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Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process. (English) Zbl 1506.74246

Summary: Compensation of the thermal distortion that occurs during the fabrication process is an important issue in the field of metal additive manufacturing. Considering the problem in forming a lattice structure inside an object to reduce the thermal distortion, we developed a lattice volume fraction distribution optimization method. Assuming that the linear elastic problem is solved using the finite element method (FEM), an inherent strain method applying a layer-by-layer process utilizing the element activation during the FEM is formed as a recurrence relation, and the sensitivity of an objective function is derived based on the adjoint method. The unit lattice shape is a simple cube with a cube or a sphere-shaped air hole, and its distribution is optimized by considering the minimum thickness of the wall surrounding it as a design variable. The effective stiffness tensor of the lattice is derived using a homogenization method. The functions of the effective properties with respect to the design variables are approximated through polynomial functions. The optimization problem is formulated as an unconstrained minimization problem. The design variables are optimized using the method of moving asymptotes. Herein, the validity of the proposed method is discussed based on quasi two-dimensional and three-dimensional numerical studies including a re-analysis through full-scale thermo-mechanical analysis.

MSC:

74N99 Phase transformations in solids
74S05 Finite element methods applied to problems in solid mechanics
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[1] Gibson, I.; Rosen, D.; Stucker, B., Additive Manufacturing Technologies (2010), Springer
[2] Mercelis, P.; Kruth, J. P., Residual stresses in selective laser sintering and selective laser melting, Rapid Prototyp. J., 12, 5, 254-265 (2006)
[3] Wu, A. S.; Brown, D. W.; Kumar, M.; Gallegos, G. F.; King, W. E., An experimental investigation into additive manufacturing-induced residual stresses in 316L stainless steel, Metall. Mater. Trans., 45, 13, 6260-6270 (2014)
[4] Dunbar, A. J.; Denlinger, E. R.; Gouge, M. F.; Michaleris, P., Experimental validation of finite element modeling for laser powder bed fusion deformation, Addit. Manufact., 12, 108-120 (2016)
[5] Afazov, S.; Denmark, W. A.D.; Toralles, B. L.; Holloway, A.; Yaghi, A., Distortion prediction and compensation in selective laser melting, Addit. Manufact., 17, 15-22 (2017)
[6] Denlinger, E. R.; Gouge, M.; Irwin, J.; Michaleris, P., Thermomechanical model development and in situ experimental validation of the laser powder-bed fusion process, Addit. Manufact., 16, 73-80 (2017)
[7] Schänzel, M.; Shakirov, D.; Ilin, A.; Ploshikhin, V., Coupled thermo-mechanical process simulation method for selective laser melting considering phase transformation steels, Comput. Math. Appl., 78, 7, 2230-2246 (2019) · Zbl 1443.82011
[8] Rybicki, E. F.; Schmueser, D. W.; Stonesifer, R. W.; Groom, J. J.; Mishler, H. W., A finite-element model for residual stresses and deflections in girth-butt welded pipes, J. Pressure Vessel Technol., 100, 3, 256-262 (1978)
[9] Lindgren, L.-E.; Runnemalm, H.; Näsström, M. O., Simulation of multipass welding of a thick plate, Internat. J. Numer. Methods Engrg., 44, 9, 1301-1316 (1999) · Zbl 0927.74069
[10] Lindgren, L. E., Computational Welding Mechanics (2007), Elsevier
[11] N. Keller, V. Ploshikhin, New method for fast predictions of residual stress and distortion of AM parts, in: Proceedings of the 25th Annual International Solid Freeform Fabrication Symposium, 2014, pp. 1229-1237.
[12] Keller, N., Verzugsminimierung bei selektiven Laserschmelz-verfahren durch Multi-Skalen-Simulation (2016), Universität Bremen, (Ph.D. thesis)
[13] Bugatti, M.; Semeraro, Q., Limitations of the inherent strain method in simulating powder bed fusion processes, Addit. Manufact., 23, 329-346 (2018)
[14] Liang, X.; Cheng, L.; Chen, Q.; Yang, Q.; To, A. C., A modified method for estimating inherent strains from detailed process simulation for fast residual distortion prediction of single-walled structures fabricated by directed energy deposition, Addit. Manufact., 23, 471-486 (2018)
[15] Setien, I.; Chiumenti, M.; van der Veen, S.; San Sebastian, M.; Garciandía, F.; Echeverría, A., Empirical methodology to determine inherent strains in additive manufacturing, Comput. Math. Appl., 78, 7, 2282-2295 (2019) · Zbl 1443.65370
[16] Chen, Q.; Liang, X.; Hayduke, D.; Liu, J.; Cheng, L.; Oskin, J.; Whitmore, R.; To, A. C., An inherent strain based multiscale modeling framework for simulating part-scale residual deformation for direct metal laser sintering, Addit. Manufact., 28, 406-418 (2019)
[17] Mirzendehdel, A. M.; Rankouhi, B.; Suresh, K., Strength-based topology optimization for anisotropic parts, Addit. Manufact., 19, 104-113 (2018)
[18] Liu, Y.; Li, Z.; Wei, P.; Chen, S., Generating support structures for additive manufacturing with continuum topology optimization methods, Rapid Prototyp. J., 25, 2, 232-246 (2019)
[19] Cheng, L.; Liang, X.; Bai, J.; Chen, Q.; Lemon, J.; To, A., On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing, Addit. Manufact., 27, 290-304 (2019)
[20] Ryan, L.; Kim, I. Y., A multiobjective topology optimization approach for cost and time minimization in additive manufacturing, Internat. J. Numer. Methods Engrg., 118, 7, 371-394 (2019)
[21] Seabra, M.; Azevedo, J.; Araújo, A.; Reis, L.; Pinto, E.; Alves, N.; Santos, R.; Mortágua, J. P., Selective laser melting (SLM) and topology optimization for lighter aerospace componentes, Procedia Struct. Integr., 1, 289-296 (2016)
[22] Chuang, C. H.; Chen, S.; Yang, R. J.; Vogiatzis, P., Topology optimization with additive manufacturing consideration for vehicle load path development, Internat. J. Numer. Methods Engrg., 113, 8, 1434-1445 (2018)
[23] Hollister, S. J., Porous scaffold design for tissue engineering, Nature Mater., 4, 7, 518-524 (2005)
[24] Lin, C. Y.; Wirtz, T.; LaMarca, F.; Hollister, S. J., Structural and mechanical evaluations of a topology optimized titanium interbody fusion cage fabricated by selective laser melting process, J. Biomed. Mater. Res., 83, 2, 272-279 (2007)
[25] Xiao, D.; Yang, Y.; Su, X.; Wang, D.; Sun, J., An integrated approach of topology optimized design and selective laser melting process for titanium implants materials, Bio-Med. Mater. Eng., 23, 5, 433-445 (2013)
[26] Koizumi, Y.; Okazaki, A.; Chiba, A.; Kato, T.; Takezawa, A., Cellular lattices of biomedical Co-Cr-Mo-alloy fabricated by electron beam melting with the aid of shape optimization, Addit. Manufact., 12B, 305-313 (2016)
[27] Takezawa, A.; Koizumi, Y.; Kobashi, M., High-stiffness and strength porous maraging steel via topology optimization and selective laser melting, Addit. Manufact., 18, 194-202 (2017)
[28] Takezawa, A.; Kobashi, M.; Koizumi, Y.; Kitamura, M., Porous metal produced by selective laser melting with effective isotropic thermal conductivity close to the Hashin-Shtrikman bound, Int. J. Heat. Mass. Tran., 105, 564-572 (2017)
[29] Schwerdtfeger, J.; Wein, F.; Leugering, G.; Singer, R. F.; Körner, C.; Stingl, M.; Schury, F., Design of auxetic structures via mathematical optimization, Adv. Mater., 23, 22-23, 2650-2654 (2011)
[30] Andreassen, E.; Lazarov, B. S.; Sigmund, O., Design of manufacturable 3D extremal elastic microstructure, Mech. Mater., 69, 1, 1-10 (2014)
[31] Clausen, A.; Wang, F.; Jensen, J. S.; Sigmund, O.; Lewis, J. A., Topology optimized architectures with programmable Poisson’s ratio over large deformations, Adv. Mater., 27, 37, 5523-5527 (2015)
[32] Takezawa, A.; Kobashi, M.; Kitamura, M., Porous composite with negative thermal expansion obtained by photopolymer additive manufacturing, APL Mater., 3, 7, Article 076103 pp. (2015)
[33] Takezawa, A.; Kobashi, M., Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing, Compos. B Eng., 131, 21-29 (2017)
[34] Miyamoto, Y.; Kaysser, W. A.; Rabin, B. H.; Kawasaki, A.; Ford, R., Functionally Graded Materials: Design, Processing and Applications (2013), Springer Science & Business Media
[35] Khanoki, S. A.; Pasini, D., Multiscale design and multiobjective optimization of orthopedic hip implants with functionally graded cellular material, J. Biomech. Eng., 134, 3, Article 031004 pp. (2012)
[36] Zhang, P.; Toman, J.; Yu, Y.; Biyikli, E.; Kirca, M.; Chmielus, M.; To, A. C., Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: Theory and validation, ASME J. Manuf. Sci. Eng., 137, 2, Article 021004 pp. (2015)
[37] Cheng, L.; Zhang, P.; Biyikli, E.; Bai, J.; Robbins, J.; To, A., Efficient design optimization of variable-density cellular structures for additive manufacturing: theory and experimental validation, Rapid Prototyp. J., 23, 4, 660-677 (2017)
[38] Cheng, L.; Bai, J.; To, A. C., Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints, Comput. Methods Appl. Mech. Engrg., 344, 334-359 (2019) · Zbl 1440.74284
[39] Lynch, M. E.; Mordasky, M.; Cheng, L.; To, A., Design, testing, and mechanical behavior of additively manufactured casing with optimized lattice structure, Addit. Manufact., 22, 462-471 (2018)
[40] Clausen, A.; Aage, N.; Sigmund, O., Exploiting additive manufacturing infill in topology optimization for improved buckling load, Engineering, 2, 2, 250-257 (2016)
[41] Wang, X.; Zhang, P.; Ludwick, S.; Belski, E.; To, A. C., Natural frequency optimization of 3D printed variable-density honeycomb structure via a homogenization-based approach, Addit. Manufact., 20, 189-198 (2018)
[42] Cheng, L.; Liang, X.; Belski, E.; Wang, X.; Sietins, J. M.; Ludwick, S.; To, A., Natural frequency optimization of variable-density additive manufactured lattice structure: Theory and experimental validation, J. Manuf. Sci. Eng., 140, 10, Article 105002 pp. (2018)
[43] Cheng, L.; Liu, J.; Liang, X.; To, A. C., Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design, Comput. Methods Appl. Mech. Eng., 332, 408-439 (2018) · Zbl 1440.74285
[44] Cheng, L.; Liu, J.; To, A. C., Concurrent lattice infill with feature evolution optimization for additive manufactured heat conduction design, Struct. Multidiscip. Optim., 1-25 (2018)
[45] Takezawa, A.; Zhang, X.; Kato, M.; Kitamura, M., Method to optimize an additively-manufactured functionally-graded lattice structure for effective liquid cooling, Addit. Manufact., 28, 285-298 (2019)
[46] Takezawa, A.; Zhang, X.; Kitamura, M., Optimization of an additively manufactured functionally graded lattice structure with liquid cooling considering structural performances, Int. J. Heat Mass Trans., 143, Article 118564 pp. (2019)
[47] Coelho, P. G.; Fernandes, P. R.; Guedes, J. M.; Rodrigues, H. C., A hierarchical model for concurrent material and topology optimisation of three-dimensional structures, Struct. Multidiscip. Optim., 35, 2, 107-115 (2008)
[48] Liu, L.; Yan, J.; Cheng, G., Optimum structure with homogeneous optimum truss-like material, Comput. Struct., 86, 13-14, 1417-1425 (2008)
[49] Haug, E. J.; Choi, K. K.; Komkov, V., Design Sensitivity Analysis of Structural Systems (1986), Academic Press: Academic Press Orlando · Zbl 0618.73106
[50] Guedes, J. M.; Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Engrg., 83, 2, 143-198 (1990) · Zbl 0737.73008
[51] Andreassen, E.; Andreasen, C. S., How to determine composite material properties using numerical homogenization, Comput. Mater. Sci., 83, 488-495 (2014)
[52] Svanberg, K., The method of moving asymptotes- a new method for structural optimization, Internat. J. Numer. Methods Engrg., 24, 2, 359-373 (1987) · Zbl 0602.73091
[53] Ueda, Y.; Yuan, M. G., Prediction of residual stresses in butt welded plates using inherent strains, J. Eng. Mater. Technol., 115, 4, 417-423 (1993)
[54] Liang, W.; Deng, D.; Sone, S.; Murakawa, H., Prediction of welding distortion by elastic finite element analysis using inherent deformation estimated through inverse analysis, Weld. World, 49, 11-12, 30-39 (2005)
[55] Deng, D.; Murakawa, H.; Liang, W., Numerical simulation of welding distortion in large structures, Comput. Methods Appl. Mech. Engrg., 196, 45-48, 4613-4627 (2007) · Zbl 1173.74409
[56] Murakawa, H.; Deng, D.; Ma, N.; Wang, J., Applications of inherent strain and interface element to simulation of welding deformation in thin plate structures, Comput. Mater. Sci., 51, 1, 43-52 (2011)
[57] Bendsøe, M. P.; Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Engrg., 71, 2, 197-224 (1988) · Zbl 0671.73065
[58] Bendsøe, M. P.; Sigmund, O., Topology Optimization: Theory, Methods, and Applications (2003), Springer-Verlag: Springer-Verlag Berlin · Zbl 1059.74001
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