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Single variable-based multi-material structural optimization considering interface behavior. (English) Zbl 1442.74159
Summary: Recently, there is an increasing demand for bonding systems applied to multi-material structures. Among them, adhesives have been widely used to reduce cost and weight instead of traditional mechanical fasteners and welding. However, because the adhesive part can be easily separated under tensile stress, it is necessary to set the proper position of the adhesive in the early design process so that tensile stress does not occur in the adhesive part. This study proposes a method to prevent separation of adhesive bonds between different material phases in topology optimization. The interfacial tension energy density (ITED) is introduced into the objective function to restrict the generation of regions where the material interface with the adhesive is subject to tensile stress. Instead of using multi-design variables based on the number of material phases, the phase section method which uses a single variable is applied for the multi-material topological design. By adding the ITED to the ordinary compliance objective, the proposed method does not require the analysis of the nonlinear material behavior of the bonded areas. Through numerical examples, it is confirmed that the proposed method can offer a simple but effective multi-material design process considering the interfacial behavior.
74P10 Optimization of other properties in solid mechanics
74A50 Structured surfaces and interfaces, coexistent phases
Matlab; top.m
Full Text: DOI
[1] Bendsœ, M. P.; Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Engrg., 71, 197-224 (1988) · Zbl 0671.73065
[2] Suzuki, K.; Kikuchi, N., A homogenization method for shape and topology optimization, Comput. Methods Appl. Mech. Engrg., 93, 291-318 (1991) · Zbl 0850.73195
[3] Diaz, A.; Bendsœ, M. P., Shape optimization of structures for multiple loading conditions using a homogenization method, Struct. Optim., 4, 17-22 (1992)
[4] Bendsœ, M. P., Optimal shape design as a material distribution problem, Struct. Optim., 1, 193-202 (1989)
[5] Bendsœ, M. P.; Sigmund, O., Topology Optimization: Theory, Methods and Applications (2003), Springer-Verlag: Springer-Verlag Berlin · Zbl 1059.74001
[6] Bendsœ, M. P.; Sigmund, O., Material interpolation schemes in topology optimization, Arch. Appl. Mech., 69, 635-654 (1999) · Zbl 0957.74037
[7] Sigmund, O., A 99 line topology optimization code written in Matlab, Struct. Multidiscip. Optim., 21, 2, 120-127 (2001)
[8] Sethian, J. A.; Wiegmann, A., Structural boundary design via level set and immersed interface methods, J. Comput. Phys., 163, 489-528 (2000) · Zbl 0994.74082
[9] Osher, S. J.; Santosa, F., Level set methods for optimization problems involving geometry and constraints: I. Frequencies of a two-density inhomogeneous drum, J. Comput. Phys., 171, 272-288 (2001) · Zbl 1056.74061
[10] Wang, M. Y.; Wang, X.; Guo, D., A level set method for structural topology optimization, Comput. Methods Appl. Mech. Engrg., 192, 227-246 (2003) · Zbl 1083.74573
[11] Allaire, G.; Jouve, F.; Toader, A., A structural optimization using sensitivity analysis and a level-set method, Comput. Phys., 194, 363-393 (2004) · Zbl 1136.74368
[12] Petersson, J.; Sigmund, O., Slope constrained topology optimization, Internat. J. Numer. Methods Engrg., 41, 1417-1434 (1998) · Zbl 0907.73044
[13] Eschenauer, H. A.; Kobelev, V. V.; Schumacher, A., Bubble method for topology and shape optimization of structures, Struct. Optim., 8, 42-51 (1994)
[14] Allaire, G.; De Gournay, F.; Jouve, F.; Toader, A., Structural optimization using topological and shape sensitivity via a level set method, Control Cybernet., 34, 59 (2005) · Zbl 1167.49324
[15] van Dijk, N. P.; Maute, K.; Langelaar, M.; Van Keulen, F., Level-set methods for structural topology optimization: a review, Struct. Multidiscip. Optim., 48, 437-472 (2013)
[16] Yamada, T.; Izui, K.; Nishiwaki, S.; Takezawa, A., A topology optimization method based on the level set method incorporating a fictitious energy, Comput. Methods Appl. Mech. Engrg., 199, 2876-2891 (2010) · Zbl 1231.74365
[17] Huang, X.; Xie, Y. M., Evolutionary Topology Optimization of Continuum Structures: Methods and Applications (2010), John Wiley & Sons: John Wiley & Sons West Sussex · Zbl 1279.90001
[18] Sigmund, O., Morphology-based black and white filters for topology optimization, Struct. Multidiscip. Optim., 33, 401-424 (2007)
[19] Bourdin, B., Filters in topology optimization, Internat. J. Numer. Methods Engrg., 50, 2143-2158 (2001) · Zbl 0971.74062
[20] Haber, R. B.; Jog, C. S.; Bendsœ, M. P., A new approach to variable-topology shape design using a constraint on perimeter, Struct. Optim., 11, 1-12 (1996)
[21] Duysinx, P., Layout Optimization: A Mathematical Programming ApproachDCAMM Report No. 540 (1997), Technical University of Denmark
[22] Eschenauer, H. A.; Olhoff, N., Topology optimization of continuum structures: a review, Appl. Mech. Rev., 54, 331-390 (2001)
[23] Deaton, J. D.; Grandhi, R. V., A survey of structural and multidisciplinary continuum topology optimization: post 2000, Struct. Multidiscip. Optim., 49, 1-38 (2000)
[24] Luo, Z.; Tong, L.; Luo, J.; Wei, P.; Wang, M. Y., Design of piezoelectric actuators using a multiphase level set method of piecewise constants, J. Comput. Phys., 228, 2643-2659 (2009) · Zbl 1160.78322
[25] Ghasemi, H.; Park, H. S.; Rabczuk, T., A multi-material level set-based topology optimization of flexoelectric composites, Comput. Methods Appl. Mech. Engrg., 332, 47-62 (2018) · Zbl 1439.74270
[26] Faure, A.; Michailidis, G.; Parry, G.; Vermaak, N.; Estevez, R., Design of thermoelastic multi-material structures with graded interfaces using topology optimization, Struct. Multidiscip. Optim., 56, 823-837 (2017)
[27] Wang, X.; Mei, Y.; Wang, M. Y., Level-set method for design of multi-phase elastic and thermoelastic materials, Int. J. Mech. Mater. Des., 1, 213-239 (2004)
[28] Kishimoto, N.; Izui, K.; Nishiwaki, S.; Yamada, T., Optimal design of electromagnetic cloaks with multiple dielectric materials by topology optimization, Appl. Phys. Lett., 110, Article 201104 pp. (2017)
[29] Hvejsel, C. F.; Lund, E., Material interpolation schemes for unified topology and multi-material optimization, Struct. Multidiscip. Optim., 43, 811-825 (2011) · Zbl 1274.74344
[30] Li, D.; Kim, I. Y., Multi-material topology optimization for practical lightweight design, Struct. Multidiscip. Optim., 58, 1081-1094 (2018)
[31] Wang, M. Y.; Wang, X., “Color” level sets: a multi-phase method for structural topology optimization with multiple materials, Comput. Methods Appl. Mech. Engrg., 193, 469-496 (2004) · Zbl 1060.74585
[32] Luo, Y.; Bao, J., A material-field series-expansion method for topology optimization of continuum structures, Comput. Struct., 225, Article 106122 pp. (2019)
[33] Yin, L.; Ananthasuresh, G., Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme, Struct. Multidiscip. Optim., 23, 49-62 (2001)
[34] Bruyneel, M., SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies, Struct. Multidiscip. Optim., 43, 17-27 (2011)
[35] Gao, T.; Zhang, W.; Duysinx, P., A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate, Internat. J. Numer. Methods Engrg., 91, 98-114 (2012) · Zbl 1246.74043
[36] Zuo, W.; Saitou, K., Multi-material topology optimization using ordered SIMP interpolation, Struct. Multidiscip. Optim., 55, 477-491 (2017)
[37] Liu, J.; Ma, Y., A new multi-material level set topology optimization method with the length scale control capability, Comput. Methods Appl. Mech. Engrg., 329, 444-463 (2018) · Zbl 1439.74289
[38] Seong, H. K.; Kim, C. W.; Yoo, J.; Lee, J., Multiphase topology optimization with a single variable using the phase-field design method, Internat. J. Numer. Methods Engrg., 119, 5, 334-360 (2019) · Zbl 1425.74379
[39] Vermaak, N.; Michailidis, G.; Parry, G.; Estevez, R.; Allaire, G.; Bréchet, Y., Material interface effects on the topology optimizationof multi-phase structures using a level set method, Struct. Multidiscip. Optim., 50, 623-644 (2014)
[40] Hilchenbach, C. F.; Ramm, E., Optimization of multiphase structures considering damage, Struct. Multidiscip. Optim., 51, 1083-1096 (2015)
[41] Lawry, M.; Maute, K., Level set topology optimization of problems with sliding contact interfaces, Struct. Multidiscip. Optim., 52, 1107-1119 (2015)
[42] Liu, P.; Luo, Y.; Kang, Z., Multi-material topology optimization considering interface behavior via XFEM and level set method, Comput. Methods Appl. Mech. Engrg., 308, 113-133 (2016) · Zbl 1439.74290
[43] Liu, P.; Kang, Z., Integrated topology optimization of multi-component structures considering connecting interface behavior, Comput. Methods Appl. Mech. Engrg., 341, 851-887 (2018) · Zbl 1440.74302
[44] Da, D.; Yvonnet, J.; Xia, L.; Li, G., Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage, Internat. J. Numer. Methods Engrg., 115, 604-626 (2018)
[45] Nguyen, T. T.; Yvonnet, J.; Zhu, Q.-Z.; Bornert, M.; Chateau, C., A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography, Comput. Methods Appl. Mech. Engrg., 312, 567-595 (2016) · Zbl 1439.74243
[46] Kang, Z.; Wu, C.; Luo, Y.; Li, M., Robust topology optimization of multi-material structures considering uncertain graded interface, Compos. Struct., 208, 395-406 (2019)
[47] Lazarov, B. S.; Sigmund, O., Filters in topology optimization based on Helmholtz-type differential equations, Internat. J. Numer. Methods Engrg., 86, 765-781 (2011) · Zbl 1235.74258
[48] Bertsekas, D. P., Constrained Optimization and Lagrange Multiplier Methods (2014), Academic press: Academic press Belmont, MA
[49] Svanberg, K., The method of moving asymptotes—a new method for structural optimization, Internat. J. Numer. Methods Engrg., 24, 359-373 (1987) · Zbl 0602.73091
[50] Lim, H.; Yoo, J.; Choi, J. S., Topological nano-aperture configuration by structural optimization based on the phase field method, Struct. Multidiscip. Optim., 49, 209-224 (2014)
[51] Seong, H. K.; Yoo, J., Probability distribution function inspired structural optimization for frequency response problems, Comput. Methods Appl. Mech. Engrg., 318, 783-802 (2017) · Zbl 1439.74259
[52] Choi, J. S.; Yamada, T.; Izui, K.; Nishiwaki, S.; Yoo, J., Topology optimization using a reaction-diffusion equation, Comput. Methods Appl. Mech. Engrg., 200, 29, 2407-2420 (2011) · Zbl 1230.74151
[53] Kim, C.; Seong, H. K.; Yoo, J., Study on the clear boundary determination from results of the phase field design method, Int. J. Precis. Eng. Manuf., 20, 1553-1561 (2019)
[54] Bandyopadhyay, A.; Bryan, H., Additive manufacturing of multi-material structures, Mater. Sci. Eng. R., 129, 1-16 (2018)
[55] Florea, V.; Pamwar, M.; Sangha, B.; Kim, I. Y., 3D multi-material and multi-joint topology optimization with tooling accessibility constraints, Struct. Multidiscip. Optim., 60, 2531-2558 (2019)
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