考虑增材制造填充结构强度的拓扑优化方法

doi:10.16183/j.cnki.jsjtu.2022.333

上海交通大学学报 ›› 2024, Vol. 58 ›› Issue (3): 333-341.doi: 10.16183/j.cnki.jsjtu.2022.333

考虑增材制造填充结构强度的拓扑优化方法

王辰, 刘义畅, 陆宇帆, 赖章龙, 周明东()

上海交通大学机械与动力工程学院,上海 200240

收稿日期:2022-08-30 修回日期:2022-10-13 接受日期:2022-11-10 出版日期:2024-03-28 发布日期:2024-03-28
通讯作者: 周明东,副教授,博士生导师;E-mail:mdzhou@sjtu.edu.cn.
作者简介:王辰(1995-),硕士生,从事结构拓扑优化方法研究.
基金资助:
国家重点研发计划(2021YFB1715400);国家自然科学基金(52075321)

Topology Optimization of Infill Structures for Additive Manufacturing Considering Structural Strength

WANG Chen, LIU Yichang, LU Yufan, LAI Zhanglong, ZHOU Mingdong()

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2022-08-30 Revised:2022-10-13 Accepted:2022-11-10 Online:2024-03-28 Published:2024-03-28

摘要/Abstract

摘要：

提出了一种针对给定薄壁外形的内填充结构拓扑优化方法,用于设计具有优化结构强度、满足增材制造几何要求的轻量化多孔填充结构.基于p范数函数计算结构最大应力近似值,并以最小化该值为优化目标,以提升填充结构强度.通过在优化模型中考虑局部体积约束,获得多孔填充构型,并进一步提出局部体积上限动态调整策略,提升优化过程稳定性,避免优化过程约束过强导致结构构型和应力响应突变甚至优化失败.此外,考虑了自支撑约束,保证优化所得填充结构自支撑,且支撑给定薄壁外形的悬空区域.引入了基于两场公式的优化模型,确保优化所得填充结构满足增材制造最小尺寸要求.数值算例表明,所提方法优化结果与以最小化柔度为目标的填充结构拓扑优化结果相比,在相同质量下结构强度得到了显著提升.在此基础上,在优化模型中考虑了柔度约束,讨论了填充结构刚度、强度的相互影响规律.

关键词: 填充结构强度, 拓扑优化, 增材制造, p范数应力

Abstract:

A topology optimization approach is proposed to design lightweight and high-strength porous infill structures for additive manufacturing. The maximum stress approximated by the p-norm function is minimized to enhance the structural strength. A local volume constraint is utilized to generate porous infill pattern. A continuation strategy on the upper bound of the local volume fraction is proposed to improve the stability of the optimization process and avoid the sharp rising of stress. An overhang constraint is utilized to make sure that the optimized infill structures are self-supporting and can support the given shell. Besides, two-field-based topology optimization formulations are used to ensure that the optimized infill structures satisfy the minimum length scale for additive manufacturing. The numerical results show that the optimized infill structures can significantly improve the structural strength compared with the optimized design of compliance minimization problem at the same weight. A compliance constraint is further imposed in the optimization model and the relation between stiffness and strength of the infill structures is also discussed.

Key words: infill structures strength, topology optimization, additive manufacturing, p-norm stress

中图分类号:

TH122

王辰, 刘义畅, 陆宇帆, 赖章龙, 周明东. 考虑增材制造填充结构强度的拓扑优化方法[J]. 上海交通大学学报, 2024, 58(3): 333-341.

WANG Chen, LIU Yichang, LU Yufan, LAI Zhanglong, ZHOU Mingdong. Topology Optimization of Infill Structures for Additive Manufacturing Considering Structural Strength[J]. Journal of Shanghai Jiao Tong University, 2024, 58(3): 333-341.

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参考文献 24

[1]	CLAUSEN A, AAGE N, SIGMUND O. Exploiting additive manufacturing infill in topology optimization for improved buckling load[J]. Engineering, 2016, 2(2): 250-257. doi: 10.1016/J.ENG.2016.02.006 URL
[2]	WU J, AAGE N, WESTERMANN R, et al. Infill optimization for additive manufacturing-approaching bone-like porous structures[J]. IEEE Transactions on Visualization and Computer Graphics, 2018, 24(2): 1127-1140. doi: 10.1109/TVCG.2945 URL
[3]	BRUGGI M, DUYSINX P. Topology optimization for minimum weight with compliance and stress constraints[J]. Structural and Multidisciplinary Optimization, 2012, 46: 369-384. doi: 10.1007/s00158-012-0759-7 URL
[4]	WANG M, LI L. Shape equilibrium constraint: A strategy for stress-constrained structural topology optimization[J]. Structural and Multidisciplinary Optimization, 2013, 47: 335-352. doi: 10.1007/s00158-012-0846-9 URL
[5]	LEE K, AHN K, YOO J. A novel p-norm correction method for lightweight topology optimization under maximum stress constraints[J]. Computers and Structures, 2016, 171: 18-30. doi: 10.1016/j.compstruc.2016.04.005 URL
[6]	KHAN SA, SIDDIQUI BA, FAHAD M, et al. Evaluation of the effect of infill pattern on mechanical strength of additively manufactured specimen[J]. Materials Science Forum, 2017, 887: 128-132. doi: 10.4028/www.scientific.net/MSF.887 URL
[7]	LIU Y, ZHOU M, WEI C, et al. Topology optimization of self-supporting infill structures[J]. Structural and Multidisciplinary Optimization, 2021, 63: 2289-2304. doi: 10.1007/s00158-020-02805-y
[8]	QIU W, JIN P, JIN S, et al. An evolutionary design approach to shell-infill structures[J]. Additive Manufacturing, 2020, 34: 101382. doi: 10.1016/j.addma.2020.101382 URL
[9]	GROEN J P, WU J, SIGMUND O. Homogenization-based stiffness optimization and projection of 2D coated structures with orthotropic infill[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 349: 722-742. doi: 10.1016/j.cma.2019.02.031 URL
[10]	WADBRO E, NIU B. Multiscale design for additive manufactured structures with solid coating and periodic infill pattern[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112605. doi: 10.1016/j.cma.2019.112605 URL
[11]	WU J, CLAUSEN A, SIGMUND O. Minimum compliance topology optimization of shell-infill composites for additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 326: 358-375. doi: 10.1016/j.cma.2017.08.018 URL
[12]	ZHOU M, LU Y, LIU Y, et al. Concurrent topology optimization of shells with self-supporting infills for additive manufacturing[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 390: 114430. doi: 10.1016/j.cma.2021.114430 URL
[13]	DUYSINX P, BENDSØE M. Topology optimization of continuum structures with local stress constraints[J]. International Journal for Numerical Methods in Engineering, 1998, 43(8): 1453-1478. doi: 10.1002/(ISSN)1097-0207 URL
[14]	LE C, NORATO J, BRUNS T, et al. Stress-based topology optimization for continua[J]. Structural and Multidisciplinary Optimization, 2010, 41(4): 605-620. doi: 10.1007/s00158-009-0440-y URL
[15]	CHENG G, GUO X. Epsilon-relaxed approach in structural topology optimization[J]. Structural and Multidisciplinary Optimization, 1997, 13(4): 258-266.
[16]	BRUGGI M. On an alternative approach to stress constraints relaxation in topology optimization[J]. Structural and Multidisciplinary Optimization, 2008, 36(2): 125-141. doi: 10.1007/s00158-007-0203-6 URL
[17]	YANG R, CHEN C. Stress-based topology optimization[J]. Structural and Multidisciplinary Optimization, 1996, 12(2): 98-105.
[18]	FAN Z, XIA L, LAI W, et al. Evolutionary topology optimization of continuum structures with stress constraints[J]. Structural and Multidisciplinary Optimization, 2019, 59(2): 647-658. doi: 10.1007/s00158-018-2090-4
[19]	YU H, HUANG J, ZOU B, et al. Stress-constrained shell lattice infill structural optimisation for additive manufacturing[J]. Virtual and Physical Prototyping, 2020, 15(1): 35-48. doi: 10.1080/17452759.2019.1647488 URL
[20]	BRUNS T, TORTORELLI D. Topology optimization of non-linear elastic structures and compliant mechanisms[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(26): 3443-3459. doi: 10.1016/S0045-7825(00)00278-4 URL
[21]	WANG F, LAZAROV B, SIGMUND O. On projection methods, convergence and robust formulations in topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 43(6): 767-784.
[22]	MATTHIJS L. An additive manufacturing filter for topology optimization of print-ready designs[J]. Structural and Multidisciplinary Optimization, 2017, 55(3): 871-883. doi: 10.1007/s00158-016-1522-2 URL
[23]	LAZAROV B, WANG F, SIGMUND O. Length scale and manufacturability in density-based topology optimization[J]. Archive of Applied Mechanics, 2016, 86(1): 189-218. doi: 10.1007/s00419-015-1106-4 URL
[24]	KRISTER S. The method of moving asymptotes—A new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373. doi: 10.1002/nme.v24:2 URL

考虑增材制造填充结构强度的拓扑优化方法

Topology Optimization of Infill Structures for Additive Manufacturing Considering Structural Strength

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