考虑载荷随机性的可行域调整的结构拓扑优化设计

doi:10.3901/JME.2017.23.116

机械工程学报 ›› 2017, Vol. 53 ›› Issue (23): 116-128.doi: 10.3901/JME.2017.23.116

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考虑载荷随机性的可行域调整的结构拓扑优化设计

石军¹, 荣见华^1,2, 俞燎宏^1,2, 唐承铁^1,3, 赵志军^1,4

1. 长沙理工大学汽车与机械工程学院长沙 410076;
2. 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室长沙 410114;
3. 长沙理工大学工程车辆安全性设计与可靠性技术湖南省重点实验室长沙 410114;
4. 长沙学院土木建筑工程系长沙 410003

收稿日期:2016-11-01 修回日期:2017-07-15 发布日期:2017-12-05
通讯作者: 荣见华(通信作者),男,1963年出生,博士,教授,博士研究生导师。主要研究方向为结构动力学与优化设计。E-mail:rongjhua@aliyun.com
作者简介:石军,男,1989年出生,博士研究生。主要研究方向为结构动力学与优化设计。E-mail:1457921836@qq.com;俞燎宏,男,1982年出生,博士研究生。主要研究方向为结构动力学与优化设计。E-mail:ylh310@163.com;唐承铁,男,1989年出生,硕士研究生。主要研究方向为结构动力学与优化设计。E-mail:601693839@qq.com;赵志军,男,1982年出生,博士研究生。主要研究方向为结构动力学与优化设计。E-mail:18610964@qq.com。
基金资助:
国家自然科学基金（11372055，11302033）、工程车辆轻量化与可靠性技术湖南省高校重点实验室（长沙理工大学）开放基金（2013KFJJ03）资助项目。

Feasible Domain Adjustment Topology Optimization Designs of Structures under Stochastic Loads

SHI Jun¹, RONG Jianhua^1,2, YU Liaohong^1,2, TANG Chengtie^1,3, ZHAO Zhijun^1,4

1. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410076;
2. Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle of Hunan Province, Changsha University of Science and Technology, Changsha 410114;
3. Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Changsha Vninersity of Scierue and Technology, Changsha 410114;
4. Department of Civil Engineering, Changsha University, Changsha 410003

Received:2016-11-01 Revised:2017-07-15 Published:2017-12-05

摘要/Abstract

摘要： 考虑载荷大小和方向的不确定性，以结构柔顺度的期望和方差的加权和为目标函数，结构体积为约束函数，研究稳健结构拓扑优化方法。首先给出载荷大小和方向不确定情况下结构柔顺度期望和方差及其导数的显式近似式，而后改进可行域调整方案，提出具有收敛特征的稳健结构拓扑优化设计方法，探讨结构柔顺度期望和方差的权重因子以及随机量的方差对拓扑构型的影响。给出的算例表明，不论是确定载荷拓扑优化还是随机载荷拓扑优化，方法是可行和有效的，且可获得一系列清晰的拓扑构型和稳健的优化拓扑。

关键词: 结构优化, 可行域调整, 柔顺度优化, 随机载荷, 稳健拓扑优化

Abstract: Considering stochastic cases of load values and directions, a robust structural topology optimization method for the weighted sum minimizing problem of the expected value of the compliance and its variance with a volume constraint, is proposed. Firstly, explicit approximate expressions of the compliance expected value, its variance and their derivatives are derived. Secondly, an improved feasible domain adjustment scheme and a set of algorithms for robust structural topology optimization designs are given. The effects of the weighted coefficients of the objective function and the variance of the perturbations on the optimized solutions, are investigated. Given simulation examples show that no matter determine load topology optimization or random load topology optimization,the proposed method is feasible and effective, and can be adopted to obtain a series of clear topology configurations and a robust optimal topology.

Key words: compliance optimization, feasible domain adjustment, robust topology optimization, stochastic loads, structure optimization

中图分类号:

石军, 荣见华, 俞燎宏, 唐承铁, 赵志军. 考虑载荷随机性的可行域调整的结构拓扑优化设计[J]. 机械工程学报, 2017, 53(23): 116-128.

SHI Jun, RONG Jianhua, YU Liaohong, TANG Chengtie, ZHAO Zhijun. Feasible Domain Adjustment Topology Optimization Designs of Structures under Stochastic Loads[J]. Journal of Mechanical Engineering, 2017, 53(23): 116-128.

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考虑载荷随机性的可行域调整的结构拓扑优化设计

Feasible Domain Adjustment Topology Optimization Designs of Structures under Stochastic Loads

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