Stress-based topology optimization for continua

Structural and Multidisciplinary Optimization

Volumn 41, Issue 4, 2010, Pages 605-620

  Le, Chau ^a   Norato, Julian ^b   Bruns, Tyler ^b   Ha, Christopher ^b   Tortorelli, Daniel ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b CATERPILLAR INC   (United States)

Author keywords

Normalization; Regional stress measure; Stress constraints; Topology optimization

Indexed keywords

A-DENSITY; BLACK-AND-WHITE DESIGN; EFFECTIVE ALGORITHMS; ISOTROPIC MATERIALS; LENGTH SCALE; LOCAL STRESS; STRESS CONSTRAINTS; STRESS SINGULARITIES; TOPOLOGY OPTIMIZATION;

STRUCTURAL OPTIMIZATION; TOPOLOGY;

CONSTRAINED OPTIMIZATION;

EID: 77953022690     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-009-0440-y     Document Type: Article

References (42)

1. G Allaire F Jouve H Maillot 2004 Topology optimization for minimum stress design with the homogenization method Struct Multidisc Optim 28 2-3 87 98 2094166
2. Altair Engineering (2007) Optistruct user's guide, version 8.0. Troy, MI, USA
3. MP Bendsøe 1989 Optimal shape design as a material distribution problem Struct Multidisc Optim 1 4 193 202
4. MP Bendsøe O Sigmund 1999 Material interpolation schemes in topology optimization Arch Appl Mech 69 9-10 625 654
5. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin
6. T Borrvall J Petersson 2001 Topology optimization using regularized intermediate density control Comput Methods Appl Mech Eng 190 37-38 4911 4928 1022.74035 10.1016/S0045-7825(00)00356-X 1841915 (Pubitemid 32644220)
7. B Bourdin 2001 Filters in topology optimization Int J Numer Methods Eng 50 8 2143 2158 0971.74062 10.1002/nme.116 1818051 (Pubitemid 32376018)
8. M Bruggi 2008 On an alternative approach to stress constraints relaxation in topology optimization Struct Multidisc Optim 36 2 125 141 10.1007/s00158-007-0203-6 2420819
9. M Bruggi P Venini 2008 A mixed FEM approach to stress-constrained topology optimization Int J Numer Methods Eng 73 11 1693 1714 1159.74397 10.1002/nme.2138 2397968 (Pubitemid 351454760)
10. TE Bruns 2005 A reevaluation of the SIMP method with filtering and an alternative formulation for solid-void topology optimization Struct Multidisc Optim 30 5 428 436 10.1007/s00158-005-0537-x 2216218 (Pubitemid 41720544)
11. TE Bruns DA 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)
12. GD Cheng Z Jiang 1992 Study on topology optimization with stress constraints Eng Optim 20 2 129 148 10.1080/03052159208941276
13. GD Cheng X Guo 1997 Epsilon-relaxed approach in structural topology optimization Struct Multidisc Optim 13 4 258 266
14. A Diaz O Sigmund 2007 Checkerboard patterns in layout optimization Struct Multidisc Optim 10 1 40 45
15. P Duysinx M Bendsøe 1998 Topology optimization of continuum structures with local stress constraints Int J Numer Methods Eng 43 2 1453 1478 0924.73158 10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0. CO;2-2
16. Duysinx P, Sigmund O (1998) New development in handling stress constraints in optimal material distribution. In: Proc. 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization. A collection of technical papers (held in St. Louis, Missouri), vol 3, pp 1501-1509
17. C Fleury V Braibant 1986 Structural optimization: a new dual method using mixed variables Int J Numer Methods Eng 23 3 409 428 0585.73152 10.1002/nme.1620230307 833188
18. JSO Fonseca EL Cardoso 2003 Complexity control in the topology optimization of continuum structures J Braz Soc Mech Sci Eng 25 3 293 301
19. A Friedlander JM Martínez SA Santos 1994 A new trust-region algorithm for bound constrained minimization Appl Math Optim 30 3 235 266 0821.90101 10.1007/BF01183013 1288591
20. Guilherme CEM, Fonseca JSO (2007) Topology optimization of continuum structures with epsilon-relaxed stress constraints. In: Alves M, da Costa Mattos HS (eds) Solid mechanics in Brazil, vol 1. ABCM, Rio de Janeiro, pp 239-250
21. RB Haber CS Jog MP Bendsøe 1996 A new approach to variable-topology shape design using a constraint on perimeter Struct Multidisc Optim 11 1-2 1 12
22. U Kirsch 1990 On singular topologies in optimum structural design Struct Multidisc Optim 2 3 133 142
23. Le C, Norato J, Bruns TE, Ha C, Tortorelli DA (2009) Stress-based topology optimization for continua. In: Proc. 8th world congresses of structural and multidisciplinary optimization. Lisbon, Portugal
24. R Lipton 2002 Design of functionally graded composite structures in the presence of stress constraints Int J Solids Struct 39 8 2575 2586 1032.74020 10.1016/S0020-7683(02)00129-4 1902300 (Pubitemid 34604804)
25. P Michaleris DA Tortorelli CA Vidal 1994 Tangent operators and design sensitivity formulations for transient nonlinear coupled problems with applications to elastoplasticity Int J Numer Methods Eng 37 13 2471 2499 0808.73057 10.1002/nme.1620371408
26. París J, Navarrina F, Colominas I, Casteleiro M (2007) Block aggregation of stress constraints in topology optimization of structures. In: Hernández S, Brebbia CA (eds) Computer aided optimum design of structures X. Myrtle Beach (SC), USA
27. J París F Navarrina I Colominas M Casteleiro 2009 Topology optimization of continuum structures with local and global stress constraints Struct Multidisc Optim 39 4 419 437 10.1007/s00158-008-0336-2
28. JT Pereira EA Fancello CS Barcellos 2004 Topology optimization of continuum structures with material failure constraints Struct Multidisc Optim 26 1-2 50 66 10.1007/s00158-003-0301-z 2034185
29. S Rahmatalla CC Swan 2004 Continuum topology optimization of buckling-sensitive structures Struct Multidisc Optim 27 1-2 130 135 10.1007/s00158-003-0365-9
30. GIN Rozvany 2001 On design-dependent constraints and singular topologies Struct Multidisc Optim 21 2 164 172 10.1007/s001580050181 (Pubitemid 32535052)
31. GIN Rozvany T Birker 1994 On singular topologies in exact layout optimization Struct Multidisc Optim 8 4 228 235
32. GIN Rozvany J Sobieszczanski-Sobieski 1992 New optimality criteria methods: forcing uniqueness of the adjoint strains by corner-rounding at constraint intersections Struct Multidisc Optim 4 3-4 244 246
33. GIN Rozvany M Zhou T Birker 1992 Generalized shape optimization without homogenization Struct Multidisc Optim 4 3-4 250 252
34. O Sigmund 1997 On the design of compliant mechanisms using topology optimization Mechan Struct Mach 25 4 493 524 10.1080/08905459708945415
35. 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)
36. O Sigmund J Petersson 1998 Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima Struct Multidisc Optim 16 1 68 75
37. FV Stump ECN Silva GH Paulino 2007 Optimization of material distribution in functionally graded structures with stress constraints Commun Numer Methods Eng 23 5 535 551 1114.74046 10.1002/cnm.910 2329353 (Pubitemid 46916577)
38. K Svanberg 1987 The method of moving asymptotes-a new method for structural optimization Int J Numer Methods Eng 24 2 359 373 0602.73091 10.1002/nme.1620240207 875307
39. K Svanberg M Werme 2007 Sequential integer programming methods for stress constrained topology optimization Struct Multidisc Optim 34 4 277 299 10.1007/s00158-007-0118-2 2348164 (Pubitemid 47325964)
40. RJ Yang CJ Chen 1996 Stress-based topology optimization Struct Multidisc Optim 12 2 98 105
41. M Zhou GIN Rozvany 1991 The COC algorithm, part II: topological, geometrical and generalized shape optimization Comput Methods Appl Mech Eng 89 1-3 209 336
42. M Zhou YK Shyy HL Thomas 2001 Checkerboard and minimum member size control in topology optimization Struct Multidisc Optim 21 152 158 10.1007/s001580050179 (Pubitemid 32535050)