遗传算法在轮胎结构多目标优化设计中的应用

在轮胎结构设计中应用一种基于共享小生境技术的遗传算法(简称Pareto GA),用来求解多目标优化问题的Pareto最优解集合。在综合考虑轮胎带束层的耐久性和轮胎重量的基础上,通过三维有限元分析和室内耐久性试验建立了优化轮胎带束层的数学模型,采用Pareto遗传算法对该数学模型进行求解,获得了分散性很好的Pareto最优解集合。为了检验优化的效果,应用三维有限元分析技术,对优化胎与原胎进行了分析与对比。结果表明,该优化过程达到了预期的目的。     

遗传算法在桁架结构优化设计中的应用

本文提出桁架结构系统优化设计的新方法—遗传算法。它与常规化算法的不同之处在于从多个初始点开始寻优，并采用交迭和变异算子避免过早地收敛到局部最优解，可获得全局最优解，且不受初始值影响。该算法不必求导计算，编程简单、快捷，尤其适用于具有离散变量的结构优化设计问题。     

考虑高阶剪切的轮胎Gough刚度模型

轮胎是一种帘线增强橡胶复合材料结构,Gough刚度是表征轮胎侧向变形与磨耗的一个重要参数,但缺乏理论推导。本文基于高阶剪切复合材料梁理论,研究子午线轮胎带束层角度对轮胎侧向变形的影响及Gough刚度的理论基础。在Fiala横梁模型的基础上,将轮胎简化为弹性基础上的复合材料梁。胎侧及胎面胶简化为弹性基础,带束和胎体简化为复合材料梁。考虑高阶剪切位移场及帘线-橡胶材料的各向异性,利用虚功原理建立模型方程,得到了复合材料梁在侧向载荷作用下的小挠度理论解,与有限元结果和已有文献结果对比验证了其合理性。算例分析表明,当胎体等效梁结构的高宽比固定时,对应Gough刚度极大值带束角度是固定的;不同的帘线模量和橡胶模量也会对Gough刚度极大值所对应的带束角度产生不同的影响;带束层厚度对Gough刚度极大值对应的带束角度影响较小。根据Gough刚度极大值准则得到了不同高宽比下的轮胎最佳带束角度,利用实际轮胎解剖结构进行了验证。本文提出的模型为子午线轮胎带束角度优选和磨耗设计提供了理论指导。      

基于遗传算法的离散型结构拓扑优化设计

采用遗传算法求解包括桁架结构和框架结构的离散型结构拓扑优化问题。在遗传算法的基础上,通过引入拓扑变量并修改被删除杆件的材料弹性模量,提出了一个受多工况荷载作用,能同时考虑应力、稳定及位移等约束的离散型结构拓扑优化问题统一数学模型。该模型不但能同时适用于桁架结构和框架结构等离散型结构拓扑优化问题,而且还能解决奇异最优解问题。结合上述统一数学模型和遗传算法,给出了求解离散型结构拓扑优化问题的优化方法。算例结果表明,采用该文提出的拓扑优化方法可有效、方便地对桁架结构、框架结构等离散型结构进行拓扑优化设计。     

Redundancy allocation for multi-state systems using physical programming and genetic algorithms

This paper proposes a multi-objective optimization model for redundancy allocation for multi-state series–parallel systems. This model seeks to maximize system performance utility while minimizing system cost and system weight simultaneously. We use physical programming as an effective approach to optimize the system structure within this multi-objective optimization framework. The physical programming approach offers a flexible and effective way to address the conflicting nature of these different objectives. Genetic algorithm (GA) is used to solve the proposed physical programming-based optimization model due to the following three reasons: (1) the design variables, the number of components of each subsystems, are integer variables; (2) the objective functions in the physical programming-based optimization model do not have nice mathematical properties, and thus traditional optimization approaches are not suitable in this case; (3) GA has good global optimization performance. An example is used to illustrate the flexibility and effectiveness of the proposed physical programming approach over the single-objective method and the fuzzy optimization method.     

具有单向离合器的多楔带附件驱动系统旋转振动建模及参数优化设计

建立有单向离合器装置的三轮-多楔带附件驱动系统的非线性旋转振动数学模型。用Gear数值算法求解从动轮与张紧臂的角度波动。计算结果表明,有单向离合器装置时从动轮与张紧臂的角度波动、各带段的动态张力、带-轮间的滑移率等系统动态特性均明显减小。计算、研究单向离合器弹簧刚度的大小、附件轴与从动轮转动惯量比的大小对系统动态特性的影响。以张紧臂角度波动、单向离合器弹簧扭矩、带-从动轮间的滑移率最小为优化目标,建立单向离合器弹簧刚度和附件轴转动惯量两参数优化设计数学模型。结果表明,优化后的系统参数,三轮-多楔带传动系统的动态特性均得到一定程度的改善。文中单向离合器装置三轮-多楔带传动系统的建模、动态特性求解及参数优化设计方法,为发动机前端附件驱动系统的旋转振动控制提供参考。     

车轮定位角对操纵稳定性指标影响的定量研究

 车轮定位角的存在会使轮胎的受力状态发生变化,引起车轮的侧滑,从而改变车辆的性能,因此有必要定量地研究车轮定位的前束角、外倾角对操稳性能影响．一方面,从车轮侧滑来解释前束、外倾对转向特性的影响．另一方面,从考虑前束变化的车辆双轨模型推导公式来从理论上详细阐明前束、外倾与转弯半径的关系．然后,通过仿真,分析了不同轮胎载荷状态下的前束角、外倾角．最后,基于上述分析,具体定量地研究前束角、外倾角对车辆稳态和瞬态操纵稳定性指标的影响大小和趋势,并得到稳态及瞬态特性指标与车轮定位角的定量关系,结果与理论分析一致,为车轮定位角的精确设计奠定了基础．     

Techniques to suppress intermediate density in topology optimization of compliant mechanisms

Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Such practice prevails because large-scale discrete 0–1 mathematical programming is not generally available. Although the relaxed problems become tractable, they may cause the appearance of intermediate density in the optimum topologies, especially those of structures and compliant mechanisms. Various penalty schemes have been proposed to suppress the intermediate density. Most of the past works assumed that the same penalty schemes could be effectively applied to both problems of stiffest structure design and compliant mechanism design. Differences in nature between the problems are generally neglected. This work distinguished the two problems, and observed that complaint mechanism (CM) problem does not suffer intermediate density as seriously as minimum compliance (MC) problem does. Besides allocating more material, explicit and implicit penalties were pursued to suppress intermediate density. To ensure mesh-independence and not to complicate the nonconvex objective function in CM problem, a new technique using a constraint of explicit penalty with variable bound is proposed to suppress intermediate density in topology optimization of compliant mechanisms. Together with a perimeter constraint, the new technique is also applied to MC problem. Received 13 March 2000     

纸塑复合袋磁力压紧纠偏装置设计及优化

为解决纠偏传输时纸塑复合袋易产生褶皱的问题,设计了一种磁力压紧纠偏装置。首先,综合利用磁压紧皮带、传送带和磁铁位置调整装置等零部件,完成了纸塑复合袋磁力压紧纠偏装置的结构设计,并根据纸塑复合袋的受力分析,建立了动态磁力压紧纠偏数学模型。然后,对纸塑复合袋磁力压紧纠偏装置进行有限元建模,并根据纸塑复合袋纠偏过程设置边界条件及接触参数,采用显示动力学分析方法对其动态纠偏过程进行仿真。接着,基于仿真结果,结合BP（back propagation,反向传播）神经网络和GA（genetic algorithm,遗传算法）（简称为BP-GA算法）,建立了纸塑复合袋磁力压紧纠偏装置工艺参数优化模型。最后,通过相应的计算程序,实现了纸塑复合袋磁力压紧纠偏装置工艺参数的优化。结果表明：所设计的纸塑复合袋磁力压紧纠偏装置能较好地实现纠偏功能,可使纸塑复合袋在传输时产生的褶皱符合设计要求;纠偏时该装置的最优工艺参数为电磁铁磁力为7 N,左、右两侧皮带组件的间隙为476 mm,皮带组件与纸塑复合袋之间的动摩擦系数为0.25,实验结果与基于BP-GA算法的寻优结果较为一致。研究结果可为纸塑复合袋连续磁力纠偏的深入研究提供一定的参考。     

Bending stiffness of a tire-belt structure with steel cords

The modern belt structure of a radial tire is a composite strip composed of bias-laminated rubber sheets unidirectionally reinforced with steel cords. The out-of-plane bending stiffness of the belt was analyzed by using classical lamination theory, with special consideration of the bending stiffness of steel cords made of several twisted steel filaments and the coupled bending-shear deformation. It is shown that the bending stiffness of the belt markedly decreases with increase of bias angle and is seriously influenced by restraint conditions of the coupled bending-shear strain and the anticlastic curvature. The measured results of bending stiffness and coupled bending-shear strain agree well with the theoretical predictions.     

An engineering method for complex structural optimization involving both size and topology design variables

This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second-level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second-level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.     

Optimization of laminated composite structures using a bilevel strategy

This paper aims to obtain the optimal design of laminated composite structures. The design variables are specified as the ply angles and the laminate thicknesses. The objective is to obtain a structure with minimum weight that is capable of carrying a given set of static external forces without failure. The solution strategy consists of addressing the problem sequentially at two levels, each having a different algorithm and a separate set of design variables. The optimization techniques use a combination of sensitivity analysis combined with optimality criteria and mathematical programming. The adequacy of the solution is assured by constraints limiting stresses and displacements.     

基于遗传算法的复合材料层合板削层结构铺层优化

针对应力变化较大的碳纤维增强复合材料层合板,提出削层结构铺层分级优化模式。通过将结构分解为若干子铺层并对各子铺层的位置、尺寸、铺层数以及铺层顺序进行优化,得到了满足强度和可制造性要求且质量最小的结构设计方案。该模式的第1、2级优化利用参考层对各子铺层位置及尺寸进行优化,第3级优化通过引入3次样条插值参数化方法对各子铺层层数和铺层顺序进行优化。参考层的引入可减少设计变量的数量,3次样条插值参数化方法可解决以铺层角为设计变量时设计变量数目不确定的问题。利用有限元方法对结构进行力学分析计算,并依据Tsai-Wu准则确定结构强度。在第2、3级优化中利用遗传算法对优化问题进行求解。算例计算表明:削层结构铺层分级优化模式结果合理可信。与均匀铺层方法结果比较可知:削层结构可有效减少结构质量。     

基于多工况的汽车座椅骨架轻量化设计

安全带静态拉伸工况以及行李箱动态碰撞工况是汽车座椅安全法规中的2个重要工况。在满足安全法规要求的前提下,为实现汽车座椅的轻量化设计,提出了一种基于多工况的座椅骨架轻量化设计方法。以汽车座椅安全法规为设计准则,以座椅骨架质量最小为设计目标,综合考虑静、动态工况,对座椅骨架关键构件的尺寸进行优化设计。首先,建立座椅骨架的有限元模型,并以座椅骨架的质量为响应进行灵敏度分析,确定座椅骨架关键构件尺寸优化的设计变量;然后,建立座椅骨架关键构件尺寸优化的数学模型,实现座椅骨架的轻量化设计;最后,对优化后的座椅进行静、动态工况下的有限元仿真分析和试验研究,以验证优化结果的正确性。结果表明,相较于原座椅,优化后的座椅在满足安全法规要求的前提下减重7.89%,验证了所提出的轻量化设计方法的有效性。研究结果可为汽车座椅的安全性分析和轻量化设计提供参考,具有重要的工程实用价值。     

Structure/control optimization to improve the dynamic response of space structures

An integrated structural/control optimum design algorithm is presented. The algorithm can be used to modify the structural design variables to improve the dynamic response of a space structure with constraints on the damping parameters and the frequency distribution of the closed-loop system. The method used a nonlinear mathematical programming approach to obtain a structure with minimum weight that satisfies all the constraints. Application of the algorithm is illustrated by designing a truss structure.     

A genetic algorithm for optimal unequal-area block layout design

The use of a genetic algorithm (GA) to optimise the binary variables in a mixed-integer linear programming model for the block layout design problem with unequal areas that satisfies area requirements is analysed. The performance of a GA is improved using a local search through the possible binary variables assignment; results encourage the use of this technique to find a set of feasible solutions for the block layout design with more than nine departments.     

离散复合形法的改进及应用研究

在工程设计中,复合形法是求解约束非线性规划的一种直接方法.它计算简单、适用性强,是解决工程技术问题的常用方法.通常情况下,复合形法多用于连续变量优化设计问题的求解,但在工程实际中还存在大量的离散变量优化问题.为此,我们在连续变量复合形算法的基础上,采用平均值舍入法获取离散点,并改进了复合形迭代过程和停机准则,使之成为一种能直接求解离散变量优化解的方法.几个典型工程离散变量优化设计算例的计算结果表明,我们提出的方法十分有效.     

An efficient algorithm for the optimum design of trusses with discrete variables

A method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed. The method can also be applied to continuous variables. The original formulation leads to a non-linear constrained minimization problem with inequality constraints, which is solved by means of a sequence of approximate problems using dual techniques. In the dual space, the objective function is to be maximized, depends on continuous variables, is concave and has first and second order discontinuities. In addition, the constraints deal simply with restricting the dual variables to be non-negative. To solve the problem an ad hoc algorithm from mathematical programming has been adapted. Some examples have been developed to show the effectiveness of the method.     

以减轻重量为目标的索网桁架式可展开太空天线结构的优化设计

针对索网桁架式可展开天线的结构特点和性能要求,对其结构初始设计进行了优化研究.选取天线的桁架单元壁厚和索单元半径为设计变量,并对不同类型的设计变量进行了合理的归并,继而以结构重量为优化目标,以表面精度和基频为约束条件,建立了优化设计数学模型.考虑到索网结构有限元分析给计算带来的非线性和复杂性,使用序列二次规划法对模型求解,并给出了相关动力特性的敏度分析.通过算例分析可知,采用上述优化计算方法可以在保证天线工作性能的前提下有效地降低结构的重量,同时由优化迭代过程中约束函数值的变化情况可知,在一定范围内减小桁架单元壁厚和增大索单元半径,可以有效地提高天线表面精度和改善结构动力性能.     

Reliability-based design optimization with frequency constraints using a new safest point approach

In the reliability-based design optimization (RBDO) model, the mean values of uncertain variables are usually applied as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, an RBDO solution that reduces the structural weight in non-critical regions provides not only an improved design, but also a higher level of confidence in the design. Solving such nested optimization problems is extremely expensive for large-scale multidisciplinary systems that are likewise computationally intensive. This article focuses on the study of a particular problem representing the failure mode of structural vibration analysis. A new method is proposed, called safest point, that can efficiently give the reliability-based optimum solution under frequency constraints, and then several probability distributions are developed, which are mathematically nonlinear functions, for the proposed method. Finally, the efficiency of the extended approach is demonstrated for probability distributions such as log-normal and uniform distributions, and its applicability to the design of structures undergoing fluid–structure interaction phenomena, especially the design process of aeroelastic structures, is also demonstrated.