Study of Structural Periodic-like Layout Optimization Based on Guide-weight Method

doi:10.3901/JME.2020.13.218

Abstract

Abstract: Limited by boundary dimension, optimization area of some structures cannot be divided into finite element meshes uniformly. This results in element volume dependency, which cannot be solved by conventional periodic topology optimization. A periodic-like layout optimization method is proposed based on the guide-weight method. With the minimum compliance as the objective function and the structural mass as the constraint condition, a mathematical model for the periodic-like layout optimization is constructed. The iterative criterion for periodic-like layout optimization is derived using the guide-weight method, and its physical meaning is explained and its optimization process is given. Based on the element strain energy density, an improved filtering scheme is proposed to solve the problem of element volume dependence in structural periodic-like layout optimization. The structural periodic-like layout optimization of cyclic symmetry structure, two-dimensional automobile hub structure and trapezoidal structure are researched using the proposed method. The research results show that the optimal topological form with periodic-like layout can be obtained when the number of subdomains is different. The optimal topological forms of three examples are evaluated by two evaluation indicators:performance index and relative strain energy. The feasibility and effectiveness of using the guide-weight method to solve the periodic-like layout optimization are verified.

Key words: periodic-like, layout optimization, guide-weight method, iterative formula, element volume dependency

CLC Number:

TH11

JIAO Hongyu, LI Ying, HU Shunan, ZUO Kesheng, LIN Ling, JIANG Zhengyi, YU Zhaopeng. Study of Structural Periodic-like Layout Optimization Based on Guide-weight Method[J]. Journal of Mechanical Engineering, 2020, 56(13): 218-230.

References

[1] THOMSEN C R,WANG Fengwen,SIGMUND O. Buckli-ng strength topology optimization of 2D periodic materials based on linearized bifurcation analysis[J]. Computer Methods in Applied Mechanics and Engineering,2018, 339:115-136.
[2] SUN Jialiang,TIAN Qiang,HU Haiyan. Simultaneous topology and size optimization of a 3D variable-length structure described by the ALE-ANCF[J]. Mechanism and Machine Theory,2018,129:80-105.
[3] 龙凯,贾娇. 基于ICM法的传热结构周期性拓扑优化设计[J]. 工程力学,2015,32(5):227-235. LONG Kai,JIA Jiao. Periodic topology optimization design for thermal conductive structures using ICM meth-od[J]. Engineering Mechanics,2015,32(5):227-235.
[4] 贾娇,程伟,龙凯. 基于SIMP法的周期性传热材料拓扑化[J]. 北京航空航天大学学报,2015,41(6):1042-1048. JIA Jiao,CHENG Wei,LONG Kai. Topology optimizat-ion for periodic thermal conductive material suing SIMP method[J]. Journal of Beijing University of Aeronautics and Astronautics,2015,41(6):1042-1048.
[5] HUANG Xiaodong,XIE Yinmin. Optimal design of periodic structures using evolutionary topology optimizat-ion[J]. Structural and Multidisciplinary Optimization,2008(36):597-606.
[6] ZUO Zhihao,XIE Yimin,HUANG Xiaodong. Optimal topological design of periodic structures for natural freq-uencies[J]. Journal of Structural Engineering,2011,137(10):1229-1240.
[7] XIE Yinmin,ZUO Zhihao,HUANG Xiaodong,et al. Convergence of topological patterns of optimal periodic structures under multiple scales[J]. Structural and Mult-idisciplinary Optimization,2012,46(1):41-50.
[8] ZUO Zhihao. Topology optimization of periodic structu-res[D]. Melbourne:RMIT University,2009.
[9] ZUO Zhihao,HUANG Xiaodong,XIE Yinmin,et al. Comparing optimal material microstructures with optimal periodic structures[J]. Computational Materials Science,2013,69:137-147.
[10] 付志方,王春洁. 载荷不确定的周期性结构稳健拓扑优化[J]. 北京航空航天大学学报,2017,43(4):747-753. FU Zhifan,WANG Chunjie. Robust topology optimiz-ation of periodic structures under uncertain loading[J]. J-ournal of Beijing University of Aeronautics and Astro-nautics,2017,43(4):747-753.
[11] 高彤,张卫红,朱继宏,等. 循环对称结构静力学渐进拓扑优化设计[J]. 机械工程学报,2008,44(3):166-172. GAO Tong,ZHANG Weihong,ZHU Jihong,et al. Evol-utionary static topology optimization of cycle-symmetry structures[J]. Chinese Journal of Mechanical Engineering,2008,44(3):166-172.
[12] 荣见华,廖莺,赵志军,等. 基于位移约束的类周期性连续体结构拓扑优化设计[J]. 应用力学学报,2013(6):876-881. RONG Jianhua,LIAO Ying,ZHAO Zhijun,et al. Topology optimization of periodic-like structures with displacement constraints[J]. Chinese Journal of Applied Mechanics,2013(6):876-881.
[13] HE Guanqiang,HUANG Xiaodong,WANG Hu,et al. Topology optimization of periodic structures using BESO based on unstructured design points[J]. Structural and Multidisciplinary Optimization,2016,53(2):271-275.
[14] 陈树勋,叶尚辉. 天线结构优化设计的准则法[J]. 固体力学学报,1984(4):482-497. CHEN Shuxun,YE Shanghui. Criterion method for the optimal design of antenna structure[J]. Chinese Journal of Solid Mechanics,1984(4):482-497.
[15] CHEN Shuxun,YE Shanghui. A guide-weight criterion method for the optimal design of antenna structures[J]. Engineering Optimization,1986,10(3):199-216.
[16] 陈树勋. 工程结构系统分析、综合与优化设计[M]. 北京:中国科学文化出版社,2008. CHEN Shuxun. The analysis combination and optimi-zation design of the system of engineering structure-es[M]. Beijing:Chinese Science and Culture Publishing House,2008.
[17] 陈树勋,韦齐峰,黄锦成. 结构优化导重准则及其意义与合理性[J]. 固体力学学报,2013,34(6):628-638. CHEN Shuxun,WEI Qifeng,HUANG Jincheng. Meaning and rationality of guide-weight criterion for structural optimization[J]. Chinese Journal of Solid Mechanics,2013,34(6):628-638.
[18] 陈树勋,韦齐峰,黄锦成. 质量对结构优化理性准则法计算结果的影响研究[J]. 计算力学学报,2015,32(1):33-40. CHEN Shuxun,WEI Qifeng,HUANG Jinchen. The infl-uence of structural mass on optimization effect of rational criterion methods[J]. Chinese Journal of Computational Mechanics,2015,32(1):33-40.
[19] 李枝东,刘辛军. 导重法求解单工况的拓扑优化问题[J].机械工程学报,2011,47(15):107-114. LI Zhidong,LIU Xinjun. Guide-weight method on solving topology optimization problems under single load case[J]. Journal of Mechanical Engineering,2011,47(15):107-114.
[20] LIU Xinjun,LI Zhidong,WANG Liping,et al. Solving topology optimization problems by the guide-weight method[J]. Frontiers of Mechanical Engineering,2011,6(1):136-150.
[21] LIU Xinjun,LI Zhidong,CHEN Xiang. A new solution for topology optimization problems with multiple loads:The guide-weight method[J]. Science China Technolo-gical Sciences,2011,54(6):1505-1514.
[22] 陈树勋,韦齐峰,黄锦成,等. 利用导重法进行结构轻量化设计[J]. 工程力学,2016,33(2):179-187. CHEN Shuxun,WEI Qifeng,HUANG Jincheng. Lightening structural design using guide weight method[J]. Engineering Mechanics,2016,33(2):179-187.
[23] 陈树勋,韦齐峰,黄锦成. 利用导重法进行结构拓扑优化[J]. 计算力学学报,2015,32(2):160-166. CHEN Shuxun,WEI Qifeng,HUANG Jincheng. Guide-weight method for structural topology optimization[J]. Chinese Journal of Computational Mechanics,2015,32(2):160-166.
[24] 周奇才,吴青龙,熊肖磊,等. 塔式起重机臂架周期性拓扑优化设计[J]. 同济大学学报,2017,45(10):1498-1505. ZHOU Qicai,WU Qinglong,XIONG Xiaolei,et al. Periodic topology optimization design of tower crane boom[J]. Journal of Tongji University,2017,45(10):1498-1505.
[25] ZHANG Yan,XIAO Mi,LI Hao,et al. Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered SIMP interpolation[J]. Computational Materials Science,2018,155:74-91.
[26] 陈垂福,杨晓翔. 基于步长因子改进的导重法求解拓扑优化问题[J]. 计算力学学报,2018,35(1):14-20. CHEN Chuifu,YANG Xiaoxiang. Based on step factor improved guide-weight method for solving topology optimization problems[J]. Chinese Journal of Computati-onal Mechanics,2018,35(1):14-20.
[27] HUANG Xiaodong,XIE Yinmin. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method[J]. Finite Elem. Anal. Des.,2007,43(13):1039-1049.