基于分层设计变量的复合材料层合板优化设计及灵敏度分析

在复合材料层合板的结构优化设计中,提出分层设计变量的优化方法以满足实际工程需要。在结构位移、自振频率和屈曲临界荷载灵敏度分析中,给出了刚度矩阵对分层厚度和分层角度设计变量的灵敏度计算公式,考虑了分层厚度变化引起层合板对称中心的改变,保证了计算准确性。数值算例验证了灵敏度算法的精度,应用实例显示了分层设计变量方法的实用性。     

基于傅里叶级数的缠绕复合材料刚度预测方法

采用傅里叶级数有关理论,根据缠绕复合材料内部细观结构的特点,建立了缠绕复合材料刚度预测模型。该模型将缠绕复合材料特征单元的刚度作为一个刚度场,利用二维傅里叶级数展开得到描述该刚度场的函数。算例的结果表明,本文中所建立的模型可以预测缠绕复合材料整体刚度特性,同时通过傅里叶级数各阶展开项的叠加可以反映材料内部细观结构对缠绕复合材料刚度特性的影响。      

弹性梁的刚度优化设计

利用阶梯析算法,给出了超静定弹性梁在任意载荷作用下最大挠度最小的刚度优化设计的表达式,用实例给出了在均布载荷作用下的刚度优化设计结果,并与相同的等截面兴做了比较,优化效果明显。     

输电塔结构离散变量优化设计方法

鉴于格构式输电塔结构具有杆件众多、型式复杂等显著特点,所以建设和发展既安全可靠,又经济合理的此类结构一直是工程界的研究热点和难点。因此,该文提出了一套完整的基于蚁群优化算法的输电塔结构离散变量优化设计方法。该方法是在结构的截面、拓扑和形状变量统一转化为离散变量的基础上,将4类不同层次的优化问题统一为不同规模的标准化旅行商问题,并最终采用蚁群算法实现输电塔结构的优化设计。通过对某一实际输电塔结构的优化设计表明：该文方法不仅可以简单高效的求解输电塔结构的截面、拓扑、形状和布局优化问题,而且清晰明确的阐述了不同优化内容的物理意义和优化准则,实现了优化方法和思路的统一。此外,基于蚁群算法的输电塔结构离散变量优化方法通用性强、易于程序化,而且具有非常好的工程应用前景。     

复合材料蜂窝夹层板结构的多工况优化设计研究

以复合材料蜂窝夹层板结构作为研究对象,建立了多工况优化模型,对众多的材料设计变量进行必要的取舍,通过优化分析确定复合材料蜂窝夹层板面板各分层的厚度以及蜂窝芯层的厚度等,使结构满足相应的频率约束、屈曲约束,以及强度约束、位移约束和尺寸限制等,同时达到结构的重量最轻。采用序列二次规划法对某卫星的承力筒结构进行了优化设计,优化结果表明:在满足其振动特性以及静力学特性的条件下,复合材料蜂窝承力筒的各面板层厚度以及蜂窝芯层的厚度均有所减小,减重效果显著,较好地实现了复合材料蜂窝夹层板结构的多工况优化设计。     

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%。     

基于SA算法的行星齿轮减速器离散变量优化设计

考虑制造工艺要求,将所有设计变量均视为离散变量,包括一般离散变量和伪离散变量,并就这两种情况下状态产生函数的设计原理进行深入研究,解决了将模拟退火算法用于离散变量函数优化的关键技术问题,介绍了一种基于模拟退火算法的离散变量函数优化的新方法。行星齿轮传动中各齿轮的齿数受传动比条件、同轴条件和装配条件的限制而不能任意取值,齿轮的模数也要受国家标准的制约只能取一些离散值,用以数学规划理论为基础的经典约束优化方法求解效果很差,用基于模拟退火算法的离散变量优化设计方法则可以方便快捷地获得满足各方面要求的最优设计方案。     

基于刚度-强度-重力的蜂窝纸板优化设计

分析了蜂窝纸板轻量型优化设计的刚度、强度约束函数和重量目标函数,找出了制箱或制托盘用蜂窝纸板结构优化设计方法,并用图解法举例说明了如何根据包装的具体需要优选蜂窝纸板结构.     

复合材料层板损伤过程的刚度分析

本文对典型铺设的[0₂/±45₂/90₂]_s碳/环氧复合材料层板中的典型损伤状态进行了实验观察,测定出损伤对层板刚度引起的下降率.建立了横向裂纹扩展、分层伴以横向裂纹扩展的三维有限元分析模型,计算出对层板刚度引起的下降率,并与实验值进行了比较.结果表明,横向裂纹和分层是层板的主要损伤型式,分层损伤扩展是一个主导性的稳定的损伤扩展过程,是导致刚度下降的主要因素.     

混杂纤维复合材料的拉伸刚度

对单向和多向混杂纤维复合材料的拉伸刚度进行了研究。在混合定律的基础上考虑混杂比和分散度对混杂效应的影响, 提出了单向混杂纤维复合材料拉伸模量的估算公式。通过实验得到了多向混杂纤维复合材料的拉伸模量, 并且采用经典层合板理论进行了估算, 基于混杂比以及分散度对拉伸模量的影响规律, 对多向混杂纤维复合材料拉伸模量的估算公式进行了修正。结果表明: 混杂纤维复合材料的拉伸模量与混杂比和分散度相关, 分散度的增大在一定程度上可以提高单向混杂纤维复合材料的纵向拉伸模量。采用经典层合板理论所得的拉伸模量与实验值有一定的误差, 而本文所提出的公式能够更加准确地估算混杂纤维复合材料的拉伸模量。      

Multi-objective design optimization of variable stiffness composite cylinders

The bending-induced buckling improvement in a variable stiffness (VS) composite cylinder (made by fiber steering) is studied. For such a cylinder, the effect of the variation of the direction of the load on its buckling performance of the cylinder is also examined. Compromise programming, as a multi-objective optimization method, is used to design for buckling of the VS cylinder subjected to bending load in either of the two opposite directions. Different combinations of weight factors for the structural performance in the two opposite directions were also applied to obtain the Pareto frontier as the main decision making tool for the designers in a multi-objective design problem.     

基于密度分布曲线法的复合材料变刚度铺层优化

基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计。在优化过程中需确定铺层中各单元的密度以及角度。为了使优化结果具有可制造性,优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取。为了避免在优化问题中引入过多的约束并减少设计变量的数目,提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化。根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵。优化过程中以结构柔顺度作为优化目标,结构体积作为约束,优化算法采用凸规划对偶算法。对碳纤维复合材料的算例结果表明:采用DDCM可得到较理想的优化结果,并且收敛速率较快。     

基于复合优化方法立式数控加工中心的多目标优化设计

为实现加工中心动静态性能不低于优化前性能,达到整机重量最轻的要求,本文提出了一种复合优化方法来研究多变量、多约束和多目标的数控加工中心优化设计。采用有限元分析和实验模态测试方法分析各大件动态性能,并验证了有限元模型的精确性。然后以该有限元模型为基础进行静态分析,得出各大件的最大变形及应力等。以柔度为目标,采用变密度法拓扑优化设计立柱结构的外形框架;以固有频率为目标,基于元结构的可适应性动态优化方法设计加工中心的筋板结构;以固有频率和质量为目标,基于响应面法的尺寸优化确定各结构的最优尺寸。最后将优化后的各大件进行整机装配,分析校核整机动静态性能。分析结果表明,优化后的整机在保证加工中心动静态性能的条件下,整机质量从12749kg减少到12127kg,减重达到4.9%,达到了整机的优化设计要求,说明该方法具有较高的精度和较强的工程实用性。     

复合材料副簧刚度的匹配设计方法

为了对复合材料副簧的刚度进行匹配设计,设计了包含有复合材料副簧的主副簧总成结构。采用集中载荷法计算复合材料副簧的等效载荷,根据原钢板弹簧的挠度变化来估算复合材料副簧的等效刚度。根据钢板弹簧设计理论,对复合材料副簧的等效刚度进行匹配设计。采用ABAQUS软件对设计的主副簧总成的总刚度进行有限元模拟,通过调整复合材料副簧的铺层数量来修正复合材料副簧的等效刚度。提出的匹配设计方法对复合材料板簧的推广应用具有重要意义。      

Maximum stiffness design of laminated composite plates via a constrained global optimization approach

The optimal lamination arrangements of laminated composite plates with maximum stiffness subject to side constraints are investigated via a constrained multi-start global optimization approach. In the optimal design process, the deformation analysis of laminated composite plates is accomplished by utilizing a shear deformable laminated composite finite element and the optimal design problem, which has been converted into an unconstrained minimization problem via the general augmented Lagrangian method, is solved by utilizing the proposed unconstrained multi-start global optimization technique to determine the optimal fiber angles and layer group thicknesses of the laminated composite plates for attaining maximum stiffness and simultaneously satisfying the imposed side constraints. The feasibility of the proposed constrained multi-start global optimization algorithm is validated by means of a simple but representative example and its applications are demonstrated by means of a number of examples on the maximum stiffness design of symmetrically laminated composite plates. The effects of length-to-thickness ratio, aspect ratio, and number of layer groups upon the optimum fiber angles and layer group thicknesses of the plates are investigated.     

Shape optimization of critical stiffener runouts for F-111 airframe life extension

ABSTRACT Optimal rework shapes for the most critical stiffener runout fatigue locations in the F-111 wing pivot fitting have been determined using a recently developed finite-element-based gradient-less shape optimization procedure. The resulting precise free-form shapes render the local notch stress distributions near uniform and typically provide a 30–40% reduction in peak elastic stresses as compared to the current rework shapes that exist for aircraft in service with the Royal Australian Air Force. The present numerical results are also consistent with recent preliminary experimental results, and a significant program of further validation testing is envisaged. Hence it is expected that the stress reductions predicted in the present work will be sufficient to provide a basis for extending inspection intervals by at least a factor of two; from 500 to 1000 h. Implementation of such an extension to the F-111 fleet in service with the Royal Australian Air Force would provide a very significant maintenance cost saving. The anticipated reduction in local crack growth rates would also allow achievement of the planned withdrawal date for the aircraft.     

Optimal lay-up design of variable stiffness laminated composite plates by a layer-wise optimization technique

The optimal lay-up design for the maximum fundamental frequency of variable stiffness laminated composite plates is investigated using a layer-wise optimization technique. The design variables are two fibre orientation angles per ply. Thin plate theory is used in conjunction with a p-element to calculate the fundamental frequencies of symmetrically and antisymmetrically laminated composite plates. Comparisons with existing optimal solutions for constant stiffness symmetrically laminated composite plates show excellent agreement. It is observed that the maximum fundamental frequency can be increased considerably using variable stiffness design as compared to constant stiffness design. In addition, optimal lay-ups for the maximum fundamental frequency of variable stiffness symmetrically and antisymmetrically laminated composite plates with different aspect ratios and various combinations of free, simply supported and clamped edge conditions are presented. These should prove a useful benchmark for optimal lay-ups of variable stiffness laminated composite plates.     

Concurrent optimization of stacking sequence and stiffener layout of a composite stiffened panel

This article is to optimally design laminated composite stiffened panels by optimizing both stacking sequences of the panel skin and stiffeners as well as the layout of stiffeners. Starting from initial designs of stiffener layout and stacking sequences for each stiffener and the panel skin, the problem is formulated with discrete and continuous variables, where discrete 0/1 variables represent the absence/presence of each layer in initial stacking sequences, and continuous variables represent layer thicknesses. A first-level approximate problem is established to make the problem explicit. Genetic algorithm is used to determine the existence of each layer in the laminates. When the number of retained layers in stiffener becomes zero, that stiffener can be seen as unnecessary and removed. For individual fitness calculation, a second-level approximate problem is constructed to optimize continuous ply thicknesses of retained layers. Correspondingly, laminated stacking sequences and stiffener layout are concurrently optimized.     

一种基于复合材料加筋板结构效率的稳定性优化方法

提出一种以承载效率最高作为目标的新设计方法, 对复合材料加筋板的承载能力进行优化。讨论了不同压缩与弯曲刚度的匹配模式与加筋板临界失稳载荷的关系。将全局失稳载荷、局部失稳载荷与静载荷的接近程度作为结构承载效率的量化标准, 通过静载荷的控制, 使结构的稳定性向着效率最高的方向优化。以宏观的加筋板压缩与弯曲刚度参数作为设计变量, 构建了一种可用于结构效率优化的代理模型, 避免了局部最优点的出现, 更便于数值寻优。通过有限元分析验证, 优化后壁板的临界失稳载荷与所施加的静载荷基本一致, 反映出较高的效率, 从而验证了该方法的可靠性。      

A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters

The purpose of this paper is to propose an effective solution scheme of simultaneous optimization design of layup configuration and fiber distribution for maximum stiffness design of laminated plates. Firstly, a numerical analysis of the lamination parameters feasible region for a laminated plate consisting of various given number of ply groups (each ply group may have different thickness and all the fibers in one ply group are orientated in an identical direction) is carried out, and it is found that the feasible region based on only a few ply groups is very close to the overall one determined by infinite plies. Therefore, it is suggested that the feasible region of lamination parameters of a laminated plate could be approximately determined by the layup configuration of least ply groups. Secondly, a two-step simultaneous optimization scheme of layup configuration and fiber distribution for maximum stiffness design of laminated plates is proposed. Accordingly, by using ply thickness, fiber orientation angle and fiber volume fraction in a laminated plate of least ply groups as design variables, the optimal lamination parameters for maximum stiffness is obtained. Then, taking the optimal lamination parameters as the design objective, a detailed layup design optimization is implemented by considering some limitations on manufacturing, such as preset ply thickness, and specific fiber orientation angle and a limited maximum number of consecutive plies in the same fiber orientation. Numerical examples are also presented to validate the proposed two-step optimization scheme.