横向力作用下的悬臂桁架结构拓扑优化

研究了应力约束下最小重量悬臂梁桁架结构的拓扑优化设计。根据Michell理论,首先用解析方法和有限元方法建立满应力类桁架连续体结构。然后选择其中部分杆件形成离散桁架作为近最优结构,并建立桁架的拓扑优化解析表达式。采用解析方法证明最优拓扑结构的腹杆中间结点在节长的四分之一位置。最后采用解析和数值方法对自由端受集中力和侧边受均布力作用的桁架进一步拓扑优化,确定了桁架的节数和每节的长度,最后得到拓扑优化桁架结构。得到的拓扑优化桁架比工程上普遍采用的45°腹杆桁架的体积少20%以上。     

基于混合PSO算法的桁架动力响应优化

摘 要：本文针对以结构动力响应为约束,最小重量为目标的桁架拓扑优化问题,提出了一种将微粒群算法和优化准则法结合的混合PSO算法。利用优化准则法的迭代关系找出群体中适应度最好的微粒,将其作为特殊微粒,其他微粒的寻优采用PSO的基本进化规则,位移响应约束利用特殊微粒的灵敏度信息近似计算。算例的计算结果表明,混合PSO算法适用于受简谐荷载以及脉冲荷载作用桁架结构的拓扑优化。混合PSO的计算效率比PSO算法高,其优化效果比优化准则法好。     

基于类桁架材料模型的不确定荷载下结构拓扑优化

用区间分析方法研究了不确定荷载下结构拓扑优化方法。采用类桁架材料模型建立拓扑优化类桁架连续体结构。根据区间变量运算法则推导出不确定荷载下应力约束体积最小类桁架结构的拓扑优化方法。首先采用区间分析方法得到任一点的最不利荷载工况下应变状态。在此应变状态下,利用满应力准则优化类桁架材料中杆件的方向和密度。如此反复分析和优化,直至迭代收敛。最后由类桁架中杆件分布场可以近似离散得到桁架结构。通过几个数值算例验证了方法的有效性。数值算例显示了不确定荷载下的结构拓扑优化布局更合理。     

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。     

强震作用下立体桁架结构抗连续倒塌性能研究

地震灾害发生时,主震之后通常伴有多次余震。以往的震害事故表明,主震过程可能引起立体桁架结构薄弱部位发生初始失效,并导致结构在余震中发生连续倒塌破坏。针对以上问题,采用增量动力法确定立体桁架结构薄弱部分分布规律,然后采用预定义场法引入初始失效杆件,分析不同破坏模式下该类结构破坏加速度、倒塌极限位移和塑性杆件比例等响应的变化规律,最后提出了改善结构抗连续倒塌性能的有效措施。分析结果表明:在强震作用下立体桁架结构的薄弱部位为主桁架跨中3/8L范围内的上弦杆、下弦杆及跨中支撑桁架的上弦杆。引入初始失效后结构破坏加速度降低了13.3%～40.0%,倒塌极限位移降低了1.6%～30.9%。当初始失效杆件为受压杆件时,结构产生动力失稳破坏;当初始失效杆件为受拉杆件时,结构产生动力强度破坏。针对发生动力失稳破坏的立体桁架结构,增加侧向交叉支撑使破坏模式转变成动力强度破坏,破坏加速度提高69.4%～73.7%。     

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。     

非平稳激励下薄板结构减振附加阻尼层的拓扑优化

讨论了附加阻尼层的薄板结构在非平稳随机力作用下以减振为目标的阻尼材料层的拓扑优化问题。建立了以阻尼材料的相对密度为设计变量,以结构非平稳响应位移方差最小化为目标和阻尼材料用量为约束条件的拓扑优化模型。由于结构受到非平稳随机激励作用,其随机响应可以采用时域显式法快速求解;随机响应方差对设计变量的灵敏度采用了基于伴随变量法的时域显式法进行分析,并采用优化准则法求解优化问题。数值算例验证了所提方法在非平稳随机激励作用下进行动力拓扑优化减振的可行性与有效性。     

基于改进渐进结构优化方法的结构动力优化研究

在对渐进结构优化方法基本理论分析基础上,根据结构动力学的拓扑优化特点,结合尺寸优化理论,提出了一种新的删除准则。探索了一种改进型渐进结构优化方法,并叙述基本的优化步骤。最后,融入了质量、应力、位移以及频率等动力学约束条件参数,运用该方法进行谐激励力作用下的板结构动力响应拓扑优化。算例表明,改进渐进结构优化方法对结构动力学拓扑优化问题具有一定的适用性,拓展了基本渐进结构优化方法的应用范围。     

三杆类桁架材料模型多工况最小柔度优化

研究了多工况结构柔度最小化方法。提出了3杆类桁架连续体材料模型。推导了该材料的刚度矩阵及其导数。通过优化杆件分布场得到优化的类桁架连续体。克服了目前普遍采用单元的"有"和"无"表示结构拓扑的轮廓粗糙、锯齿状边界问题。结点位置的杆件密度和方向作为设计变量,杆件在单元内的密度和方向通过结点位置的数值插值得到,并且在单元内连续变化。由于没有抑制中间密度,完全不存在数值不稳定问题。类桁架连续体由于与杆系结构有明确的对应关系,可以合理地转化杆系结构。选择杆件分布场中的部分杆件可以形成杆系结构。如果再进一步作尺寸和形状优化就可以得到最终的拓扑优化结构。     

基于对数型Heaviside近似函数作为过滤函数的动力响应结构拓扑优化ICM方法

应用ICM(Independent Continuous and Mapping)方法, 建立了以重量最小为目标函数, 以连续频率带或离散点频率的简谐激励下的响应振幅为约束的拓扑优化模型. 引入了对数型Heaviside近似函数作为过滤函数, 并做了敏度分析, 利用对偶二次规划进行优化模型的求解, 并运用敏度过滤的方法处理动力响应数值不稳定的问题. 数值算例比较了利用对数型函数和幂函数作为过滤函数时对拓扑结构的影响, 结果显示利用对数型函数较幂函数结构优化迭代次数更少, 收敛更快.     

Engineering optimization using a real-parameter genetic-algorithm-based hybrid method

A hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is proposed. The proposed algorithm incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators such that its hill-climbing ability towards the optimum solution is improved. The algorithm is used to optimize the weight of four planar or space truss structures and the results are compared with those obtained using other well-known optimization schemes. The evaluation trials investigate the performance of the algorithm in optimizing over discrete sizing variables only and over both discrete sizing variables and continuous configuration variables. The results show that the proposed algorithm consistently outperforms the other optimization methods in terms of its weight-saving capabilities. It is also shown that the global searching ability and convergence speed of the proposed algorithm are significantly improved by the inclusion of adaptive mechanisms to adjust the values of the genetic operators. Hence the hybrid algorithm provides an efficient and robust technique for solving engineering design optimization problems.     

Truss optimization on shape and sizing with frequency constraints based on genetic algorithm

Truss optimization on shape and sizing with frequency constraints are highly nonlinear dynamic optimization problems. Coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence while multiple frequency constraints often cause difficult dynamic sensitivity analysis. So optimal criteria method and mathematical programming, which need complex dynamic sensitivity and are easily trapped into the local optima, are difficult to solve the problems. To solve the truss shape and sizing optimization simply and effectively, a Niche Hybrid Genetic Algorithm (NHGA) is proposed. The objective of NHGA is to enhance the exploitation capacities while preventing the premature convergence simultaneously based on the new hybrid architecture. Niche techniques and adaptive parameter adjustment are used to maintain population diversity for preventing the premature convergence while simplex search is used to enhance the local search capacities of GAs. The proposed algorithm effectively alleviates premature convergence and improves weak exploitation capacities of GAs. Several typical truss optimization examples are employed to demonstrate the validity, availability and reliability of NHGA for solving shape and sizing optimization of trusses with multiple frequency constraints.     

Evolutionary Algorithm Integrating Stress Heuristics for Truss Optimization

The optimal truss design using problem-oriented evolutionary algorithm is presented in the paper. The minimum weight structures subjected to stress and displacement constraints are searched. The discrete design variables are areas of members, selected from catalogues of available sections. The integration of the problem specific knowledge into the optimization procedure is proposed. The heuristic rules based on the concept of fully stressed design are introduced through special genetic operators, which use the information concerning the stress distribution of structural members. Moreover, approximated solutions obtained by deterministic, sequential discrete optimization methods are inserted into the initial population. The obtained hybrid evolutionary algorithm is specialized for truss design. Benchmark problems are calculated in numerical examples. The knowledge about the problem integrated into the evolutionary algorithm can enhance considerably the effectiveness of the approach and improve significantly the convergence rate and the quality of the results. The advantages and drawbacks of the proposed method are discussed.     

随机参数智能桁架结构振动控制中主动杆的优化配置

该文研究压电智能桁架结构振动主动控制中结构物理参数，作用荷载和控制力同时具有随机性时，压电主动杆的最优配置和增益优化问题，采用智能结构的状态空间模型建立了以最大耗散能准则来基础的目标函数，建立了具有动应力，动位移可靠约束的主动杆的优化配置和增益优化模型，对结构动力响应的数字特征进行了推导，并通过一智能桁架结构的优化配置计算，说明该优化配置模型的合理性和有效性。     

GENETIC ALGORITHMS AS AN APPROACH TO OPTIMIZE REAL-WORLD TRUSSES

Genetic algorithms, a search technique which combines Darwinian ‘survival-of-the-fittest’ with randomized well structured information, is applied to the problems of real-world truss optimization. In this work a population of binary strings or ‘chromosomes’, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population, so that over the generations the genetic algorithm gets better and better and at the end of the convergence, a ‘rebirth’ of the population is used to improve the usual process. An overview of the genetic algorithm will be described, continuing the rebirth effect; then, the chromosome representation of trusses is exposed. Afterwards, the objective scalar function is defined taking into account that it seems reasonable in real world to optimize trusses in minimum weight trying, at the same time, to use the minimum number of cross-section types obtained from the market. It also seems reasonable to have the possibility to change the shape of the conceptual design, moving some joints. To simulate nearly real conditions, several load cases, constraints in the elastic joint displacements, ultimate tensile and elastic and plastic buckling in the bars have been taken into account. A hyperstatic 10 bars truss is subjected to a deep analysis in different situations in order to evaluate with other authors when possible as truss optimization with two criteria and buckling effect has not been found in specialized literature. A 160-bar transmission tower is also optimized.     

基于演化算法的带频率约束的桁架结构形状和尺寸优化

具有频率约束的桁架结构形状和尺寸优化设计是一个难度大的非线性动力优化问题。形状和尺寸变量的耦合通常导致收敛困难,而频率约束则使得动力灵敏度分析困难,传统的优化准则法和数学规划法难于求解。将单纯形算法、子空间变维技术、均匀变异有机融入郭涛算法,提出一种混合演化算法,避开繁琐的动力灵敏度分析,简单、有效地求解这类桁架形状和尺寸优化问题。典型的桁架算例验证了算法的有效性和可靠性。     

桁架动力学形状优化的统一设计变量方法

研究了具有多种约束 ,特别是动力学约束 (频率约束 )作用下的平面桁架形状优化问题。提出一种将两类不同性质的设计变量 (尺寸变量、节点几何坐标变量 )变换为统一形式的无量纲设计变量的方法 ,解决了不同性质变量耦合引起的收敛困难问题 ,并拓展了设计空间。联合运用内点罚函数法、DFP法 (即变尺度法 )和一维搜索技术 (二次插值法 ) ,将约束优化问题转化为无约束序列优化问题 ,得到了满意的优化结果。算例表明本文方法对桁架形状优化的有效性 ,并显示了算法的简洁性和工程设计实用性     

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.     

自适应桁架结构局部力反馈振动控制及其主动构件的配置研究

本文主要研究利用自适应桁架结构自身的主动构件实现控制结构动态特性的理论和有效性以及主动构件的最优配置问题。首先，基于自适应桁架结构的有限元模型，将主动构件的弹性内力直接用于实现反馈控制桁架结构的振动特性；然后，引用模态耗散能因子和模态应变能因子的概念，研究了主动构件的优化配置问题。通过一平面自适应桁架结构的优化配置计算和数值仿真，说明了文中提出的控制方法和主动构件优化配置的有效性。