Multicomponent topology optimization method considering assemblability using a fictitious physical model
##article.authors##
- Ryoma Hirosawa School of Engineering, The University of Tokyo
- Masaki Noda Graduate School of Engineering, The University of Tokyo
-
Kei Matsushima
Graduate School of Engineering, The University of Tokyo
https://orcid.org/0000-0002-0352-8770
- Yuki Noguchi Graduate School of Engineering, The University of Tokyo https://orcid.org/0000-0003-3917-4369
- Takayuki Yamada Graduate School of Engineering, The University of Tokyo
DOI:
https://doi.org/10.51094/jxiv.33Keywords:
Topology optimization, Assemblability, Extended level set method, Multicomponent design, Fictitious physical model, Finite element method, FreeFEMAbstract
This paper proposes a multicomponent topology optimization method that considers assemblability. Generally, it is difficult to consider assemblability in topology optimization; however, in this study, we achieve it by introducing a fictitious physical model. To perform multicomponent topology optimization, the extended level set method is used to represent multiple components. First, the assembly constraints are formulated using a fictitious physical model limited to two components. Then, by considering stepwise assembly, the constraint is extended to three or more components. In addition, topology optimization algorithms are constructed using the finite element method. Several numerical examples demonstrate that the proposed method can obtain structures with assemblability and has low initial structure dependence.
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References
M. P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering 71 (2) (1988) 197–224. doi:10.1016/0045-7825(88)90086-2.
M. P. Bendsøe, Optimal shape design as a material distribution problem, Structural optimization 1 (4) (1989) 193–202. doi:10.1007/BF01650949.
M. P. Bendsøe, O. Sigmund, Material interpolation schemes in topology optimization, Archive of Applied Mechanics 69 (9) (1999) 635–654. doi:10.1007/s004190050248.
G. Allaire, Shape Optimization by the Homogenization Method, Springer, 2002.
K. Suzuki, N. Kikuchi, A homogenization method for shape and topology optimization, Computer Methods in Applied Mechanics and Engineering 93 (3) (1991) 291–318. doi:10.1016/0045-7825(91)90245-2.
J. A. Sethian, A. Wiegmann, Structural boundary design via level set and immersed interface methods, Journal of Computational Physics 163 (2) (2000) 489–528. doi:10.1006/jcph.2000.6581.
G. Allaire, F. de Gournay, F. Jouve, A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method, Control and Cybernetics 34 (1) (2005) 59–80.
T. Yamada, K. Izui, S. Nishiwaki, A. Takezawa, A topology optimization method based on the level set method incorporating a fictitious interface energy, Computer Methods in Applied Mechanics and Engineering 199 (45) (2010) 2876–2891. doi:10.1016/j.cma.2010.05.013.
S. Amstutz, H. Andr¨a, A new algorithm for topology optimization using a level-set method, Journal of Computational Physics 216 (2) (2006) 573–588. doi:10.1016/j.jcp.2005.12.015.
A. R. D´ıaaz, N. Kikuchi, Solutions to shape and topology eigenvalue optimization problems using a homogenization method, International Journal for Numerical Methods in Engineering 35 (7) (1992) 1487–1502. doi:10.1002/nme.1620350707.
Z.-D. Ma, N. Kikuchi, H.-C. Cheng, Topological design for vibrating structures, Computer Methods in Applied Mechanics and Engineering 121 (1) (1995) 259–280. doi:10.1016/0045-7825(94)00714-X.
A. Gersborg-Hansen, M. P. Bendsøe, O. Sigmund, Topology optimization of heat conduction problems using the finite volume method, Structural and Multidisciplinary Optimization 31 (4) (2006) 251–259. doi:10.1007/s00158-005-0584-3.
T. Yamada, K. Izui, S. Nishiwaki, A level set-based topology optimization method for maximizing thermal diffusivity in problems including design-dependent effects, Journal of Mechanical Design 133 (3) (2011) 031011. doi:10.1115/1.4003684.
G. Jing, H. Isakari, T. Matsumoto, T. Yamada, T. Takahashi, Level set-based topology optimization for 2D heat conduction problems using BEM with objective function defined on design-dependent boundary with heat transfer boundary condition, Engineering Analysis with Boundary Elements 61 (2015) 61–70. doi:10.1016/j.enganabound.2015.06.012.
J. Yoo, N. Kikuchi, J. Volakis, Structural optimization in magnetic devices by the homogenization design method, IEEE Transactions on Magnetics 36 (3) (2000) 574–580. doi:10.1109/20.846220.
T. Yamada, H. Watanabe, G. Fujii, T. Matsumoto, Topology optimization for a dielectric optical cloak based on an exact level set approach, IEEE Transactions on Magnetics 49 (5) (2013) 2073–2076. doi:10.1109/TMAG.2013.2243120.
J. Du, N. Olhoff, Minimization of sound radiation from vibrating bi-material structures using topology optimization, Structural and Multidisciplinary Optimization 33 (4) (2007) 305–321. doi:10.1007/s00158-006-0088-9.
Y. Noguchi, T. Yamada, Level set-based topology optimization for graded acoustic metasurfaces using two-scale homogenization, Finite Elements in Analysis and Design 196 (2021) 103606. doi:10.1016/j.finel.2021.103606.
L. Wang, P. K. Basu, J. P. Leiva, Automobile body reinforcement by finite element optimization, Finite Elements in Analysis and Design 40 (8) (2004) 879–893. doi:10.1016/S0168-874X(03)00118-5.
W. Saleem, F. Yuqing, W. Yunqiao, Application of topology optimization and manufacturing simulations - a new trend in design of aircraft components, Proceedings of the International MultiConference of Engineers and Computer Scientists 2.
T. Yamada, K. Izui, S. Nishiwaki, M. Sato, O. Tabata, An optimal structural design method for capacitive ultrasonic transducers: Topology optimization with uniform cross-section surface constraint based on the level set method (in Japanese), Transactions of the JSME, Series A 76 (771) (2010) 1403–1411.
S. Liu, Q. Li, W. Chen, L. Tong, G. Cheng, An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures, Frontiers of Mechanical Engineering 10 (2) (2015) 126–137. doi:10.1007/s11465-015-0340-3.
Q. Li, W. Chen, S. Liu, L. Tong, Structural topology optimization considering connectivity constraint, Structural and Multidisciplinary Optimization 54 (4) (2016) 971–984. doi:10.1007/s00158-016-1459-5.
L. Zhou, W. Zhang, Topology optimization method with elimination of enclosed voids, Structural and Multidisciplinary Optimization 60 (1) (2019) 117–136. doi:10.1007/s00158-019-02204-y.
Y. Zhou, T. Nomura, K. Saitou, Multicomponent topology optimization for additive manufacturing with build volume and cavity free constraints, Journal of Computing and Information Science in Engineering 19 (2) (2019) 021011. doi:10.1115/1.4042640.
Y. Zhou, T. Nomura, K. Saitou, Anisotropic multicomponent topology optimization for additive manufacturing with build orientation design and stress-constrained interfaces, Journal of Computing and Information Science in Engineering 21 (1) (2020) 011007. doi:10.1115/1.4047487.
C. Wang, Simultaneous optimization of build orientation and topology for self-supported enclosed voids in additive manufacturing, Computer Methods in Applied Mechanics and Engineering 388 (2022) 114227. doi:10.1016/j.cma.2021.114227.
L. Crispo, I. Y. Kim, Part consolidation for additive manufacturing: A multilayered topology optimization approach, International Journal for Numerical Methods in Engineering 122 (18) (2021) 4987–5027. doi:10.1002/nme.6754.
L. Luo, I. Baran, S. Rusinkiewicz, W. Matusik, Chopper: Partitioning models into 3D-printable parts, ACM Transactions on Graphics 31 (6) (2012) 129:1–129:9. doi:10.1145/2366145.2366148.
M. Attene, Shapes in a box: Disassembling 3D objects for efficient packing and fabrication, Computer Graphics Forum 34 (8) (2015) 64–76. doi:10.1111/cgf.12608.
Z. Zhou, K. Hamza, K. Saitou, Decomposition templates and joint morphing operators for genetic algorithm optimization of multicomponent structural topology, Journal of Mechanical Design 136 (2) (2013) 021004. doi:10.1115/1.4026030.
D. Guirguis, K. Hamza, M. Aly, H. Hegazi, K. Saitou, Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach, Structural and Multidisciplinary Optimization 51 (3) (2015) 733–748. doi:10.1007/s00158-014-1154-3.
Y. Oh, C. Zhou, S. Behdad, Part decomposition and assembly-based (Re) design for additive manufacturing: A review, Additive Manufacturing 22 (2018) 230–242. doi:10.1016/j.addma.2018.04.018.
Y. Oh, C. Zhou, S. Behdad, Part decomposition and 2D batch placement in single-machine additive manufacturing systems, Journal of Manufacturing Systems 48 (2018) 131–139. doi:10.1016/j.jmsy.2018.07.006.
Y. Oh, H. Ko, T. Sprock, W. Z. Bernstein, S. Kwon, Part decomposition and evaluation based on standard design guidelines for additive manufacturability and assemblability, Additive Manufacturing 37 (2021) 101702. doi:10.1016/j.addma.2020.101702.
Z. Wang, P. Song, M. Pauly, State of the art on computational design of assemblies with rigid parts, Computer Graphics Forum 40 (2) (2021) 633–657. doi:10.1111/cgf.142660.
O. Sigmund, S. Torquato, Design of materials with extreme thermal expansion using a three-phase topology optimization method, Journal of the Mechanics and Physics of Solids 45 (6) (1997) 1037–1067. doi:10.1016/S0022-5096(96)00114-7.
Y.Wang, Z. Luo, Z. Kang, N. Zhang, A multi-material level set-based topology and shape optimization method, Computer Methods in Applied Mechanics and Engineering 283 (2015) 1570–1586. doi:10.1016/j.cma.2014.11.002.
P. Gangl, A multi-material topology optimization algorithm based on the topological derivative, Computer Methods in Applied Mechanics and Engineering 366 (2020) 113090. doi:10.1016/j.cma.2020.113090.
M. Noda, Y. Noguchi, T. Yamada, Extended level set method: A multiphase representation with perfect symmetric property, and its application to multi-material topology optimization, Computer Methods in Applied Mechanics and Engineering 393 (2022) 114742. doi:10.1016/j.cma.2022.114742.
T. Yamada, Y. Noguchi, Topology optimization with a closed cavity exclusion constraint for additive manufacturing based on the fictitious physical model approach, Additive Manufacturing 52 (2022) 102630. doi:10.1016/j.addma.2022.102630.
Y. Sato, T. Yamada, K. Izui, S. Nishiwaki, Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization, The International Journal of Advanced Manufacturing Technology 92 (1) (2017) 1391–1409. doi:10.1007/s00170-017-0218-0.
F. Hecht, New development in freefem++, Journal of Numerical Mathematics 20 (3-4) (2012) 251–266. doi:10.1515/jnum-2012-0013.
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Submitted: 2022-03-28 03:54:34 UTC
Published: 2022-04-01 06:04:47 UTC
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Copyright (c) 2022
Ryoma Hirosawa
Masaki Noda
Kei Matsushima
Yuki Noguchi
Takayuki Yamada
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
