基于子结构方法的离散结构协同优化

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清华大学辅仁网/2017-07-07

基于子结构方法的离散结构协同优化

钟薇¹, 苏瑞意², 桂良进¹, 范子杰¹

1. 清华大学汽车工程系, 汽车安全与节能国家重点实验室, 北京 100084;
2. 北京机电工程总体设计部, 北京 100854

Collaborative optimization of discrete structures based on a substructuring method

ZHONG Wei¹, SU Ruiyi², GUI Liangjin¹, FAN Zijie¹

1. State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China;
2. Beijing System Design Institute of Electromechanical Engineering, Beijing 100854, China

摘要:

输出: BibTeX | EndNote (RIS)

摘要针对复杂离散结构优化存在设计变量多、寻优困难等问题, 提出一种基于子结构方法的分解协调策略, 并采用基于子结构分解协同优化框架求解。将大规模结构分解为多个不重叠的、规模较小的子结构, 每个子结构对应一个学科。将原优化问题的设计变量、优化目标以及约束分配至各个学科。每一轮系统迭代中, 系统层仅进行一次完整结构的有限元分析, 学科层执行子结构优化和有限元分析。耦合状态变量由系统层输入, 在学科层作为定值。系统层进行整体结构分析后更新耦合状态变量值, 以协调学科之间耦合状态变量的差异。该方法将复杂的整体结构优化问题分解为多个并行、独立的子结构优化问题。算例表明: 相比于整体结构优化, 该协同优化方法显著降低了整体结构分析次数, 能够更加稳定地找到更优解。

关键词 ：离散结构,结构优化,子结构方法,协同优化

Abstract：A decomposition strategy based on substructuring is developed for optimizing complex discrete structures with a large number of design variables and a collaborative architecture is used as the solver. A large structure is decomposed into several small substructures with no overlap, where each substructure corresponds to a discipline. The variables, objectives and constraints in the original problem are assigned to the separate disciplines. Only one finite element analysis of the complete structure is performed at the system level during each iteration with optimization and finite element analyses of the substructures at the discipline levels. Coupled state variables are passed from the system level to the disciplines as constants. The coupled state variables are updated after each finite element analysis of the complete structure at the system level to coordinate the differences in the coupled state variables among disciplines. Thus, a complex structural optimization problem is decomposed into several parallel, self-governed subproblems. The results of numerical examples demonstrate that this cooperative optimization method requires less evaluations of the complete structure and is able to obtain better results with better stability than optimizing the complete structure as a whole.

Key words：discrete structure structural optimization substructuring method collaborative optimization

收稿日期: 2015-11-09 出版日期: 2016-07-01

ZTFLH:

TH123

通讯作者:范子杰, 教授, E-mail: zjfan@tsinghua.edu.cnE-mail: zjfan@tsinghua.edu.cn

引用本文:

钟薇, 苏瑞意, 桂良进, 范子杰. 基于子结构方法的离散结构协同优化[J]. 清华大学学报（自然科学版）, 2016, 56(6): 572-579.
ZHONG Wei, SU Ruiyi, GUI Liangjin, FAN Zijie. Collaborative optimization of discrete structures based on a substructuring method. Journal of Tsinghua University(Science and Technology), 2016, 56(6): 572-579.

链接本文:

http://jst.tsinghuajournals.com/CN/10.16511/j.cnki.qhdxxb.2016.22.014或 http://jst.tsinghuajournals.com/CN/Y2016/V56/I6/572

图表:

图１　标准协同优化算法的基本框图

图２　结构分解示意图

图３　本文的离散结构协同优化算法框图(两个子学科)

图４　２０Ｇ杆桁架结构

表１　２０Ｇ杆桁架结构求解结果

图５　２０Ｇ杆桁架结构子结构质量迭代曲线

表２　２０Ｇ杆桁架结构协同优化与整体优化结果对比

图６　７２Ｇ杆空间桁架结构

表３　７２Ｇ杆空间桁架结构的载荷工况

表４　７２Ｇ杆桁架子结构输入的结构内部边界条件

表５　７２Ｇ杆空间桁架结构求解结果

图７　７２Ｇ杆空间桁架结构子结构质量迭代曲线

表６　７２Ｇ杆空间桁架结构协同优化与整体优化结果对比

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