The stacking sequence optimization of stiffened laminated curved panels with different loading and stiffener spacing

An efficient procedure to obtain the optimal stacking sequence and the minimum weight of stiffened laminated composite curved panels under several loading conditions and stiffener layouts has been developed based on the finite element method and the genetic algorithm that is powerful for the problem with integer variables. Often, designing composite laminates ends up with a stacking sequence optimization that may be formulated as an integer programming problem. This procedure is applied for a problem to find the stacking sequence having a maximum critical buckling load factor and the minimum weight. The object function in this case is the weight of a stiffened laminated composite shell. Three different types of stiffener layouts with different loading conditions are investigated to see how these parameters influence on the stacking sequence optimization of the panel and the stiffeners. It is noticed from the results that the optimal stacking sequence and lay-up angles vary depending on the types of loading and stiffener spacing.     

STACKING SEQUENCE OPTIMIZA- TION OF LAMINATED COMPOSITE CYLINDER SHELL FOR MAXIMAL BUCKLING LOAD

A new optimization method for the optimization of stacking of composite glass fiber laminates is developed. The fiber orientation and angle of the layers of the cylindrical shells are sought considering the buckling load. The proposed optimization algorithm applies both finite element analysis and the mode-pursuing sampling （MPS）method. The algorithms suggest the optimal stacking sequence for achieving the maximal buckling load. The procedure is implemented by integrating ANSYS and MATLAB. The stacking sequence designing for the symmetric angle-ply three-layered and five-layered composite cylinder shells is presented to illustrate the optimization process, respectively. Compared with the genetic algorithms, the proposed optimization method is much faster and efficient for composite staking sequence plan.     

基于改进模拟退火算法的复合材料层合板屈曲优化

针对复合材料层合板的屈曲优化问题,提出一种改进的直接搜索模拟退火算法来求解最大化临界屈曲载荷系数的铺层顺序设计问题。改进算法引入搜索范围动态调整的新点产生方式实现全局搜索和局部搜索的协调,提高了算法的计算稳定性和计算效率。以离散铺层角为设计变量,采用里兹法进行屈曲响应分析以考虑弯扭耦合影响,通过典型多极值屈曲优化问题分析比较了算法改进措施的有效性。不同角度增量、铺层数、长宽比和载荷比的层合板屈曲优化结果表明,改进算法能有效地进行层合板铺层顺序优化。     

应用扰动广义微分求积法的复合材料层合板剪切屈曲分析与优化

广义微分求积(GDQ)法求解复合材料层合板剪切屈曲时存在计算精度差、计算振荡不收敛问题,研究发现该现象源于载荷矩阵存在奇异,为此,提出扰动GDQ法,通过扰动主对角线权重系数以改善载荷矩阵的奇异性来消除计算振荡。数值算例验证了扰动策略的有效性,实现复合材料层合板剪切屈曲问题的高效稳定求解。在此基础上,结合直接搜索模拟退火算法,开展了含剪切载荷的复合材料层合板铺层顺序优化。结果表明：剪切工况时对称复合材料层合板的优化铺层不受铺层数和铺设形式影响,优化铺层角随长宽比增大而趋于60°;而剪切与轴压组合工况下较小的剪切力能改善层合板屈曲性能,随着剪切力的增大,优化屈曲性能逐渐降低,优化铺层趋同于剪切工况。研究结果为复合材料层合板的剪切屈曲性能设计提供了参考。     

Post-buckling and delamination propagation behavior of composite laminates with embedded delamination

Delamination occurred due to poor manufacturing process or in-service actions significantly affects the mechanical and failure behavior of laminated composite structures. In this study, the buckling and post-buckling delamination behavior of laminated composite with an embedded initial delamination under in-plane compression was studied experimentally and numerically. First, compression tests for laminated composite specimens with embeded initial delamination were performed and the buckling and delamination responses were obtained. Then the experimental test was numerically simulated using finite element methods with the progressive failure accounted for by using cohesive zone modeling. The load-displacement curve, strain behavior and delamination shapes of experimental specimens obtained from load cells, strain gages installed at different locations, and C scan images, respectively, were compared with the FEM results, and good agreements were attained. The effect of the buckling modes, laminate stacking sequence and shape of initial delamination on the buckling load and propagation behavior was studied by considering different ply stacking and shapes of initial delaminations. It was found that the buckling mode determined the growth direction of the delamination propagation, and the stacking sequence influenced the extent of the propagation area, while the orientation of the delamination affected the buckling loads.     

Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element

The paper deals with the validation of a recently proposed hexahedral solid-shell finite element in the buckling analysis of a laminated composite plate with delaminations. The object is to study the buckling behavior of structures with delaminations using the enhanced assumed strain (EAS) solid shell element with 5, 7 and 9 parameters. The EAS three-dimensional finite element formulation presented in this paper is free from shear locking and leads to accurate results for distorted element shapes. The developed FE model is used to study the effects of some parameters in the buckling load, such as the stacking sequences, delamination size, aspect ratio, width-to-thickness ratio. The feasibility of the proposed method is confirmed by numerical examples. Results show that using hexahedral solid-shell finite element in the buckling analysis is more efficient than using the enhanced solid finite element.     

某手掷式无人机机翼结构拓扑优化设计研究

为解决某型手掷式无人机机翼结构重量占比高的问题,采用一种多变量结构拓扑优化设计方法。以结构重量最小为优化目标,以Fluent软件计算的气动力为载荷输入,以Nastran软件计算的结构最大形变、最大应力和屈曲特征值为约束,以机翼结构尺寸为优化变量进行减重优化设计。结构性能仿真结果表明,优化后机翼结构减重21.7%且满足结构安全性能约束要求。可提升该无人机续航时间38%,增加有效载荷278 g。优化后机翼结构尺寸的变化规律也为同类型飞机机翼结构设计提供了参考。     

复合材料加筋板在剪切载荷下的屈曲特性研究

通过对复合材料薄壁加筋板结构进行剪切载荷下的屈曲试验研究,得到结构的屈曲模态、屈曲失稳载荷以及破坏形式,并通过有限元方法对结构的屈曲进行数值分析,分析得到的复合材料薄壁加筋板结构的屈曲模态和试验结果一致,屈曲载荷与试验结果吻合较好.试验还发现复合材料薄壁加筋板结构有较高的后屈曲承载能力,后屈曲过程中由于桁条脱胶会造成屈曲模态的变化.还分析了筋条的连续性对屈曲载荷的影响.     

Coupled modification of natural frequencies and buckling loads of composite cylindrical panels

This paper proposes a new method for performing predefined simultaneous modification of natural frequencies and buckling loads of composite cylindrical panels. The method is based on the fact that both natural frequencies and buckling loads are eigenvalues of an algebraic system of simultaneous equations. First- and second-order derivatives of these eigenvalues are calculated and the first two terms in Taylor expansion are used for developing a modification procedure that is defined as an inverse eigenvalue problem. A four-layered composite cylindrical panel with an arbitrary angle-ply stacking sequence is considered as a case study and several simultaneous modifications for natural frequencies and buckling loads are carried out. It is shown that the proposed method can perform the predefined modification with an acceptable accuracy even for large perturbations in objective functions.     

Simultaneous topology and size optimization of locomotive structure using multinary genetic algorithms

Structural optimization of a typical locomotive carbody subjected to various operational loads is investigated using a simultaneous topology and size optimization approach. The proposed approach builds on a string representation of the structure in which the presence or absence of a structural element between specific nodes, as well as its cross-section, are represented by integers. Strings representing various structure topologies are then evolved according to a modified Genetic algorithm with improved genetic operators. The efficiency of the proposed model is verified through applying it to optimize the carbody structure of ER24PC locomotive. Operational load cases and performance criteria are adopted from the European standard EN12663. It is shown that the results based on the present optimal design have higher safety factors compared to the original design without a significant increase in weight. Besides, the computational cost of the optimization process is shown to be considerably less than that of the classical binary Genetic algorithm.

     

航空电子设备复合材料结构优化设计概述

复合材料由于其良好的性能而在航空电子设备中的应用越来越广泛。讨论了航空电子设备复合材料结构优化设计技术,对优化的数学模型展开论述,介绍了优化的五个层次的材料工艺优化、拓扑优化、位置优化、尺寸优化和铺层优化,同时阐述了它们的特点和相应的优化算法。继而针对航空电子设备,研究了复合材料结构综合优化方法。通过对某型天线罩进行结构优化设计,结果表明了优化方法的可行性。     

A lightweight design approach for an EMU carbody using a material selection method and size optimization

This study proposes a weight reduction design approach for urban transit carbody using a material selection method and size optimization. First, the material selection method, which uses specific stiffness and strength indices to predict the weight reduction rate, is set up when the materials of the under-frame and roof structure are substituted. The CFRP was chosen as the best weight reduction material in terms of the material selection method but was not appropriate for application to an urban transit carbody as a thin panel because of out-of-plane deformation. Therefore, we applied CFRP-AL honeycomb sandwich composites to the under-frame and roof structures, and the size optimization method was subsequently applied to derive a lightweight composite hybrid carbody design. Finally, the proposed approach was applied to an urban transit carbody, i.e., a Korean electrical multiple units carbody made of aluminum extrusion profiles. The weight of the optimized composite hybrid carbody design was 29.0% lighter than that of the original K-EMU. The resulting composite hybrid carbody design satisfied the design guidelines of the Performance test standard for K-EMU according to the corresponding FE simulations.

     

复合材料加筋结构的神经网络响应面优化设计

针对复合材料加筋结构优化设计的复杂性,提出利用人工神经网络结构近似分析响应面来反映结构设计输入与结构响应输出的全局映射关系的优化方法。通过正交试验设计选取合适的结构有限元分析样本点,进行神经网络响应面的构建和训练;将神经网络响应面作为目标函数或者约束条件,汇同其他常规约束条件完成优化模型的建立,并应用遗传算法(GA)进行优化,从而形成一套适应性强的的高效优化方法。以复合材料翼身融合体帽型加筋板的质量优化为实例,建立加筋板模型的重量响应面目标函数、强度和翘曲稳定性响应面约束条件;通过PATRAN/NASTRAN有限元软件进行有限元计算,获取用于响应面训练的样本点数值。算例结果表明,该方法能以很少的有限元分析次数取得高精度的响应面近似模型,并且使优化计算耗时大为减少,优化效率大大提高。     

A new method based on LPP and NSGA-II for multiobjective robust collaborative optimization

The multiobjective robust collaborative optimization framework consists of optimization both at the system and autonomous subsystem levels. Linear physical programming is used in the system level optimization, which avoids the difficulty in choosing the multidimensional Pareto set. The non-dominated sorting genetic algorithm (NSGA-II) is used in the subsystem optimization with physical objectives. The interdisciplinary incompatibility function and physical objectives have different priority levels. At the first priority level, the best individual should be in the feasible region of the subsystem. At the second priority level, the interdisciplinary incompatibility function of the best individual should be no more than the feasibility threshold. The physical objectives are improved after the achievement of the above levels. A method for producing initial population with feasibility and diversity is proposed to improve the calculation efficiency and accuracy of the subsystem optimization at the first priority level. A method for setting dynamic feasibility threshold is proposed for the non-dominated sorting to help the physical objectives to obtain better solutions at the second priority level. Finally, the results of the speed reducer show that the presented method is efficient.     

正置正交加筋薄壁柱壳优化设计参数化有限元方法研究

利用有限元软件建立轴压正置正交加筋薄壁圆柱壳的参数化有限元分析模型,研究结构参数对薄壁加筋圆柱壳结构的临界载荷和屈曲模式的影响。随着蒙皮厚度的增加,结构的屈曲模式由局部屈曲逐步变化到总体屈曲,屈曲载荷上升;随着加筋厚度或宽度的增加,由总体屈曲变化到局部屈曲,屈曲载荷上升。通过等体积时的参数变化对屈曲载荷和屈曲模式的影响研究,表明在对应某体积的设计中,只有一种设计使结构屈曲载荷达到最大,而当此最大的屈曲载荷等于设计载荷时,是最轻重量的设计。在此基础上发展一种基于APDL(Ansys parametric design language)语言的薄壁加筋圆柱壳结构优化设计方法,利用该方法给出设计算例的优化结果。     

Buckling analysis of filament-wound thick composite cylinder under hydrostatic pressure

Underwater vehicles that operate in deep waters require a pressure hull to maintain the sufficient strength and stiffness against external hydrostatic pressure. We investigated the validity of the finite element method (FEM) that is applied to a buckling analysis of the filament-wound composite cylinder, subjected to an external hydrostatic pressure. Two methods were suggested for the buckling analysis of a filament-wound thick composite cylinder under hydrostatic pressure: using the equivalent properties of the composite, and using stacking sequence. The hydrostatic pressure test was conducted to verify the FEA. Test results were compared with the previous results obtained by FEM on the buckling of a filament-wound composite cylinder under hydrostatic pressure. FEM analysis results were in good agreement with the test results. The difference between FEM results and the test results was approximately 1∼5%.     

基于整数编码并行遗传算法的复合材料螺旋桨结构优化设计

提出一种针对大型复合材料结构铺层厚度和铺层顺序同时进行优化的整数编码并行遗传算法,并将该优化方法应用于复合材料螺旋桨结构优化问题.首先,在区域划分的基础上,对每一单层设定一个长度控制因子来决定单层的铺设区域,以实现对大型复合材料结构的整体一次性优化.然后对遗传算法进行改进,使之成为一种能同时优化铺层厚度和铺层顺序的高效算法.并采用并行编程语言标准MPI( message passing interface)构建并行编程环境,利用主从式并行遗传算法框架,实现遗传算法在单机多进程上的并行计算.最后针对复合材料螺旋桨结构进行优化设计,以验证该方法的高效性,并分析并行遗传算法的加速效果.     

Multi-objective optimization of hygro-thermally curvature-stable antisymmetric laminates with extension-twist coupling

This paper investigates hygro-thermally curvature-stable (HTCS) antisymmetric laminates with extension-twist coupling. Stacking sequences are designed to obtain optimal extension-twist coupling and buckling strength. A new objective function that maximizes both extension-twist coupling and buckling strength is established by using the weighted sum method. Multi-objective optimization of HTCS antisymmetric laminates is performed for T300/976 graphite/epoxy laminates. Results are presented for the laminates that consist of 6–14 even plies. The effects of the weighting coefficients on the extension-twist coupling and buckling load are analyzed. The robustness of the optimization method is verified by using Monte Carlo simulation for laminates with fiber orientation that slightly deviates from the theoretically designed direction.     

微小型空间相机碳纤维整体式主框架轻量化设计

针对某微小型离轴空间相机结构紧凑、质量轻的设计要求,设计了一个高度轻量化的整体式碳纤维主框架。首先,根据空间相机具体功能的设计指标和光学系统,确定主框架的材料和结构形式,设计出碳纤维整体式主框架的基本构型。接着对铺层厚度参数化优化,并考虑碳纤维复合材料的制造约束,确定了主框架碳纤维铺层的厚度、比例。将参数化优化的结果进行离散化,进行碳纤维铺层顺序的优化,确定了最佳的堆叠次序,完成了碳纤维的铺层优化设计,实现了主框架的轻量化设计,解决了复杂碳纤维零件优化的问题。然后对设计完的碳纤维主框架结构代入整机有限元模型中,进行有限元仿真分析,验证主框架的性能指标。最后,将整机装配完成进行动力学试验,并与有限元分析结果进行对比验证。经过优化,碳纤维主框架的质量为4.5 kg,相机一阶频率为81 Hz,动力学试验得到的相机整机的一阶频率为78 Hz,仿真误差为3.7%,符合仿真结果,进一步说明了设计的合理性以及正确性。本文提出的空间相机碳纤维整体式主框架设计方法对微小型离轴三反式空间相机结构设计以及碳纤维零件的轻量化优化设计具有一定的借鉴意义。     

Optimum shape for buckling and post-buckling behavior of a laminated composite panel with I-type stiffeners

A shape optimization of stiffener was conducted to increase buckling load or failure load with stiffened laminated composite panel of I-type under compression loading. Design variables are cap length, web length, and/or thickness under the constraint of volume constancy. The objective function is buckling load and failure load of post-buckling based on Tsai-Hill theory using ABAQLJS 5.8 for analysis and Optimizer on Broydon-Fletcher Goldfarb-Sharno Method and Augmented Lagrange Multiplier Method. The effects of relative length of a web and a cap of stiffener on buckling load and failure load of post-buckling were investigated with the results of optimum design.