DOI: 10.1007/s00158-010-0602-y. On projection methods, convergence and robust formulations in topology optimization

On projection methods, convergence and robust formulations in topology optimization

10.1007/s00158-010-0602-y

Crossref journal-article

Springer Science and Business Media LLC

Structural and Multidisciplinary Optimization (297)

Bibliography

Wang, F., Lazarov, B. S., & Sigmund, O. (2010). On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization, 43(6), 767â784.

Authors 3

Fengwen Wang (first)
Boyan Stefanov Lazarov (additional)
Ole Sigmund (additional)

References 31 Referenced 1,410

Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393 (10.1016/j.jcp.2003.09.032) / J Comput Phys by G Allaire (2004)
Ambrosio L, Buttazzo G (1993) An optimal design problem with perimeter penalization. Calc Var Partial Differ Equ 1:55–69 (10.1007/BF02163264) / Calc Var Partial Differ Equ by L Ambrosio (1993)
Amir O, Bendsoe MP, Sigmund O (2009) Approximate reanalysis in topology optimization. Int J Numer Methods Eng 78(12):1474–1491 (10.1002/nme.2536) / Int J Numer Methods Eng by O Amir (2009)
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224 (10.1016/0045-7825(88)90086-2) / Comput Methods Appl Mech Eng by MP Bendsøe (1988)
Bendsøe MP, Sigmund O (2004) Topology optimization—theory, methods and applications. Springer, Berlin / Topology optimization—theory, methods and applications by MP Bendsøe (2004)
Borel PI, Frandsen LH, Harpøth A, Kristensen M, Jensen JS, Sigmund O (2005) Topology optimised broadband photonic crystal Y-splitter. Electron Lett 41(2):69–71 (10.1049/el:20057717) / Electron Lett by PI Borel (2005)
Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158 (10.1002/nme.116) / Int J Numer Methods Eng by B Bourdin (2001)
Bruns T, Tortorelli D (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459 (10.1016/S0045-7825(00)00278-4) / Comput Methods Appl Mech Eng by T Bruns (2001)
Díaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Struct Multidisc Optim 10:40–45 (10.1007/BF01743693) / Struct Multidisc Optim by A Díaz (1995)
Guest J (2009) Topology optimization with multiple phase projection. Comput Methods Appl Mech Eng 199(1–4):123–135. doi:10.1016/j.cma.2009.09.023 (10.1016/j.cma.2009.09.023) / Comput Methods Appl Mech Eng by J Guest (2009)
Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254 (10.1002/nme.1064) / Int J Numer Methods Eng by J Guest (2004)
Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on the perimeter. Struct Optim 11(1):1–11 (10.1007/BF01279647) / Struct Optim by RB Haber (1996)
Jensen JS, Sigmund O (2005) Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide. J Opt Soc Am B Opt Phys 22(6):1191–1198 (10.1364/JOSAB.22.001191) / J Opt Soc Am B Opt Phys by JS Jensen (2005)
Jog CS, Haber RB (1996) Stability of finite element models for distributed-parameter optimization and topology design. Comput Methods Appl Mech Eng 130(3–4):203–226 (10.1016/0045-7825(95)00928-0) / Comput Methods Appl Mech Eng by CS Jog (1996)
Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2010) Heaviside projection based topology optimization by a pde-filtered scalar function. Struct Multidisc Optim. doi:10.1007/s00158-010-0562-2 (10.1007/s00158-010-0562-2) / Struct Multidisc Optim by A Kawamoto (2010)
Kirsch U (2008) Reanalysis of structures. Springer, Berlin / Reanalysis of structures by U Kirsch (2008)
Lazarov B, Sigmund O (2009) Sensitivity filters in topology optimisation as a solution to Helmholtz type differential equation. In: Proc. of the 8th world congress on structural and multidisciplinary optimization. Lisbon, Portugal / Proc. of the 8th world congress on structural and multidisciplinary optimization by B Lazarov (2009)
Lazarov B, Sigmund O (2010) Filters in topology optimizat ion based on Helmholtz type differential equations. Int J Numer Methods Eng. doi:10.1002/nme.3072 (10.1002/nme.3072)
Luo J, Luo Z, Chen S, Tong L, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198(2):318–331 (10.1016/j.cma.2008.08.003) / Comput Methods Appl Mech Eng by J Luo (2008)
Poulsen TA (2003) A new scheme for imposing a minimum length scale in topology optimization. Int J Numer Methods Eng 57(6):741–760 (10.1002/nme.694) / Int J Numer Methods Eng by TA Poulsen (2003)
Sardan Ö, Petersen DH, Mølhave K, Sigmund O, Bøggild P (2008) Topology optimized electrothermal polysilicon microgrippers. Microelectron Eng 85:1096–1099. doi:10.1016/j.mee.2008.01.049 (10.1016/j.mee.2008.01.049) / Microelectron Eng by Ö Sardan (2008)
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524 (10.1080/08905459708945415) / Mech Struct Mach by O Sigmund (1997)
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33(4–5):401–424 (10.1007/s00158-006-0087-x) / Struct Multidisc Optim by O Sigmund (2007)
Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sin 25(2):227–239. doi:10.1007/s10409-009-0240-z (10.1007/s10409-009-0240-z) / Acta Mech Sin by O Sigmund (2009)
Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75 (10.1007/BF01214002) / Struct Optim by O Sigmund (1998)
Stainko R, Sigmund O (2007) Tailoring dispersion properties of photonic crystal waveguides by topology optimization. Waves Random Complex Media 17:477–489 (10.1080/17455030701501851) / Waves Random Complex Media by R Stainko (2007)
Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373 (10.1002/nme.1620240207) / Int J Numer Methods Eng by K Svanberg (1987)
Wang F, Jensen J, Sigmund O (2010) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties (submitted) (10.1364/JOSAB.28.000387)
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246 (10.1016/S0045-7825(02)00559-5) / Comput Methods Appl Mech Eng by MY Wang (2003)
Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside funtions. Struct Multidisc Optim 41:495–505 (10.1007/s00158-009-0452-7) / Struct Multidisc Optim by S Xu (2010)
Yoon GH, Sigmund O (2008) A monolithic approach for topology optimization of electrostatically actuated devices. Comput Methods Appl Mech Eng 197:4062–4075. doi:10.1016/j.cma.2008.04.004 (10.1016/j.cma.2008.04.004) / Comput Methods Appl Mech Eng by GH Yoon (2008)

Dates

Type	When
Created	14 years, 8 months ago (Dec. 23, 2010, 8:08 a.m.)
Deposited	2 years, 11 months ago (Sept. 17, 2022, 5:03 a.m.)
Indexed	4 minutes ago (Aug. 30, 2025, 11:41 p.m.)
Issued	14 years, 8 months ago (Dec. 24, 2010)
Published	14 years, 8 months ago (Dec. 24, 2010)
Published Online	14 years, 8 months ago (Dec. 24, 2010)
Published Print	14 years, 2 months ago (June 1, 2011)

Funders 0

None

BibTeX

@article{Wang_2010, title={On projection methods, convergence and robust formulations in topology optimization}, volume={43}, ISSN={1615-1488}, url={http://dx.doi.org/10.1007/s00158-010-0602-y}, DOI={10.1007/s00158-010-0602-y}, number={6}, journal={Structural and Multidisciplinary Optimization}, publisher={Springer Science and Business Media LLC}, author={Wang, Fengwen and Lazarov, Boyan Stefanov and Sigmund, Ole}, year={2010}, month=dec, pages={767–784} }

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