Multi-objective optimization of actively controlled structures with topological considerations

Abstract

This paper presents a novel approach for the optimum design of actively controlled structures using both cooperative and Stackelberg game theoretic formulations wherein the structural topology is also optimized. Most of the available literature for design of actively controlled structures deals with structures of a predetermined topology. It is recognized that the structural performance can be improved significantly by the optimization of topology. The optimum topology is created herein by minimizing the strain energy. Once the optimum topology is obtained, a simultaneous sizing and control system optimization of the optimum topology is performed which (i) maximizes the energy dissipated by the controller, (ii) minimizes the structural weight, and (iii) minimizes the controller performance index. The design variables include actuator locations, member cross-sectional areas and entries of state and control weighting matrices. The multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the levels. Two numerical examples illustrating the proposed approach are presented wherein topological, structural and control system aspects of the problem are addressed comprehensively.

Multi-objective topology optimization design and test for support structure of star sensor

“…一般用于结构的概念设计阶段， 结合形状优化和尺寸优化，可以完成结构的全局设 计。 在实际工程应用中，结构的设计通常存在多项 指标，多目标拓扑优化就是通过协调各个设计指标 的比重，权衡多个目标进行优化设计。 目前，国内 外对多目标拓扑优化有了一定的研究，范文杰等 [ 4] 提出一种适用于连续体结构的多目标拓扑优化设 计方法，采用折衷规划法和平均频率法定义了振动 固有频率和多刚度拓扑优化的目标函数，对客车车 架结构进行多目标拓扑优化设计，提高了振动固有 频率和刚度；倪昀等 [ 5] 针对柔顺机构的多目标拓扑 优化设计，采用混合元胞自动机方法，建立应变能 最小化和互应变能最大化的目标函数，结果证明该 方法用于柔顺机构可行有效，迭代次数较少；张璟 鑫等 [ 6] 将平均距离的基本原理和多目标拓扑优化 相结合，提出一种广义的平均距离法，用于构建多 目标拓扑优化的目标函数，对汽车悬架控制臂进行 多目标拓扑优化仿真研究，结果表明平均距离理念 可以灵活地构建多目标拓扑优化的目标函数；Ali, Arjumand 等 [ 7] 提出一种利用拓扑理论对主控机 构 进行多目标优化的方法，在结构的拓扑优化中引入 Stackelberg 博弈理论公式，结构的最优拓扑形式以 应变能最小进行建立，多目标拓扑优化设计问题可 以像 Stackelberg 博弈一样得到解决，并且利用两个 例子说明了这种方法可应用于主控机构的多目标 优化设计。 文中以某微小卫星上的纳型星敏感器为例，对 其支撑结构进行多目标拓扑优化设计，利用有限元 方法对其进行力学分析，并进行了振动试验。 将分 析数据和振动试验数据进行分析对比，结果表明该 结构能够满足安装需求和力学性能条件，达到设计 要求。 model of the support structure was established under the restriction of the lowest natural frequency. The topology optimization design was carried out by using OptiStruct software.…”