Correction: On projection methods, convergence and robust formulations in topology optimization (Structural and Multidisciplinary Optimization, (2011), 43, 6, (767-784), 10.1007/s00158-010-0602-y);On projection methods, convergence and robust formulations in topology optimization

Structural and Multidisciplinary Optimization

Volumn 43, Issue 6, 2011, Pages 767-784

  Wang, Fengwen ^a   Lazarov, Boyan Stefanov ^a   Sigmund, Ole ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Compliant mechanisms; Manufacturing constraints; Robust design; Topology optimization

Indexed keywords

MECHANISMS; MESH GENERATION; TOPOLOGY;

FILTERING TECHNIQUE; MANUFACTURABILITY; MANUFACTURING CONSTRAINT; MESH CONVERGENCE; OPTIMIZED DESIGNS; PROJECTION METHOD; ROBUST DESIGNS; ROBUST FORMULATIONS; TOPOLOGY OPTIMISATION; TRANSITION REGIONS;

COMPLIANT MECHANISMS;

EID: 79958124593     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-022-03326-6     Document Type: Erratum

References (31)

1. G Allaire F Jouve AM Toader 2004 Structural optimization using sensitivity analysis and a level-set method J Comput Phys 194 1 363 393 2033390 1136.74368 10.1016/j.jcp.2003.09.032 (Pubitemid 38184245)
2. L Ambrosio G Buttazzo 1993 An optimal design problem with perimeter penalization Calc Var Partial Differ Equ 1 55 69 1261717 0794.49040 10.1007/BF02163264
3. O Amir MP Bendsoe O Sigmund 2009 ) Approximate reanalysis in topology optimization Int J Numer Methods Eng 78 12 1474 1491 2527186 1183.74216 10.1002/nme.2536
4. MP Bendsøe N Kikuchi 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
5. Bendsøe MP, Sigmund O (2004) Topology optimization-theory, methods and applications. Springer, Berlin
6. PI Borel LH Frandsen A Harpøth M Kristensen JS Jensen O Sigmund 2005 Topology optimised broadband photonic crystal Y-splitter Electron Lett 41 2 69 71 10.1049/el:20057717 (Pubitemid 40245850)
7. B Bourdin 2001 Filters in topology optimization Int J Numer Methods Eng 50 9 2143 2158 1818051 0971.74062 10.1002/nme.116 (Pubitemid 32376018)
8. T Bruns D Tortorelli 2001 Topology optimization of non-linear elastic structures and compliant mechanisms Comput Methods Appl Mech Eng 190 26-27 3443 3459 1014.74057 10.1016/S0045-7825(00)00278-4 (Pubitemid 32379192)
9. A Díaz O Sigmund 1995 Checkerboard patterns in layout optimization Struct Multidisc Optim 10 40 45
10. J Guest 2009 Topology optimization with multiple phase projection Comput Methods Appl Mech Eng 199 1-4 123 135 10.1016/j.cma.2009.09.023 2566218 10.1016/j.cma.2009.09.023
11. J Guest J Prevost T Belytschko 2004 Achieving minimum length scale in topology optimization using nodal design variables and projection functions Int J Numer Methods Eng 61 2 238 254 2081218 1079.74599 10.1002/nme.1064 (Pubitemid 39174684)
12. RB Haber CS Jog MP Bendsøe 1996 A new approach to variable-topology shape design using a constraint on the perimeter Struct Optim 11 1 1 11 10.1007/BF01279647
13. JS Jensen O Sigmund 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 (Pubitemid 40889883)
14. CS Jog RB Haber 1996 Stability of finite element models for distributed-parameter optimization and topology design Comput Methods Appl Mech Eng 130 3-4 203 226 1393566 0861.73072 10.1016/0045-7825(95)00928-0 (Pubitemid 126382777)
15. A Kawamoto T Matsumori S Yamasaki T Nomura T Kondoh S Nishiwaki 2010 Heaviside projection based topology optimization by a pde-filtered scalar function Struct Multidisc Optim 10.1007/s00158-010-0562-2 1183.70005
16. Kirsch U (2008) Reanalysis of structures. Springer, Berlin
17. 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
18. 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
19. J Luo Z Luo S Chen L Tong MY Wang 2008 A new level set method for systematic design of hinge-free compliant mechanisms Comput Methods Appl Mech Eng 198 2 318 331 1194.74272
20. TA Poulsen 2003 A new scheme for imposing a minimum length scale in topology optimization Int J Numer Methods Eng 57 6 741 760 1983326 1062.74592 10.1002/nme.694 (Pubitemid 36761881)
21. Ö Sardan DH Petersen K Mølhave O Sigmund P Bøggild 2008 Topology optimized electrothermal polysilicon microgrippers Microelectron Eng 85 1096 1099 10.1016/j.mee.2008.01.049 10.1016/j.mee.2008.01.049
22. O Sigmund 1997 On the design of compliant mechanisms using topology optimization Mech Struct Mach 25 4 493 524 10.1080/08905459708945415 (Pubitemid 127608207)
23. O Sigmund 2007 Morphology-based black and white filters for topology optimization Struct Multidisc Optim 33 4-5 401 424 10.1007/s00158-006-0087-x (Pubitemid 46362319)
24. O Sigmund 2009 Manufacturing tolerant topology optimization Acta Mech Sin 25 2 227 239 10.1007/s10409-009-0240-z 10.1007/s10409-009-0240-z
25. O Sigmund J Petersson 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 (Pubitemid 128647652)
26. R Stainko O Sigmund 2007 Tailoring dispersion properties of photonic crystal waveguides by topology optimization Waves Random Complex Media 17 477 489 2440173 1191.78049 10.1080/17455030701501851 (Pubitemid 350018212)
27. K Svanberg 1987 The method of moving asymptotes-a new method for structural optimization Int J Numer Methods Eng 24 359 373 875307 0602.73091 10.1002/nme.1620240207 (Pubitemid 17525942)
28. Wang F, Jensen J, Sigmund O (2010) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties (submitted)
29. MY Wang X Wang D Guo 2003 A level set method for structural topology optimization Comput Methods Appl Mech Eng 192 1-2 227 246 1083.74573 10.1016/S0045-7825(02)00559-5 (Pubitemid 36080904)
30. S Xu Y Cai G Cheng 2010 Volume preserving nonlinear density filter based on heaviside funtions Struct Multidisc Optim 41 495 505 2601469 10.1007/s00158-009-0452-7
31. GH Yoon O Sigmund 2008 A monolithic approach for topology optimization of electrostatically actuated devices Comput Methods Appl Mech Eng 197 4062 4075 10.1016/j.cma.2008.04.004 2458129 1194.74279 10.1016/j.cma.2008.04.004