空间桁架结构动力学形状优化设计

在多阶固有频率约束条件下,采用“渐进结点移动法”,对空间桁架结构的形状进行优化设计,使结构重量达到最小。首先分析固有频率相对结点位置的一阶导数,确定结点移动的效率,即灵敏度数。根据灵敏度分析结果,优先移动效率较高的结点。然后,利用库恩-塔克优化条件检验所得结果,保证优化过程收敛于最小重量设计。最后,用二个典型数值算例验证本文算法的有效性和可靠性。     

基于Newmark法敏度计算的刚架结构动力优化

提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。     

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。     

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。     

SHAPE DESIGN SENSITIVITY ANALYSIS AND OPTIMIZATION FOR STRUCTURAL DURABILITY

In this paper, a design sensitivity analysis (DSA) method for fatigue life of 3-D solid structural components of mechanical systems with respect to shape design parameters is presented. The DSA method uses dynamic stress DSA obtained using an analytical approach to predict dynamic stress increment due to design changes; computes fatigue life of the component, including crack initiation and crack propagation, using the predicted dynamic stress; and uses the difference of the new life and the original life at the same critical point to approximate the sensitivity of fatigue life. A tracked vehicle roadarm is presented in this paper to demonstrate accuracy and efficiency of the DSA method. Also, this method is applied to support design optimization of the tracked vehicle roadarm considering crack initiation lives as design constraints. © 1997 by John Wiley & Sons, Ltd.     

离散变量结构优化的拟满应力设计方法

本文以满应力设计思想为基础,提出了适用于离散变量结构优化设计计算的拟满应力设计方法。该方法能直接计算具有应力约束和截面尺寸约柬的离散变量结构优化设计问题,也能处理同时具有稳定性约束和位移约束的多工况、多约束、多变量的离散变量结构优化设计问题。算例结果表明,拟满应力设计方法对于离散变量结构优化计算是非常有效的。     

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。     

SENSITIVITY ANALYSIS AND OPTIMIZATION OF ELASTIC-PLASTIC STRUCTURES

Elastic-plastic analysis problems formulated as quadratic programming problems involve energy functional and equilibrium and yield constraints that depend on the design, material and loading. In this paper we consider the problem of determining the variation of structural response with respect to variations of these parameters. A general result for discrete structures is presented and implications for optimal design are discussed.     

LAGRANGEAN RELAXATION AND SUBGRADIENT OPTIMIZATION APPLIED TO OPTIMAL DESIGN WITH DISCRETE SIZING

The discrete sizing problem in optimal design is adressed. Lagrangean dual approaches earlier published are briefly reviewed and it is noted that quite sophisticated procedures have been used to solve the dual problems. The simple concept of Lagrangean relaxation combined with subgradient optimization and Lagrangean heuristics has, however, not been applied to the discrete sizing problem. In this paper a scheme based on this concept is described and tested on some small problems. The results indicate that subgradient optimization is completely capable of solving the dual problem. Moreover it is possible to devise heuristics that construct feasible solutions to the original problem, using the Lagrangean subproblem solution.     

基于物质点描述的双向渐进式拓扑优化方法

:为了克服连续体结构拓扑优化中的数值不稳定现象,定义了表征物质点及其领域有无的物质点拓扑变量,提出基于物质点描述的双向渐进式拓扑优化方法.基于过滤法构造拓扑变量场的插值函数,从而在拓扑优化模型中自然消除了棋盘格现象.为适用于不同单元类型和网格离散形式等,重新定义了灵敏度密度.通过二维数值算例对理论方法进行验证.结果表明:方法在连续体结构拓扑优化设计中具有可行性和有效性.     

空间桁架结构拓扑优化设计的线性规划方法

本文以杆件内力为设计变量,构造了多工况作用下空间桁架结构拓扑优化的线性规划模型,考虑了应力和位移约束,能够避免奇异最优拓扑和不稳定结构的产生。     

单层空间网格结构刚性节点优化设计方法研究

单层网格结构中的节点不仅须传递轴力,也须传递两个方向上的弯矩。因此,单层网格结构中的节点为受力复杂的刚性节点,应具有合理的结构形式和良好的力学性能。同时,单层网格结构节点连接复杂、高空施工难度大,节点与杆件应有可靠、方便、通用的连接方式。该文提出了单层网格结构刚性节点优化设计方法：通过构造设计节点端,实现节点与杆件的连接;通过对受力复杂的节点核进行拓扑优化,开发高效的受力节点形式。在优化模型中,通过与外荷载无关的自平衡力系表示节点弯曲刚度,使得优化后的节点在任意方向上均有良好的弯矩传递能力。为避免拓扑优化中将力直接施加在设计域而导致的应力奇异问题及节点形式受限的缺点,通过施加加速度场,以体积惯性力等效集中荷载,降低了优化结果对边界条件的敏感性,获得了稳定、可靠的优化结果,解决了刚性节点拓扑优化中的关键技术难点。并以一个实际结构中的节点为例进行优化设计。通过分析节点端连接性能、力学性能以及与传统节点进行对比,验证了将拓扑优化和构造设计相结合的刚性节点优化设计方法。     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。     

基于人工材料的结构拓扑渐进优化设计

首先,提出了一种在结构边界和孔洞周围附加人工材料的思路。在此基础上,结合ESO方法和应力灵敏度,建立了结构有限单元增、删的准则, 给出了一种新的拓扑优化算法。算例表明该方法能采用固定有限元网格中不同的初始优化结构就可获得优化拓扑。由于其概念上的简洁性和应用上的有效性,该方法具有一定的工程应用价值。     

结构动力鲁棒优化设计方法综述

如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。     

声场-结构耦合系统灵敏度分析及优化设计研究

给出了低频声－结构耦合系统的有限元方程，并在此基础上提出声一结构耦合系统的包含尺寸和形状设计变量的优化设计模型，建立基于灵敏度分析求解的优化设计方法，重点推导了耦合系统的特征频率和声压级响应关于设计变量的灵敏度方程。在JIFEX软件中实现上述理论和算法，并通过灵敏度比较和优化设计的数值算例，进一步说明该研究方法对声结构耦合系统的工程设计具有实用意义。     

COMPARATIVE EVALUATION OF DIFFERENT OPTIMIZATION ALGORITHMS FOR STRUCTURAL DESIGN APPLICATIONS

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.     

APPROXIMATE DISCRETE VARIABLE OPTIMIZATION OF FRAME STRUCTURES WITH DUAL METHODS

The purpose of this work is to present an efficient method for optimum design of frame structures, using approximation concepts. A dual strategy in which the design variables can be considered as discrete variables is used. A two-level approximation concept is used. In the first level, all the structural response quantities such as forces and displacements are approximated as functions of some intermediate variables. Then the second level approximation is employed to convert the first-level approximation problem into a series of problems of separable forms, which can be solved easily by dual methods with discrete variables. In the second-level approximation, the objective function and the approximate constraints are linearized. The objective of the first-level approximation is to reduce the number of structural analyses required in the optimization problem and the second level approximation reduces the computational cost of the optimization technique. A portal frame and a single layer grid are used as design examples to demonstrate the efficiency of the proposed method.