Feasible Domain Adjustment Topology Optimization Designs of Structures under Stochastic Loads

doi:10.3901/JME.2017.23.116

Abstract

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

CLC Number:

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.

References

[1] 王德伦,申会鹏,孙元,等.发杂零件结构设计的概念单元方法[J].机械工程学报, 2015, 52(7):152-163. WANG Delun, SHEN Huipeng, SUN Yuan. et al. A novel approach for conceptual structural design of complex machine elements[J]. Journal of Mechanical Engineering, 2015, 52(7):152-163.
[2] 焦洪宇,周奇才,李英,等.桥式起重机轻量化主梁结构模型试验研究[J]. 机械工程学报, 2015, 51(23):168-174. JIAO Hongyu, ZHOU Qicai, LI Ying, et al. Structural model test of lightweight girder of bridge crane[J]. Journal of Mechanical Engineering, 2015, 51(23):168-174.
[3] 于靖军,郝广波,陈贵敏,等.柔性机构及其应用研究进展[J].机械工程学报, 2015, 51(13):53-68. YU Jingjun, HAO Guangbo, CHEN Guimin. et al. State-of-art of compliant mechanisms and their applications[J]. Journal of Mechanical Engineering, 2015, 51(13):53-68.
[4] JING Shikai,ZHANG He,ZHOU Jingtao,et al.Optimum weight design of functionally graded material gears[J]. Chinese Journal of Mechanical Engineering, 2015, 28(6):1186-1193.
[5] BEN-TAL A, BENDSøE M P. A new method for optimal truss topology design[J]. SIAM Journal on Optimization, 1993, 3(2):322-358.
[6] GUEST J K, IGUSA T. Structural optimization under uncertain loads and nodal locations[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 198(1):116-303.
[7] SCHUELLER G I, JENSEN H A. Computational methods in optimization considering uncertainties:An overview[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 198(1):2-13.
[8] LEE K H, PARK G J. Robust optimization considering tolerances of design variables[J]. Computers & Structures, 2001, 79(1):77-86.
[9] KANG Zhan, LUO Yangjun. Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(41-44):3228-3238.
[10] CHEN S, CHEN W, LEE S. Level set based robust shape and topology optimization under random field uncertainties[J]. Structural Multidisciplinary Optimization, 2010, 41(4):507-524.
[11] CONTI S, HELD H, PACH M, et al. Shape optimization under uncertainty:A stochastic programming perspective[J]. Siam Journal on Optimization, 2009, 19(4):1610-1632.
[12] DUNNING P D, KIM H A, MULLINEUX G.Introducing loading uncertainty in topology optimization[J]. AIAA Journal, 2011, 49(4):760-768.
[13] ZHAO Junpeng, WANG Chunjie. Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 273:204-218.
[14] ZhAO Junpeng, WANG Chunjie. Robust topology optimization of structures under loading uncertainty[J]. AIAA Journal, 2014, 52(2):398-407.
[15] 付志方,赵军鹏,王春洁. 多工况线性结构稳健拓扑优化设计[J].力学学报, 2015, 47(4):642-650. FU Zhifang, ZHAO Junpeng, WANG Chunjie. Robust topology optimization design of structures with multiple-uncertainty load case[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4):642-650.
[16] CARRASCO M, IVORRA B, RAMOS A M, et al. Stochastic topology design optimization for continuous elastic materials[J]. Computer Methods in Applied Mechanics & Engineerin, 2015, 28:131-154.
[17] DEATON J D, GRANDHI R V. A survey of structural and multidisciplinary continuum topology optimization:post 2000[J]. Structural Multidisciplinary Optimization, 2014, 49:1-38.
[18] RONG Jianhua, LIU Xiaohua, YI Jijun. An efficient structural topological optimization method for continuum structures with multiple displacement constraints[J]. International Journal of Finite Elements in Analysis and Design, 2011, 47:913-921.
[19] RONG Jianhua, YI Juehong. A structural topological optimization method for multi-displacement constraint problems and any initial topology configuration[J]. International Journal of Acta Mechanica Sinica, 2010, 26:735-744.
[20] RONG Jianhua, TANG Zhili, XIE Yimin, et al. Topological optimization design of structures under random excitations using SQP method[J], Engineering Structures, 2013, 56:2098-2106.
[21] 荣见华,邢晓娟,邓果.一种变位移约束限的结构拓扑优化方法[J].力学学报, 2009, 41(3):518-529. RONG Jianhua, XING Xiaojuan, DENG Guo. A structural topological optimization method with variable displacement constraint[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3):518-529.
[22] 荣见华,葛森,邓果,等.基于位移和应力灵敏度的结构拓扑优化设计[J].力学学报, 200, 41(4):431-439. RONG Jianhua, GE Sen, DENG Guo, et al. Structural topological optimization based on displacement and stress sensitivity analyses[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4):431-439.
[23] SVANBERG K. A class of globally convergent optimization methods based on conservative convex separable approximations[J]. Siam Journal on Optimization, 2002, 12:555-573.
[24] RONG Jianhua, XIAO Tingting, YU Liaohong, et al. Continuum structural topological optimizations with stress constraints based on an active constraint technique[J].International Journal for Numerical Methods in Engineering, 2016, 108(4):326-360.
[25] SIGMUND O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization, 2001, 21:120-127.
[26] 王尚.考虑载荷大小和方向不确定性的连续体结构拓扑优化[D].大连:大连理工大学, 2015. WANG Shang. Topology optimization of continuum structures considering uncertainties in loadingmagnitude and direction[D]. Dalian:Dalian University of Technology, 2015.