Structural topology optimization with local finite-life fatigue constraints

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (16) : 110-119.

JIANG Xudong1，WU Ziwang1，TENG Xiaoyan2

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Abstract

Topology optimization method is a feasible design strategy to improve fatigue-resistance performance of engineering structures. To reduce the computational cost due to numerous local fatigue constraint, a global fatigue damage measure based on P-norm method is traditionally introduced in current literatures. However there exists a gap at the optimal solution subjected to the weak constraints compared with accurate local fatigue constraint. To solve the fatigue-constrained problem, a scheme based on the augmented Lagrangian method is adopted to address the problem consistently with the local definition of fatigue damage without using traditional aggregation techniques. Under proportional loadings with various amplitude, the Palmgren-Miner linear damage hypothesis combined with Sines fatigue criterion is employed to evaluate the fatigue strength at every material point. In the augmented Lagrangian, the lightweight design model with satisfying the fatigue constraints locally is established and then is solved by globally convergent method of moving asymptotes. Moreover, a general topology optimization framework using unstructured polygonal finite element meshes is developed to realize the lightweight design of fatigue-resistance structures with complex geometrical boundary. The numerical results of several benchmark examples show that the optimal configuration obtained by local fatigue constraints provides a superior fatigue-resistance performance with less material usage to that by P-norm aggregative fatigue constraints. Therefore, topology optimization with local fatigue constraints contributes to effectiveness of material usage and enhancement of fatigue-resistance performance.

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topology optimization / aggregation-free approach / local finite-life fatigue constraints / augmented Lagrangian method / polygonal finite element meshes

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JIANG Xudong1，WU Ziwang1，TENG Xiaoyan2. Structural topology optimization with local finite-life fatigue constraints[J]. Journal of Vibration and Shock, 2023, 42(16): 110-119

References

[1] ZHU J, ZHOU H, WANG C, et al. A review of topology optimization for additive manufacturing: Status and challenges[J]. Chinese Journal of Aeronautics, 2021, 34(1): 91-110.
[2] 廉艳平, 王潘丁, 高杰, 等. 金属增材制造若干关键力学问题研究进展[J].力学进展, 2021, 51(03): 648-701.
LIAN Yanping, WANG Panding, GAO Jie, et al. Fundamental mechanics problems in metal additive manufacturing: A state-of-art review [J]. Advances in Mechanics. 2021, 51(03): 648-701.
[3] HOLMBERG E, TORSTENFELT B, KLARBRING A. Fatigue constrained topology optimization [J]. Structural and Multidisciplinary Optimization, 2014, 50: 207-219.
[4] VERBART A, LANGELAAR, KEULEN F V. Damage approach: A new method for topology optimization with local stress constraints [J]. Structural and Multidisciplinary Optimization, 2015, 53: 1081-1098.
[5] 占金青, 龙良明, 刘敏, 等. 基于最大应力约束的柔顺机构拓扑优化设计[J]. 机械工程学报, 2018, 54(23): 32-38.
ZHAN Jinqing, LONG Liangming, LIU Min, et al. Topological design of compliant mechanisms with maximum stress constraint [J]. Journal of Mechanical Engineering, 2018, 54(23): 32-38.
[6] 王选, 刘宏亮, 龙凯, 等. 基于改进的双向渐进结构优化法的应力约束拓扑优化[J]. 力学学报. 2018, 50(2): 385-394.
WANG Xuan, LIU Hongliang, LONG Kai, et al. Stress-constrained topology optimization based on improved bi-directional evolutionary optimization method [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 385-394.
[7] SILVA G A, BECK A T, SIGMUND O. Topology optimization of compliant mechanisms with stress constraints and manufacturing error robustness [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 354:3 97-421.
[8] SILVA G A, BECK A T, SIGMUND O. Stress-constrained topology optimization considering uniform manufacturing uncertainties [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 344: 512-537.
[9] EMMENDOERFER H J R, SILVA E C N, FANCELLO E A. Stress-constrained level set topology optimization for design-dependent pressure load problems [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 344: 569-601.
[10] OLIVER G L, GLAUCIO H P. PolyStress: a Matlab implementation for local stress-constrained topology optimization using the augmented Lagrangian method [J]. Structural and Multidisciplinary Optimization, 2021, 63: 2065-2097.
[11] TALISCHI C, PAULINO G H, PEREIRA A, et al. Polytop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Structural and Multidisciplinary Optimization, 2012, 45(3): 329-357.
[12] OEST J, LUND E. Topology optimization with finite-life fatigue constraints [J]. Structural and Multidisciplinary Optimization, 2017, 1-15.
[13] 叶红玲, 苏鹏飞, 王伟伟, 等. 疲劳寿命约束下的连续体结构拓扑优化[J]. 北京工业大学学报, 2020, 46(3): 236-244.
YE Hongling, SU Pengfei, WANG Weiwei, et al. Continuum topology optimization with fatigue life constraints [J]. Journal of Beijing University of Technology, 2020, 46(3): 236-244.
[14] CHEN Z, LONG K, WEN P, et al. Fatigue-resistance topology optimization of continuum structure by penalizing the cumulative fatigue damage [J]. Advances in Engineering Software, 2020, 150: 102924.(变幅载荷)
[15] NABAKI K, SHEN J, HUANG X. Evolutionary topology optimization of continuum structures considering fatigue failure [J]. Materials and Design, 2019, 166: 107586
[16] 占金青, 刘天舒, 刘敏, 等. 考虑疲劳性能的柔顺机构拓扑优化设计[J]. 机械工程学报, 2021, 57(3): 59-68.
ZHAN Jinqing, LIU Tianshu, LIU Min, et al. Topological design of compliant mechanisms considering fatigue constraints [J]. Journal of Mechanical Engineering, 2021, 57(3): 59-68.
[17] 侯杰, 朱继宏, 王创, 等. 考虑机械连接载荷和疲劳性能的装配结构拓扑优化设计方法[J]. 科学通报, 2019, 64(1): 79-86.
HOU Jie, ZHU Jihong, WANG Chuang, et al. Topology optimization of the multi-fasteners jointed structure considering joint load constraint and fatigue constraints [J]. Science China Press, 2019, 64(1): 79-86.
[18] GAO X, RICCARDO C, ANDREA T, et al. Innovative formulation for topological fatigue optimisation based on material defects distribution and TopFat algorithm [J]. International Journal of Fatigue, 2021, 147: 106176.
[19] ZHANG S, LE C, GAIN AL, et al. Fatigue-based topology optimization with non-proportional loads [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 345: 805-25.
[20] SURESH S, LINDSTROM S B, THORE C J, et al. Topology optimization using a continuous-time high-cycle fatigue model [J]. Structural and Multidisciplinary Optimization, 2020, 61: 1011-1025.
[21] JEONG S H, CHOI D H, YOON G H. Fatigue and static failure considerations using a topology optimization method [J]. Applied Mathematical Model, 2015, 39 (3-4): 1137-1162.
[22] LEE J W, YOON G H, JEONG S H. Topology optimization considering fatigue life in the frequency domain [J]. Computers Mathematics with Applications, 2015, 70: 1852-77.
[23] ZHAO L, XU B, HAN Y, et al. Structural topological optimization with dynamic fatigue constraints subject to dynamic random loads [J]. Engineering Structures, 2020, 205: 110089.
[24] 贺新峰, 于德介. 基于ESLs结构优化法的搅拌车副车架疲劳设计[J]. 振动与冲击, 2013, 32(14): 64-69.
HE Xinfeng, YU Dejie. Fatigue design of auxiliary frame of an agitator truck based on ESLs structural optimization method [J]. Journal of Vibration and Shock, 2013, 32(14): 64-69.
[25] JEONG S H, LEE J W, YOON G H, et al. Topology optimization considering the fatigue constraint of variable amplitude load based on the equivalent static load approach [J]. Applied Mathematical Model, 2018, 56: 626-47.
[26] WANG F, LAZAROV B S, SIGMUND O. On projection methods, convergence and robust formulations in topology optimization [J]. Structural and Multidisciplinary Optimization, 2011, 43(6): 767-784.
[27] BOURDIN B. Filters in topology optimization [J]. International Journal for Numerical Methods in Engineering, 2001, 50(9): 2143-2158.
[28] STEPHENS R I, FATEMI A, STEPHENS R R, et al. Metal fatigue in engineering[M].2nd ed. New York :John Wiley & Sons, 2000.
[29] KIYONO C Y, VATANABE S L, SILVA E C N, et al. A new multi-p-norm formulation approach for stress-based topology optimization design [J]. Composite Structures, 2016, 156(11): 10-19.
[30] GIRALDO-LONDONO O, PAULINO G H. A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr-Coulomb, Bresler-Pister, and William-Warnke [J]. Proceedings of the Royal Society A, 2020, 476: 20190861.
[31] SVANBERG K. A class of globally convergent optimization methods based on conservative convex separable approximations [J]. SIAM Journal on Optimization, 2002, 12(2): 555-573.
[32] SENHORA F V, GIRALDO-LONDONO O, MENEZES I F M, Pet al. Topology optimization with local stress constraints: a stress aggregation-free approach [J]. Structural and Multidisciplinary Optimization, 2020, 62(4): 1639-1668.
[33] OEST J, SORENSEN R, OVERGAARD L C T, et al. Structural optimization with fatigue and ultimate limit constraints of jacket structures for large offshore wind turbines [J]. Structural and Multidisciplinary Optimization, 2017, 55: 779-793.