Robust Topology Optimization of Periodic Structures under Uncertain Dynamic Loads

doi:10.3901/JME.2024.23.304

Abstract

Abstract: The periodic structure attracts widespread attention in the structure design of aerospace, energy power and other fields due to the light weight and energy absorption performance. However, most of the existing works of topology optimization for periodic structures only considers the effects of static loads. Considering the inevitable existing of dynamic loads in practical engineering and the impact of loads uncertainty on the design results, it is necessary to carry out the periodic structure topology optimization method under dynamic loads uncertainty. Comprehensive considering the uncertainty of the dynamic load magnitude, direction, position, and excitation frequency, the weighted summation of mean and standard deviation of the module of dynamic structure compliance is set as the objective function with constraint is imposed to the structure volume fraction. The hybrid dimension reduction method and Gaussian integration method are used to quantify and propagate the loads uncertainty and the sensitivity formulation of objective function with respect to the design variables are derived. Two numerical examples are used to verify the effectiveness of the proposed method and the influence of dynamic loads uncertainty on the topology optimization design of periodic structures.

Key words: periodic structure, robustness, topological optimization, dynamic loads, load uncertainty

CLC Number:

TH122
O327

CAI Jinhu, HUANG Jing, HUANG Long, FU Zhifang, WU Hongyu, YIN Lairong. Robust Topology Optimization of Periodic Structures under Uncertain Dynamic Loads[J]. Journal of Mechanical Engineering, 2024, 60(23): 304-319.

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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2024.23.304

http://www.cjmenet.com.cn/EN/Y2024/V60/I23/304

References

[1] ZHU J H，ZHANG W H，XIA L. Topology optimization in aircraft and aerospace structures design[J]. Archives of Computational Methods in Engineering，2015，23(4)：595-622.
[2] LUO Z，TONG L Y，KANG Z. A level set method for structural shape and topology optimization using radial basis functions[J]. Computers & Structures，2009，87(7-8)：425-434.
[3] LIU L，YAN J，CHENG G D. Optimum structure with homogeneous optimum truss-like material[J]. Computers & Structures，2008，86(13-14)：1417-1425.
[4] LI Q H，XU R，LIU J，et al. Topology optimization design of multi-scale structures with alterable microstructural length-width ratios[J]. Composite Structures，2019，230：111454.
[5] HUANG X D，XIE Y M. Optimal design of periodic structures using evolutionary topology optimization[J]. Structural and Multidisciplinary Optimization，2007，36(6)：597-606.
[6] FU J J，XIA L，GAO L，et al. Topology optimization of periodic structures with substructuring[J]. Journal of Mechanical Design，2019，141(7)：071403.
[7] LI M，JIA G F，CHENG Z B，et al. Generative adversarial network guided topology optimization of periodic structures via Subset Simulation[J]. Composite Structures，2021，260：113254.
[8] HE G Q，HUANG X D，WANG H，et al. Topology optimization of periodic structures using BESO based on unstructured design points[J]. Structural and Multidisciplinary Optimization，2015，53(2)：271-275.
[9] THOMAS S，LI Q，STEVEN G. Finite periodic topology optimization with oriented unit-cells[J]. Structural and Multidisciplinary Optimization，2021，64(4)：1765-1779.
[10] XIE Y M，ZUO Z H，HUANG X D，et al. Convergence of topological patterns of optimal periodic structures under multiple scales[J]. Structural and Multidisciplinary Optimization，2012，46(1)：41-50.
[11] ZUO Z H，XIE Y M，HUANG X D. Optimal topological design of periodic structures for natural frequencies[J]. Journal of Structural Engineering，2011，137(10)：1229-1240.
[12] CAI J H，WANG C J，FU Z F. Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases[J]. International Journal for Numerical Methods in Engineering，2020，121(7)：1456-1483.
[13] KANG Z，LUO Y J. 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.
[14] LIU J，WEN G L，QING Q X，et al. Robust topology optimization for continuum structures with random loads[J]. Engineering Computations，2018，35(2)：710-732.
[15] LIU J T，GEA H C. Robust topology optimization under multiple independent unknown-but-bounded loads[J]. Computer Methods in Applied Mechanics and Engineering，2018，329：464-479.
[16] 罗阳军，亢战. 连续体结构非概率可靠性拓扑优化[J]. 力学学报，2007，23(1)：125-131. LUO Yangjun，KANG Zhan. Non-probabilistic reliability-based topology optimization of continuum structures[J]. Chinese Journal of Theoretical and Applied Mechanics，2007，23(1)：125-131.
[17] KHARMANDA G，OLHOFF N，MOHAMED A，et al. Reliability-based topology optimization[J]. Structural and Multidisciplinary Optimization，2004，26(5)：295-307.
[18] WANG D. Effects of design sensitivity schemes for incorporating loading uncertainty in robust topology optimization[J]. Engineering Optimization，2023，55(2)：344-361.
[19] WANG D，GAO W F. Robust topology optimization under multiple independent uncertainties of loading positions[J]. International Journal for Numerical Methods in Engineering，2020，121(22)：4944-4970.
[20] 杜鼎新，王栋. 载荷方向不确定条件下结构动态稳健性拓扑优化设计[J]. 力学学报，2023，55(11)：2588-2598. DU Dingxin，WANG Dong. Robust dynamic topology optimization of continuum structure subjected to harmonic excitation with loading direction uncertainty[J]. Chinese Journal of Theoretical and Applied Mechanics，2023，55(11)：2588-2598.
[21] 王栋. 载荷作用位置不确定条件下结构动态稳健性拓扑优化设计[J]. 力学学报，2021，53(5)：1439-1448. WANG Dong. Robust dynamic topology optinization of continuu structure subjected to harmonic excitation of loading position uncertainty[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(5)：1439-1448.
[22] GUEST J K，IGUSA T. Structural optimization under uncertain loads and nodal locations[J]. Computer Methods in Applied Mechanics and Engineering，2008，198(1)：116-124.
[23] JEONG S，SEONG H K，KIM C W，et al. Structural design considering the uncertainty of load positions using the phase field design method[J]. Finite Elements in Analysis and Design，2019，161：1-15.
[24] WANG D，GAO W F. Robust topology optimization under load position uncertainty[J]. International Journal for Numerical Methods in Engineering，2019，120(11)：1249-1272.
[25] 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 cases[J]. Chinese Journal of Theoretical and Applied Mechanics，2015，47(4)：642-650.
[26] LIU J，WEN G L，QING Q X，et al. An efficient method for topology optimization of continuum structures in the presence of uncertainty in loading direction[J]. International Journal of Computational Methods，2017，14(05)：1750054.
[27] PENG X，LI J Q，JIANG S F，et al. Robust topology optimization of continuum structures with loading uncertainty using a perturbation method[J]. Engineering Optimization，2018，50(4)：584-598.
[28] ZHAO J P，WANG C J. Robust topology optimization of structures under loading uncertainty[J]. AIAA Journal，2014，52(2)：398-407.
[29] ZHAO J P，WANG C J. 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.
[30] ZHENG J，DING S N，JIANG C，et al. Concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties[J]. International Journal for Numerical Methods in Engineering，2022，123(4)：1078-1097.
[31] ZHENG J，LUO Z，LI H，et al. Robust topology optimization for cellular composites with hybrid uncertainties[J]. International Journal for Numerical Methods in Engineering，2018，115(6)：695-713.
[32] ZHENG Y F，GAO L，XIAO M，et al. Robust topology optimization considering load uncertainty based on a semi-analytical method[J]. The International Journal of Advanced Manufacturing Technology，2018，94(9)：3537-3551.
[33] DENG J D，CHEN W. Concurrent topology optimization of multiscale structures with multiple porous materials under random field loading uncertainty[J]. Structural and Multidisciplinary Optimization，2017，56(1)：1-19.
[34] ZHANG X P，HE J J，TAKEZAWA A，et al. Robust topology optimization of phononic crystals with random field uncertainty[J]. International Journal for Numerical Methods in Engineering，2018，115(9)：1154-1173.
[35] ZHAO J P，WANG C J. Robust structural topology optimization under random field loading uncertainty[J]. Structural and Multidisciplinary Optimization，2014，50(3)：517-522.
[36] 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 Zhifang，WANG Chunjie. Robust topology optimization of periodic structures under uncertain loading[J]. Journal of Beijing University of Aeronautics and Astronautics，2017，43(4)：747-753.
[37] CAI J H，YANG Z J，WANG C J，et al. Concurrent topology optimization of composite macrostructure and microstructure under uncertain dynamic loads[J]. Structural Engineering and Mechanics，2022，81(3)：267-280.
[38] ZHENG J，LUO Z，JIANG C，et al. Robust topology optimization for concurrent design of dynamic structures under hybrid uncertainties[J]. Mechanical Systems and Signal Processing，2019，120：540-559.
[39] LIU B S，HUANG X D，HUANG C F，et al. Topological design of structures under dynamic periodic loads[J]. Engineering Structures，2017，142：128-136.
[40] STEIN M. Large sample properties of simulations using latin hypercube sampling[J]. Technometrics，1987，29(2)：143-151.
[41] HUANG X D，XIE Y M. Evolutionary topology optimization of continuum structures: methods and applications[M]. Chichester: John Wiley & Sons，2010.
[42] LI Y，XIE Y M. Evolutionary topology optimization for structures made of multiple materials with different properties in tension and compression[J]. Composite Structures，2021，259：113497.
[43] 赵军鹏，王春洁. 载荷不确定条件下的结构拓扑优化算法[J]. 北京航空航天大学学报，2014，40(7)：959-964. ZHAO Junpeng，WANG Chunjie. Structural topology optimization algorithm under uncertain load conditions[J]. Journal of Beijing University of Aeronautics and Astronautics，2014，40(7)：959-964.