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.     

基于分级优化的复合材料带加强筋板屈曲优化

对工程中常用复合材料带加强筋板结构的优化方法进行研究。由于优化变量较多且变量类型涉及离散型和连续型两种类型,因此优化中引入了分级优化方法。在结构质量一定的前提下,确定各加强筋最优的位置、截面尺寸、铺层数及铺层顺序,以提高整体结构的抗屈曲性能。代理层的引入使优化问题可以在先不考虑铺层顺序的情况下对其余变量进行优化,通过析因实验设计方法确定剩余变量中影响结构屈曲载荷的主要变量和次要变量,并分别在第1、2级优化中独立对两类变量进行优化,在优化过程中根据变量的类型及取值范围,对部分变量建立径向基代理模型以提高优化效率。第3级优化采用遗传算法对铺层顺序进行优化。优化结果表明:优化后方案比原方案的抗屈曲能力提高了3.21倍。     

Multi-physics design and optimization of flexible matrix composite driveshafts

Flexible matrix composites (FMCs) consist of low modulus elastomers such as polyurethanes which are reinforced with high-stiffness continuous fibers such as carbon. This fiber–resin system is more compliant compared to typical rigid matrix composites and hence allows for higher design flexibility. Continuous, single-piece FMC driveshafts can be used for helicopter applications. In the present investigation, an optimization tool using a genetic algorithm approach is developed to determine the best combination of stacking sequence, number of plies and number of in-span bearings for a minimum-weight, spinning, misaligned FMC helicopter driveshaft. In order to gain more insight into designing driveshafts, various loading scenarios are analyzed and the effect of misalignment of the shaft is investigated. This is the first time that a self-heating analysis of a driveshaft with frequency- and temperature-dependent material properties is incorporated within a design optimization model.     

A scatter search algorithm for stacking sequence optimisation of laminate composites

This paper explores the metaheuristic approach called scatter search for lay-up sequence optimisation of laminate composite panels. Scatter search is an evolutionary method that has recently been found to be promising for solving combinatorial optimisation problems. The scatter search framework is flexible and allows the development of alternative implementations with varying degree of sophistication. The main objective of this paper is to demonstrate the effectiveness of the proposed scatter search algorithm for the combinatorial problem like stacking sequence optimisation of laminate composite panels. Preliminary investigations have been carried out to compare the optimal stacking sequences obtained using scatter search algorithm for buckling load maximisation with the best known published results. Studies indicate that the optimal buckling load factors obtained using the proposed scatter search algorithm found to be either superior or comparable to the best known published results.

Later, two case studies have been considered in this paper. Thermal buckling optimisation of laminated composite plates subjected to temperature rise is considered as the first case study. The results obtained are compared with an exact enumerative study conducted on the problem to demonstrate the effectiveness and performance of the proposed scatter search algorithm. The second case study is optimisation of hybrid laminate composite panels for weight and cost with frequency and buckling constraints. The two objectives are considered individually and also collectively to solve as multi-objective optimisation problem. Finally the computational efficiency of the proposed scatter search algorithm has been investigated by comparing the results with various implementations of genetic algorithm customised for laminate composites. It was shown in this paper through numerical experiments that the scatter search is capable of finding practical solutions for optimal lay-up sequence optimisation of composite laminates and results are comparable and sometimes even superior to genetic algorithms.     

Optimum design for buckling of plain and stiffened composite axisymmetric shell panels/shells

The buckling of plain and discretely stiffened composite axisymmetric shell panels/shells made of repeated sublaminate construction is studied using the finite element method. In repeated sublaminate construction, a full laminate is obtained by repeating a basic sublaminate, which has a smaller number of plies. The optimum design for buckling is obtained by determining the layup sequence of the plies in the sublaminate by ranking, so as to achieve maximum buckling load for a specified thickness. For this purpose, a four-noded 48-dof quadrilateral composite thin shell element, together with fully compatible two-noded 16-dof composite meridional and parallel circle stiffener elements are used.     

Optimization of laminated composites subject to uncertain buckling loads

Optimal design of composite laminates under buckling load uncertainty is presented. The laminates are subjected to biaxial compressive loads and the buckling load is maximized under worst case in-plane loading which is computed using an anti-optimization approach. The magnitudes of the in-plane loads are not known a priori resulting in load uncertainty subject to the only constraint that the loads belong to a given uncertainty domain. Results are given for continuous and discrete fibre orientations which constitute the optimization problem coupled to load anti-optimization problem leading to a nested solution method. It is observed that the stacking sequence of a laminate designed for a deterministic load case only differs considerably from that of a robust laminate designed taking load uncertainties into account. Consequently the buckling load carried by a deterministic design is considerably less than the one carried by a robust design when both are subjected to uncertain loads.     

Optimization of hybrid laminated composites using the multi-objective gravitational search algorithm (MOGSA)

The multi-objective gravitational search algorithm (MOGSA) technique is applied to hybrid laminates to achieve minimum weight and cost. The investigated laminate is made of glass–epoxy and carbon–epoxy plies to combine the economical attributes of the first with the light weight and high-stiffness properties of the second in order to make the trade-off between the cost and weight as the objective functions. The first natural flexural frequency was considered as a constraint. The results obtained using the MOGSA, including the Pareto set, optimum stacking sequences and number of plies made of either glass or carbon fibres, were compared with those using the genetic algorithm (GA) and ant colony optimization (ACO) reported in the literature. The comparisons confirmed the advantages of hybridization and showed that the MOGSA outperformed the GA and ACO in terms of the functions’ value and constraint accuracy.     

RTM整体成型复合材料翼盒的固有模态及稳定性

采用基于水溶性型芯的RTM成型技术制备了整体化的复合材料翼盒, 并对翼盒进行了自由振动模态试验; 采用三维壳单元, 建立了翼盒固有模态及稳定性有限元分析模型, 该模型分析的翼盒固有模态与试验结果吻合很好, 验证了有限元模型的有效性; 为研究翼盒固有模态及稳定性的铺层效应, 采用该模型分析计算了4种铺层方案的翼盒的固有模态及稳定性。研究结果表明: 对称铺层蒙皮有利于提高翼盒轴向压缩与轴向扭转屈曲载荷及固有频率, 而不利于面外弯曲和弯扭组合情况; 腹板减薄和增加腹板45°铺层均不利于提高, 甚至会大幅度降低屈曲载荷及固有频率, 弯扭组合加载最容易导致失稳。     

铺设角度与铺层顺序对层合板稳定性的影响

以层合板结构的临界屈曲载荷系数最大化为优化目标,基于改进型模拟退火算法对层合板结构铺设角度和铺层顺序进行优化。由于层合板结构的铺层角度是离散变量,模拟退火算法适合求解离散变量的优化问题。利用模拟退火算法优化层合板铺层,在算法内采用并行计算、引入记忆功能同时设置双阈值终止准则,有效地提高了优化过程的收敛速度,同时避免优化过程中出现局部最优解。以临界屈曲载荷系数作为目标函数,选取复合材料层合板的铺设角度顺序为设计变量,采用改进的模拟退火算法得出复合材料层合板的最优铺设角度以及铺层顺序。     

复合材料层合板稳定性的铺层优化设计

提出采用神经网络和遗传算法来优化设计复合材料层合板,建立了满足铺层结构稳定性的优化铺层体系,优化体系分两步进行优化,第一步,当给出总的铺层数时,由已建立的神经网络模型确定规定角度下的铺层数,确立基本的铺层结构,第二步,采用遗传算法优化这种铺层结构下的铺层顺序,最终在同样重量下获得了最佳的结构铺层。     

Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation

This study describes a new method of experimental design to obtain a response surface of buckling load of laminated composites. Many evaluations for genetic algorithms for stacking sequence optimizations require high computational cost. That evaluation cost can be reduced by an approximation using a response surface. For a response surface for stacking sequence optimizations, lamination parameters are adopted as variables of the approximation function of the entire design space instead of ply angles for each ply. This study presents, proposes and investigates a new method of experimental design in detail. For most analytical tools, stacking sequences is demand as input data and lamination parameters cannot be applied directly to the tools. Therefore, the present study proposes and applies a new D-optimal set of laminates to the stacking sequence optimizations of the problem of maximization of buckling load of a composite cylinder. The new experimental design is a set of stacking sequences selected from candidate stacks using D-optimality. Consequently, the D-optimal set of laminates is shown to be effective for design of experiments of response surfaces for maximization of the buckling load of composite structures.     

Optimum buckling design of composite stiffened panels using ant colony algorithm

Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions.     

Mechanical Buckling Analysis of Composite Panels with/without Cutouts

A simplified analytical solution suitable for simple stacking sequences was developed using the Euler buckling theory,the structure’ s equations of equilibrium and laminate panel mathematical formulation.Comparing these results with numerical results reveals the accuracy of the method and even more,allows us to validate the numerical analysis.Therefore,two important results are obtained:a simplified analytical solution for the buckling problem and validation of the numerical results.Another important and novel finding is related to the influence of the angle ply orientation and of the cutouts,on the buckling load.Under symmetrical boundary conditions and loading case,rectangular panels with elliptical cutouts,give better results for 90° oriented plies than for 0 oriented ones.With a compression load applied in the X direction,and with material properties 10 times better in X direction than in Y direction,the best results are obtained when the load is aligned with the Y direction associated to the material reference frame.Moreover,panels with cutouts seem to behave better than panels without cutouts under certainply orientation angles.     

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。      

Determination of optimum effective parameters on thermal buckling of hybrid composite plates with quasi-square cut-out using a genetic algorithm

ABSTRACT

The thermal buckling load on perforated composite plates is affected by several parameters, including design variables such as cut-out orientation, fibre angle, bluntness of cut-out corners, cut-out size to plate size ratio and stacking sequence. This study investigates the effect of these parameters on the thermal buckling load of a composite plate with a quasi-square cut-out. Optimal values of the parameters are determined using a genetic algorithm to achieve the maximum buckling load. The composite used herein is a four-layer laminated composite plate. The stacking sequences of the plate are also studied. Stability equations are obtained using first order shear deformation theory. The results showed that a plate with a quasi-square cut-out is more resistant to thermal buckling than one with a circular cut-out; thermal buckling of a composite plate is dependent on various parameters, and the maximum thermal buckling load can be achieved by appropriate selection of these parameters.     

Experimental and numerical studies on buckling of laminated composite skew plates with circular holes under uniaxial compression

This article deals with experimental and finite element studies on the buckling of isotropic and laminated composite skew plates with circular holes subjected to uniaxial compression. The influence of skew angle, fiber orientation angle, laminate stacking sequence, and aspect ratio on critical buckling load are evaluated using the experimental method (using Methods I through V) and finite element method using MSC/NASTRAN. Method I yields the highest experimental value and Method IV the lowest experimental value for critical buckling load in the case of isotropic skew plates with circular holes. For all laminate stacking sequences considered, Method V yields the highest experimental value for critical buckling load for skew angle = 0° and Method IV yields the highest experimental value for critical buckling load for skew angles = 15° and 30°. For all laminate stacking sequences and skew angles considered, Method II yields the lowest experimental value for critical buckling load. The maximum discrepancy between the experimental values given by Method IV and the finite element solution is about 10% in the case of isotropic skew plates. The maximum discrepancy between the experimental values given by Method II and the finite element solution is about 21% in the case of laminated composite skew plates considered. The percentage of discrepancy between the numerical or finite element solution and experimental value increases as the skew angle increases. The critical buckling load decreases as the aspect ratio increases.     

面内线性变化载荷作用复合材料层合板的振动与屈曲优化

采用广义微分求积（GDQ）法开展了不同边界条件下承受面内线性变化载荷作用复合材料层合板振动与屈曲的分析与优化。针对GDQ法求解面内线性变化载荷工况复合材料层合板屈曲问题存在计算振荡、不收敛现象,提出载荷扰动策略实现了GDQ法对复合材料层合板屈曲问题的稳定高效求解。基于基础圆频率和临界屈曲载荷系数的归一化指标,分析了铺层角度对复合材料层合板综合性能的影响,并结合直接搜索模拟退火算法开展了复合材料层合板的铺层顺序优化。结果表明:铺层角度变化对屈曲性能的影响明显强于频率特性;面内线性变化载荷中,以弯曲载荷作用下复合材料层合板的优化综合性能受边界条件变化的影响最小,而优化铺层角度受边界条件变化的影响最大。研究结果为复杂载荷作用下复合材料层合板的设计提供了参考。      

Stress distribution in outer and inner plies of textile laminates and novel boundary conditions for unit cell analysis

The local stress–strain distribution in a unit cell of a textile laminate depends on the distance of the ply to the surface, the number of plies in the laminate, and the stacking sequence. A conventional meso FE analysis employs boundary conditions for a unit cell of the textile composite based on the assumption of periodicity in the thickness direction. In that case, the stress concentration can be drastically underestimated, especially in outer plies. This paper describes the interaction of plies, local stresses and displacements. To avoid the analysis of the whole laminate and to reduce it to the boundary value problem on one unit cell only, novel boundary conditions are introduced. These conditions are based on the analysis of a single unit cell: they account for the number of the plies in the laminate, distinguish between the outer and inner plies, and reproduce the meso stress–strain state with good precision.     

Failure mechanisms on composite specimens subjected to compression after impact

Composite panels are widely used in aeronautic and aerospace structures due to their high strength/weight ratio. The stiffness and the strength in the thickness direction of laminated composite panels is poor since no fibres are present in that direction and out-of-plane impact loading is considered potentially dangerous, mainly because the damage may be left undetected. Impact loading in composite panels leads to damage with matrix cracking, inter-laminar failure and eventually fibre breakage for higher impact energies. Even when no visible impact damage is observed at the surface on the point of impact, matrix cracking and inter-laminar failure can occur, and the carrying load of the composite laminates is considerably reduced. The greatest reduction in loading is observed in compression due to laminae buckling in the delaminated areas. The objective of this study is to determine the mechanisms of the damage growth of impacted composite laminates when subjected to compression after impact loading. For this purpose a series of impact and compression after impact tests were carried out on composite laminates made of carbon fibre reinforced epoxy resin matrix. An instrumented drop-weight-testing machine and modified compression after impact testing equipment were used together with a C-scan ultrasonic device for the damage identification. Four stacking sequences of two different epoxy resins in carbon fibres representative of four different elastic behaviours and with a different number of interfaces were used. Results showed that the delaminated area due to impact loading depends on the number of interfaces between plies. Two buckling failure mechanisms were identified during compression after impact, which are influenced more by the delamination area than by the stacking sequence.     

Development of novel cost effective hybrid ply carbon-fibre composites

A carbon-fibre/epoxy hybrid material has been developed which comprises ultra-high-performance fibres in the principal load-bearing direction and standard carbon fibres in the secondary orientations. The effect of stacking sequence on mechanical properties, including impact damage tolerance, has been studied and the results compared with non-hybrid data. By optimising the stacking sequence the hybrid material exhibited a mechanical performance similar to that of the ultra-high-performance material and a performance superior to the standard material. The energy absorbed during low velocity impact was analysed in terms of an initiation and propagation energy. The energy absorbed through delamination initiation was increased by placing 45 ° fibres in the surface plies and by placing ultra-high-performance fibres in the 0 ° plies. The energy absorbed during delamination growth was independent of the fibre type and determined solely by the matrix material. On the basis of current pre-preg prices the hybrid material corresponds to a significant cost saving of 12% through the use of lower cost standard fibres in the secondary stressed layers.