[en] When using the robust topology optimization formulation in the density framework, the minimum size of the solid and void phases must be imposed implicitly through the parameters that define the density filter and the smoothed Heaviside projection. Finding these parameters can be time consuming and cumbersome, hindering a general code implementation of the robust formulation. Motivated by this issue, in this article we provide analytical expressions that explicitly relate the minimum length scale and the parameters that define it. The expressions are validated on a density-based framework. To facilitate the reproduction of results, MATLAB codes are provided.
Disciplines :
Mechanical engineering
Author, co-author :
Trillet, Denis ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Duysinx, Pierre ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Fernandez Sanchez, Eduardo Felipe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Andreasen CS, Elingaard MO, Aage N (2020) Level set topology and shape optimization by density methods using cut elements with length scale control. Struct Multidiscip Optim: 1–23
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202 DOI: 10.1007/BF01650949
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224 DOI: 10.1016/0045-7825(88)90086-2
Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158 DOI: 10.1002/nme.116
Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods Appl Mech Eng 190(26-27):3443–3459 DOI: 10.1016/S0045-7825(00)00278-4
Chen S, Chen W (2011) A new level-set based approach to shape and topology optimization under geometric uncertainty. Struct Multidiscip Optim 44(1):1–18 DOI: 10.1007/s00158-011-0660-9
Christiansen R, Lazarov B, Jensen J, Sigmund O (2015) Creating geometrically robust designs for highly sensitive problems using topology optimization: acoustic cavity design. Struct Multidiscip Optim 52:737–754 DOI: 10.1007/s00158-015-1265-5
Clausen A, Andreassen E (2017) On filter boundary conditions in topology optimization. Struct Multidiscip Optim 56(5):1147– 1155 DOI: 10.1007/s00158-017-1709-1
da Silva GA, Beck AT, Sigmund O (2019) Topology optimization of compliant mechanisms with stress constraints and manufacturing error robustness. Comput Methods Appl Mech Eng 354:397– 421 DOI: 10.1016/j.cma.2019.05.046
Fernández E, Kk Yang, Koppen S, Alarcón P, Bauduin S, Duysinx P (2020) Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization. Comput Methods Appl Mech Eng 368:113157 DOI: 10.1016/j.cma.2020.113157
Fernández E, Ayas C, Langelaar M, Duysinx P (2021) Topology optimization for large-scale additive manufacturing: Generating designs tailored to the deposition nozzle size (Under Review)
Lazarov BS, Sigmund O (2011) Filters in topology optimization based on helmholtz-type differential equations. Int J Numer Methods Eng 86(6):765–781 DOI: 10.1002/nme.3072
Pedersen C, Allinger P (2006) Industrial implementation and applications of topology optimization and future needs, vol 137. Springer, Berlin, pp 229–238
Pellens J, Lombaert G, Lazarov B, Schevenels M (2018) Combined length scale and overhang angle control in minimum compliance topology optimization for additive manufacturing. Struct Multidiscipl Optim
Qian X, Sigmund O (2013) Topological design of electromechanical actuators with robustness toward over-and under-etching. Comput Methods Appl Mech Eng 253:237–251 DOI: 10.1016/j.cma.2012.08.020
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. J Struct Mech 25(4):493–524
Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48 (6):1031–1055 DOI: 10.1007/s00158-013-0978-6
Silva G, Beck A, Sigmund O (2020) Topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity. Comput Methods Appl Mech Eng 365:112972 DOI: 10.1016/j.cma.2020.112972
Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784 DOI: 10.1007/s00158-010-0602-y
Wang F, Jensen J, Sigmund O (2011b) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. JOSA B 28:387–397 DOI: 10.1364/JOSAB.28.000387
Wang F, Lazarov BS, Sigmund O, Jensen JS (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472 DOI: 10.1016/j.cma.2014.03.021
Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside functions. Struct Multidiscip Optim 41(4):495–505 DOI: 10.1007/s00158-009-0452-7
Yan S, Wang F, Sigmund O (2018) On the non-optimality of tree structures for heat conduction. Int J Heat Mass Transf 122:660–680 DOI: 10.1016/j.ijheatmasstransfer.2018.01.114
Zhou M, Fleury R, Patten S, Stannard N, Mylett D, Gardner S (2011) Topology optimization-practical aspects for industrial applications. In: 9th World congress on structural and multidisciplinary optimization
Zhu JH, Zhang WH, Xia L (2016) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng 23:595–622 DOI: 10.1007/s11831-015-9151-2
