraint is demonstrated as a feasibility study. The method successfully obtained optimal stacking sequences with the strength constraint at low computational cost.     

Adhesive joining of composite journal bearings to back-up metals

Composite journal bearings are becoming popular for marine applications because they eliminate the possibility of seizure to steel journals, which is a drawback of white metal bearings. However, a reliable joining method for composite bearings to steel housings is required. In this work, hybrid composite journal bearings composed of carbon/phenolic and glass/epoxy laminated composites were manufactured with different stacking sequences and adhesively bonded to steel housings. The effect of deformations of the composite bearings due to thermal residual stresses on the adhesive joint performance was estimated with respect to stacking sequence by finite element method, and compared to the experimental results. From the measured and experimental results, it was found that the outward radial deformation of the composite bearings was beneficial to the adhesively bonded joint strength of the hybrid composite journal bearing.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Enhanced strength analysis method for composite open-hole plates ensuring design office requirements

The use of unidirectional carbon fibre-reinforced composites in the design of primary structures, such as the centre wing box, has spread increasingly over the past few years. However, composite structures can be weakened by the introduction of geometrical singularities, such as holes or notches. The semi-empirical aspect of the current open-hole failure approaches requires the allowables to be systematically fitted against specific test results. This point constitutes a strong limitation for optimum design. A simplified strength analysis method for perforated plates is presented, ensuring design office requirements in terms of precision and computational time. The predictions of the proposed approach are compared successfully with a large experimental database, with different configurations of perforations, different stacking sequences and in different Carbon/Epoxy materials.     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

基于铺层设计特征的碳纤维增强复合材料悬架控制臂结构优化

基于铺层设计特征,提出一种使用碳纤维复合材料对承载结构件进行结构优化设计的方法和流程.该方法综合考虑结构几何特征、材料铺层方式、铺层厚度及铺层角度在设计环节中的序列关系,通过几何设计空间构建、离散变量多目标优化、基于工艺可行性的最优决策等方法实现结构设计.以碳纤维增强复合材料悬架控制臂的轻量化设计为例:首先,以钢质控制臂结构为参考建立复合材料控制臂的几何设计空间;然后,以复合材料铺层便利性为原则对其进行结构设计,采用准各向同性铺层对控制臂的铺层厚度进行设计;进而,以提高控制臂刚度和1阶固有频率为目标,使用优化算法对铺层角度进行多目标优化设计;最后,以工艺可行性为约束对优化结果进行筛选并最终完成结构设计.结果表明,所设计复合材料结构具有更大的刚度和1阶固有频率,并且与钢质结构相比减重47.9%.所提出的方法能够较好地兼顾结构特征和复合材料设计要求之间的关系,为复合材料结构优化设计理论与方法的发展提供有益参考.     

Multiobjective stacking sequence optimization for laminated composite structures

A Pareto-based multiobjective evolutionary algorithm is presented for stacking sequence optimization of composite structural parts. Special attention has been paid to engineering design guidelines for stacking sequence design. These guidelines are included into the formulation of the optimization problem as constraints or additional objectives. A new initialization strategy is proposed following mechanical considerations. The method is applied to the optimal design of a composite plate for weight minimization and maximization of the buckling margins under three hundred load cases that make also the originality of this work. It is shown that the introduction of new ply orientations compared to the classical 0°, ±45° and 90° plies can lead to significantly improved optimal designs.     

基于低能量冲击损伤阻抗的复合材料薄壁结构铺层顺序设计

建立了有效的复合材料层合板结构冲击损伤分析方法,层合板面内损伤采用改进的Chang/Chang 失效准则做判据,得到面内各类损伤形式。层间损伤采用与Mixed-Mode粘接元等效的TIEBREAK接触模拟。利用此分析方法,从复合材料薄壁结构设计需要出发,研究了在低能量冲击下,铺层的层间角度、铺层方向、铺层重叠对层合板结构冲击损伤阻抗的影响规律,并对它们的综合影响进行了总体分析,得到了能提高层合板结构损伤阻抗的铺层顺序设计指导。最后用该设计指导对某种铺层结构进行了重新设计和有限元模拟,验证了该设计指导的可行性和有效性。     

Low-velocity impact damage on dispersed stacking sequence laminates. Part I: Experiments

The stacking sequence design of composite laminates is often limited to combinations of 0°, 90°, and ±45° fibre angle plies. Furthermore, in order to comply to certain stiffness requirements, clustering of plies becomes unavoidable. Although such laminates might have the desired stiffness properties, they may show poor impact and/or compression-after-impact behaviour.A method to redesign the traditional stacking sequences such that the alternative laminates have improved damage resistance whilst keeping similar in-plane and bending stiffness properties as their original traditional stacking sequences is proposed. This method makes use of optimisation tools based on genetic algorithms. In the alternative laminates, the difference between fibre angles of two consecutive plies is maximised and allowed to vary in the 0–90° fibre angle range at intervals of 5°. Manufacturing of such laminates is practical nowadays as the industry is changing its production techniques into accurate automated fibre-placement and tape-laying technologies. A two-step approach is proposed for the design of laminates. In the first step, the optimal laminate is designed in the traditional fashion to cope with the expected quasi-static loads on the structure. The second step consists of redesigning this laminate to better withstand impact loads by dispersing its stacking sequence while keeping similar stiffness properties as in the first step.A traditional laminate and two dispersed stacking sequence alternative layups were tested under low-velocity impact and compression-after-impact loads in order to compare their impact resistance and damage tolerance characteristics. The evaluation of these laminates will also be carried out by the innovative numerical tools proposed in the follow-up of the present paper.     

Determination of the out-of-plane tensile strength using four-point bending tests on laminated L-angle specimens with different stacking sequences and total thicknesses

Laminated composite materials are increasingly used for the design of aircraft primary structures subjected to complex 3D loadings. The delamination observed in curved parts ensuring the junction between the different perpendicular panels is one of the most critical failure mechanisms. The present article proposes a complete protocol to identify the out-of-plane tensile strength of specimens composed of unidirectional plies. Firstly, a method to design a four-point bending (4 PB) test on L-angle specimens has been proposed. Secondly, a test campaign on T700GC/M21 laminated L-angle specimens has been performed at ONERA. Thirdly, the analysis of these tests with different methods has been performed to demonstrate that such a test is relevant to determine the material out-of-plane tensile strength, which seems to be independent of the stacking sequence and of the total thickness of the specimen, thus allowing the use of this strength in a 3D failure criterion. Finally, the different advantages and drawbacks of 4 PB tests performed on curved beams are discussed.     

Parametric study on design of composite–foam–resin concrete sandwich structures for precision machine tool structures

In this paper, sandwich structures for micro-EDM machines are optimized by using parametric study varying composite geometries and parameters like stacking sequence, thickness and rib geometry. The structures are composed of fibre reinforced composites for skin material and resin concrete and PVC foam (Closed cell, Divinycell) for core materials. Column structure was designed by a beam with cruciform rib and performance indices such as static bending stiffness (EI) and specific bending stiffness (EI/ρ) for dynamic stability are examined by controlling the thickness and stacking sequence of composites. For the machine tool bed, which usually has a plate shape, was designed to have high stiffness in two directions at the same time controlling stacking sequence and rib geometry; that is, rib thickness and number of ribs. The sensitivity of design parameters like rib thickness and composite skin thickness was examined and the optimal condition for high stiffness structure was suggested. Finite element analysis was also performed to verify the static and dynamic robustness of the machine structure. L-shaped joint for combining bed and column of the micro-EDM machine was proposed and fabricated using adhesive bonding. The dynamic performance such as damping characteristics was investigated by vibration tests. From the results optimal configuration and materials for high precision micro-EDM machines are proposed.     

Producing toughened PP/HA-LLDPE ternary bio-composite using a two-step blending method

The mechanical and morphological properties of polypropylene/hydroxyapatite/linear low density polyethylene ternary bio-composites which were produced by blending of polypropylene (PP), hydroxyapatite, modified and unmodified linear low density polyethylene (LLDPE) were studied. In this research, effects of LLDPE weight percent, modification of PP/LLDPE interface by a high crystallizable high density polyethylene, and the method of blending on tensile strength, Young’s modulus and impact absorbed energy of composites were investigated. Results of mechanical tests showed that by adding LLDPE to these composites, ultimate tensile strength and Young’s modulus of the composites dropped slightly, while their impact strength was increased significantly. Mechanical properties of composites were improved by modification of PP/LLDPE interface and changing from one-step blending to two-step blending. However, for the composites produced by two-step blending, by adding modified LLDPE (15 wt.%), the impact strength was 90% more than that of pure PP/HA composites. Fractography of the surface fractures of the impact samples for both types of composites were performed using a scanning electron microscope (SEM). Two different toughening mechanisms of these composites were distinguished by drawing a schematic sketch of the mechanisms.     

Defects in woven preforms: Formation mechanisms and the effects of laminate design and layup protocol

Defects, such as in-plane waviness and out-of-plane tow wrinkles, cause significant reductions in the mechanical performance of RTM-manufactured composite parts based on woven preforms. To avoid this problem and achieve a greater acceptance rate in industrial processes, the mechanisms behind these defects must be understood. This paper presents a mechanism for the formation of these defects, which is supported through layup trials of woven preforms. Laminate design and layup protocol were found to be significant drivers behind the mechanism. Defect severity can be controlled through intelligent stacking sequence design and reducing ply bridging by manual forming actions and ply–ply adhesion during layup.     

Design of inspecting machine for next generation LCD glass panel with high modulus carbon/epoxy composites

In this paper, an imperfection detecting machine which has composite–aluminium hybrid beam structure with high-modulus carbon/epoxy composites in order to enhance dynamic stiffness and damping capacity of the structure is introduced. For the optimal design of the composite-aluminium hybrid beam structure, geometric shape of cross-section of aluminium beam, the stacking sequence and thickness of composite which is to be reinforced onto the aluminium beam are determined by considering the fundamental natural frequency and deformation of the structure under service conditions. The dynamic characteristics of the structure are analyzed by the finite element method, and the results show good agreement with the modal testing results.

In addition, new designs of beam structure are also proposed for the next generation inspecting system which has much longer beam length. Parametric study for composite X-axis beam system and optimisation scheme of joint inserts are performed in the designing process.     

An optically-based inverse method to measure in-plane permeability fields of fibrous reinforcements

Structural composite manufacturing relying on Liquid Composite Molding technologies is strongly affected by local variability of the fibrous reinforcement. Optical techniques using light transmission are used and allow field measurements of areal weight (and fibre volume fraction) of glass fibre reinforcement. The coupling of obtained areal weight mappings along with injection flow fronts is used to extract in-plane permeability fields. The current work presents results with a focus on glass random mats, but the method can be adapted to any glass fibrous medium. A study of convergence and error due to discretization is performed. Also the influence of the stacking of fibrous layers on the preform variability is analyzed. The major advantage of the proposed technique is a relatively fast acquisition of statistical data on reinforcement variability, which can be later utilized in stochastic based process simulations.     

Probabilistic optimal design of laminates using improved particle swarm optimization

A new approach to the particle swarm optimization (PSO) is proposed for the solution of non-linear optimization problems with constraints, and is applied to the reliability-based optimum design of laminated composites. Special mutation-interference operators are introduced to increase swarm variety and improve the convergence performance of the algorithm. The reliability-based optimum design of laminated composites is modelled and solved using the improved PSO. The maximization of structural reliability and the minimization of total weight of laminates are analysed. The stacking sequence optimization is implemented in the improved PSO by using a special coding technique. Examples show that the improved PSO has high convergence and good stability and is efficient in dealing with the probabilistic optimal design of composite structures.     

Planar defects in layered hydroxides: Simulation and structure refinement of β-nickel hydroxide

Although nickel hydroxide can be obtained by various methods in a highly ordered form, this work shows that most such preparations are not free of stacking faults. The stacking faults belong to more than one type, which differ from one another in their structure as described by the local stacking sequence. The incidence of such residual stacking faults varies in the range 1-3% depending on the method of preparation.