基于PCE方法的翼型不确定性分析及稳健设计

由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注. 不确定性分析是稳健型设计的关键. 因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD 方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析. 首先以RAE2822 翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差. 接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性. 优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小. 通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.      

基于PCE方法的翼型不确定性分析及稳健设计简

由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注. 不确定性分析是稳健型设计的关键. 因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD 方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析. 首先以RAE2822 翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差. 接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性. 优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小. 通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.     

跨音速翼型和机翼的气动优化设计

以NACA0012翼型和ONERA－M6机翼为基准,分别把可变误差多面体法（VEP）和遗传算法（GA）两种不同的优化方法与求解二维和三维欧拉方程的气动分析相结合,进行跨音速翼型和机翼的气动优化设计,并在其基础上对两种不同性质的优化方法在气动优化设计应用中的优化质量和计算效率进行比较,在优化设计的过程中,翼型通过解析函数线性叠加法来表示,机翼通过不变的翼型和可变的平面形状来表示,二维和三维欧拉方程采用Jamenson提出的有限体积方案,显式四步RungeKutta时间推进求解。     

基于高阶矩的稳健优化设计研究

采用随机响应量的前四阶统计矩来度量目标函数和概率约束条件的稳健性, 通过引入“权重因子”来确定新构造的目标函数中原 函数和敏感系数的比重, 利用加权组合法将稳健优化设计这一多目标优化问题转化为单目标问题, 从而建立新的基于高阶矩的稳健优化设计数学模型. 矩估计方法可高效地评估目标函数和概率约束条件的统计矩, 且不需要搜索技术, 因此不构成嵌套循环(即稳健优化过程是单循环的), 从而可以大大降低优化的计算工作量. 对多个桁架结构进行了确定性优化设计、可靠性优化设计、传统的和该文所提的稳健优化设计, 验证了所建立的基于高阶矩的稳健优化设计数学模型的合理性和正确性, 比较并解释了计算所得的优化结果.     

基于多目标优化策略的结构可靠性稳健设计

应用可靠性稳健优化设计理论和多目标决策方法,将结构可靠性稳健优化设计转化为多目标优化问题。运用灰色理论中的关联分析法,选取粒子群算法中的全局极值和个体极值,提出了灰色粒子群算法求解可靠性稳健优化设计问题。与传统方法相比,该方法简便易行并能迅速准确地得到结构可靠性稳健优化设计信息。     

基于混沌多项式方法的层流超临界翼型稳健设计研究

开展层流超临界翼型稳健设计研究。针对传统的基于蒙特卡洛不确定分析方法的稳健设计系统计算量巨大、效率低下等问题,引入了混沌多项式方法,建立了新型稳健设计系统。采用RAE2822翼型稳健设计验证了设计系统的可靠性、高效性。结果表明,混沌多项式方法在保证设计精度的基础上设计效率提高了10倍左右。采用该系统进行了层流超临界翼型稳健设计研究,设计的结果表明:对于层流超临界翼型设计需要兼顾层流区长度、阻力发散特性;基于多目标稳健设计方法可以权衡设计点特性和阻力的波动特性;设计后翼型与原始翼型相比,设计点阻力减小了10cunts,阻力发散马赫数提高了0.01,在整个马赫数范围内维持了低的阻力特性。     

基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

多可信度代理模型已经成为提高基于代理模型的优化算法效率和可信度水平最有效的手段之一.然而目前流行的co-Kriging和分层Kriging (HK)等多可信度代理模型泛化能力不足,缺乏对高阶/高非线性建模问题的适应性,难以广泛应用.文章基于发展的自适应多可信度多项式混沌-Kriging (MF-PCK)代理模型,在提高建模效率和对高阶/高非线性问题近似准确率的同时,建立了基于该自适应MF-PCK模型的高效全局气动优化方法.在发展的方法中,提出了基于MF-PCK模型的新型变可信度期望改进加点方法,使代理优化算法效率进一步提高.为了验证发展方法的全面表现,将其应用在经典的数值函数算例以及多个跨音速气动外形的确定性优化和稳健优化设计中,并与基于Kriging和HK模型的代理优化算法进行了全面比较.结果表明,发展的新型多可信度全局气动优化方法其优化效率相对于基于Kriging和HK模型的优化效率显著提高,结果更好也更加可靠,并且稳健优化设计效率和结果也更符合工程应用需求,证明了其相对于基于Kriging和HK模型的代理优化算法的显著优势.     

非正态分布参数的梁结构的刚度可靠性稳健设计

将刚度可靠性设计理论和稳健设计方法相结合,讨论了具有非正态分布参数的梁结构的刚度可靠性稳健设计问题,提出了刚度可靠性稳健设计的计算方法.把可靠性灵敏度融入可靠性优化设计模型之中,将刚度可靠性的稳健设计归结为满足可靠性要求的多目标优化问题.在基本随机参数的前四阶矩已知的情况下,通过计算机程序可以实现具有非正态分布参数的梁结构的刚度可靠性稳健设计,迅速准确地得到具有非正态分布参数的梁结构刚度可靠性稳健设计信息.     

翼型多目标气动优化设计方法

将数值优化软件modeFRONTIER同计算流体力学(CFD)软件相结合,对NACA0012翼型的气动性能进行优化.计算采用N-S方程作为主控方程以计算翼型气动性能,分别采用多目标遗传算法(MOGA)和多目标模拟退火算法(MOSA)作为翼型的气动性能优化算法.计算结果表明,优化后的翼型相对于优化前的翼型的气动性能有很大提高(升阻比增幅可达182%).     

高空长航时无人机高升阻比两段翼型设计研究

针对某特定无人机的使用设计要求,在单段翼型设计研究的基础上,尝试了高升阻比低雷诺数两段翼型的设计方法的分析与研究.采用求解椭圆型方程加控制点约束条件的"椭圆-控制点切割法"完成了两段翼型外形的生成,并针对巡航构型的襟翼偏角对缝道参数进行了优化;应用MSES计算分析程序对所设计的两段翼型的气动特性进行了分析评估.计算结果表明:本文所设计的两段翼型的最大升力系数达到2.72,最大升阻比为158.71;与原始单段翼型相比,最大升力系数增大了74.35%,最大升阻比增大了28.64%.     

Design optimization for manufacturability of axisymmetric continuum structures using metamorphic development

In this study, optimal shapes/profiles of axisymmetric continuum structures optimized for performance and manufacturability are sought, using a topology/shape optimization method called metamorphic development (MD). The optimization seeks to find an optimum cross-sectional profile and minimum weight design, subjected to von-Mises stress constraints under coupled thermal and pressure loadings. Both quadrilateral and triangular finite elements (FE) were used to ‘metamorphically’ develop the structure. Two different design optimization approaches were taken, by defining a set of finite ‘restricted’ and ‘unrestricted’ design domains. Manufacturability of the optimized structures was considered. Prior to manufacturing, a post-optimization process was performed. A comparison was then performed for both sets of optimized solutions to demonstrate whether the ‘restricted’ design domain solution gave greater or lesser performance characteristics compared to the ‘unrestricted’ design domain solution which could only be manufactured by additive manufacturing technologies (AMT). The results of the optimization demonstrated the success of the MD method in generating practical design solutions which meet both performance requirements and manufacturing considerations.     

Buckling optimization of flexible columns

A novel approach to the optimization of flexible columns against buckling is presented. Previous published studies, considering either continuous or discrete finite element models, are always constrained to specific relations between stiffness and mass distributions of the column. These, besides yielding impractical configurations that do not conform to manufacturing and production requirements, result in designs that are certainly suboptimal. The present model formulation considers columns that can be practically made of uniform segments with the true design variables defined to be the cross-sectional area, radius of gyration and length of each segment. Exact structural analysis is performed, ensuring the attainment of the absolute maximum critical buckling load for any number of segments, type of cross section and type of boundary conditions. Detailed results are presented and discussed for clamped columns having either solid or tubular cross-sectional configurations, where useful design trends have been recommended for optimum patterns with two, three and more segments. It is shown that the developed optimization model, which is not restricted to specific properties of the cross section, can give higher values of the critical load than those obtained from constrained-continuous shape optimization. In fact, the model has succeeded in arriving at the global optimal column designs having the absolute maximum buckling load without violating the economic feasibility requirements.     

Application of dual kriging to structural shape optimization based on the boundary contour method

Summary The paper presents an approach in which the coupling of dual kriging and the boundary contour method (BCM) is applied to structural shape optimization problems in mechanical engineering design. The problems consist of optimizing the shape of an elastic body, which requires minimizing an objective function subject to some given constraints, such as those of displacement, stress or manufacturing. The originality of the present work is involved with the use of two novel methods that are combined here to solve structural shape optimization problems. The first one, called dual kriging, is a general, versatile interpolation and geometric modeling tool. The second one is a new variant of the boundary element method (BEM), called the BCM, which achieves a further reduction in dimensionality of analysis problems. Based on the advantages of these two methods, the coupling approach presented here is expected to offer an effective as well as a straightforward manner for solving shape optimal design problems. Received 18 December 1997; accepted for publication 21 April 1998     

随机参数连续体结构的动力学拓扑优化

构造了基于概率的连续体结构动力特性拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总重量极小化为目标函数,满足结构多阶固有频率约束的可靠性要求为约束条件。利用分布函数法对模型中的可靠性约束进行了等价化处理。采用了渐进结构优化(ESO)的求解策略与方法。通过算例验证了文中所提出的设计模型及求解策略与方法的合理性和有效性。     

超静定型钢桁架优化设计的面积比法

满应力准则是对超静定型钢桁架进行优化设计的有效方法．但这种方法的主要缺点在于收敛速度很慢甚至不收敛,这给设计工作带来很大的不便．对问题进行了研究,在“型钢压杆稳定设计直接法”的基础上,提出了满应力优化设计的一种新方法——面积比法,有效地提高了设计过程的收敛速度,降低了设计成本,供有关结构设计人员参考．     

Optimal Modification of Shape for Two-Dimensional Elastic Bodies

A variational formulation is presented for shape optimal design of two-dimensional elastic bodies. Optimal modification or remodel of a specified shape is determined for reinforcing (addition of material), lightening (removal of material), or redistribution of material by a specified amount. Necessary conditions are obtained in analytical form to provide the basis for an algorithm to solve the optimal remodel design problem computationally. The method is demonstrated for examples in both torsion and plane stress problems, including cases in which the optimal modification calls for introduction of a hole into an original shape.     

最佳边坡形状的力学分析及应用研究

 基于弹性力学和热力学的基本理论，分析了最佳边坡形状和合 理边坡角的计算方法, 并得出最佳边坡形状方程. 实例应用表明，计 算结果与边坡实际基本一致，说明该方法确定边坡的最佳形状和合理 边坡角是可行的、有效的，该方法适用于边坡设计和边坡稳定性研究.     

Optimization of tensegrity structures

This paper concerns the design of tensegrity structures with optimal mass-to-stiffness ratio. Starting from an initial layout that defines the largest set of allowed element connections, the procedure seeks the topology, geometry and prestress of the structure that yields optimal designs for different loading scenarios. The design constraints include strength constraints for all elements of the structure, buckling constraints for bars, and shape constraints. The problem formulation accommodates different symmetry constraints for structure parameters and shape. The static response of the structure is computed by using the nonlinear large displacement model. The problem is cast in the form of a nonlinear program. Examples show layouts of 2D and 3D asymmetric and symmetric structures. The influence of the material parameters on the optimal shape of the structure is investigated.     

三轴转台框架的形状优化设计

本文叙述了三轴转台四种不同的布局型式。提出了用Ｂｅｚｉｅｒ曲线和Ｆｏｕｒｉｅｒ级数描述三轴转台框架的形状，将形状优化设计问题转换为可用参数优化设计方法求解的形式。建立了ＯＵＴ型三轴转台外框架结构的形状优化设计数学模型，然后给出了用增广乘子法对问题进行求解的步骤     

Multilevel functional preconditioning for shape optimisation

We study the application of a multi-level preconditioner to a practical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu (BPX) series. We extend it to the unstructured parametrization of 3D shapes by using the volume–agglomeration heuristics. The choice of the smoothing parameter is analysed from functional arguments. Application to the shape design for optimising aerodynamic and sonic boom performances of a wing is demonstrated.