An Efficient Method for Topology Optimization of Continuum Structures in the Presence of Uncertainty in Loading Direction

被引：23
作者：
Liu, Jie [1 ,2 ]
Wen, Guilin [1 ]
Qing, Qixiang [1 ]
Xie, Yi Min [2 ,3 ]
机构：
[1] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha, Hunan, Peoples R China
[2] RMIT Univ, Ctr Innovat Struct & Mat, Sch Engn, Melbourne, Vic, Australia
[3] XIE Archi Struct Design Shanghai Co Ltd, Shanghai 200433, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2017年 / 14卷 / 05期
基金：
高等学校博士学科点专项科研基金;
关键词：
Uncertainty; loading direction; BESO; interval mathematics; topology optimization; GEOMETRICALLY NONLINEAR STRUCTURES; LEVEL SET METHOD; HOMOGENIZATION METHOD; DYNAMIC-RESPONSE; CONVEX MODELS; DESIGN; SHAPE;
D O I：
10.1142/S0219876217500542
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.
引用
收藏
页数：23
相关论文
共 39 条
[11]   An efficient approach to reliability-based topology optimization for continua under material uncertainty [J].
Jalalpour, Mehdi ;
Tootkaboni, Mazdak .
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 2016, 53 (04) :759-772
[12]   Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads [J].
Jang, H. H. ;
Lee, H. A. ;
Lee, J. Y. ;
Park, G. J. .
AIAA JOURNAL, 2012, 50 (01) :226-234
[13]   Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis [J].
Jansen, M. ;
Lombaert, G. ;
Schevenels, M. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 285 :452-467
[14]   Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties [J].
Jung, HS ;
Cho, S .
FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2004, 41 (03) :311-331
[15]   An efficient approach for reliability-based topology optimization [J].
Kanakasabai, Pugazhendhi ;
Dhingra, Anoop K. .
ENGINEERING OPTIMIZATION, 2016, 48 (01) :1-15
[16]   Optimization of flexible multibody dynamic systems using the equivalent static load method [J].
Kang, BS ;
Park, GJ ;
Arora, JS .
AIAA JOURNAL, 2005, 43 (04) :846-852
[17]   Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models [J].
Kang, Zhan ;
Luo, Yangjun .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2009, 198 (41-44) :3228-3238
[18]   Reliability-based topology optimization [J].
Kharmanda, G ;
Olhoff, N ;
Mohamed, A ;
Lemaire, M .
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 2004, 26 (05) :295-307
[19]   Topology optimization with geometric uncertainties by perturbation techniques [J].
Lazarov, B. S. ;
Schevenels, M. ;
Sigmund, O. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2012, 90 (11) :1321-1336
[20]   Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method [J].
Lee, Hyun-Ah ;
Park, Gyung-Jin .
JOURNAL OF MECHANICAL DESIGN, 2012, 134 (03)
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