Robust topology optimization accounting for misplacement of material

Structural and Multidisciplinary Optimization

Volumn 47, Issue 3, 2013, Pages 317-333

  Jansen, Miche ^a   Lombaert, Geert ^a   Diehl, Moritz ^a   Lazarov, Boyan S ^b   Sigmund, Ole ^b   Schevenels, Mattias ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Geometric imperfections; Random fields; Robust design optimization; Topology optimization

Indexed keywords

GEOMETRIC IMPERFECTION; MINIMUM COMPLIANCE DESIGN; OBJECTIVE FUNCTIONS; RANDOM FIELDS; ROBUST DESIGN OPTIMIZATION; ROBUST OPTIMIZATION; SMALL PERTURBATIONS; STANDARD DEVIATION;

MACHINE DESIGN; MECHANISMS; MONTE CARLO METHODS; OPTIMIZATION; SAMPLING; SHAPE OPTIMIZATION; STRUCTURAL DESIGN;

GEOMETRY;

EID: 84880571060     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-012-0835-z     Document Type: Article

References (42)

1. Abramowitz M, Stegun I (1970) Handbook of mathematical functions, 9th edn. Dover Publications, New York
2. Andreassen E, Clausen A, Schevenels M, Lazarov B, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidisc Optim 43:1-16
3. Asadpoure A, Tootkaboni M, Guest J (2011) Robust topology optimization of structures with uncertainties in stiffness - application to truss structures. Comput Struct 89(11-12):1131-1141
4. Baitsch M, Hartmann D (2006) Optimization of slender structures considering geometrical imperfections. Inverse Probl Sci Eng 14(6):623-637 (Pubitemid 43982858)
5. Ben-Tal A, Nemirovski A (1997) Robust truss topology design via semidefinite programming. SIAM J Optim 7(4):991-1016
6. Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidisc Optim 1:193-202
7. Bendsøe M, Sigmund O (2004) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin
8. Beyer H, Sendhoff B (2007) Robust optimization - a comprehensive survey. Comput Methods Appl Mech Eng 196(33-34):3190-3218 (Pubitemid 46780137)
9. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143-2158 (Pubitemid 32376018)
10. Brittain K, Silva M, Tortorelli D (2011) Minmax topology optimization. Struct Multidisc Optim 45:1-12
11. 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 (Pubitemid 32379192)
12. Chen S, Chen W (2011) A new level-set based approach to shape and topology optimization under geometric uncertainty. Struct Multidisc Optim 44:1-18
13. Chen S, Chen W, Lee S (2010) Level set based robust shape and topology optimization under random field uncertainties. Struct Multidisc Optim 41:507-524
14. Ditlevsen O (1996) Dimension reduction and discretization in stochastic problems by regression method. In: Casciati F, Roberts J (eds) Mathematical models for structural reliability analysis, pp 51-138
15. Eurocode 3 (1994) Design of steel structures. European Commitee for Standardization
16. Ghanem R, Spanos P (1991) Stochastic finite elements: a spectral approach. Springer-Verlag, New York
17. Guest J, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Methods Appl Mech Eng 198(1):116-124
18. 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 (Pubitemid 39174684)
19. Guest J, Asadpoure A, Ha SH (2011) Eliminating beta-continuation from heaviside projection and density filter algorithms. Struct Multidisc Optim 44:443-453
20. Jalalpour M, Igusa T, Guest J (2011) Optimal design of trusses with geometric imperfections: accounting for global instability. Int J Solids Struct 48(21):3011-3019
21. JCSS (1999) JCSS probabilistic model code part 3: resistance models. Joint Comittee on Structural Safety
22. Kogiso N, Ahn W, Nishiwaki S, Izui K, Yoshimura M (2008) Robust topology optimization for compliant mechanisms considering uncertainty of applied loads. J Adv Mech Des Syst Manuf 2(1):96-107
23. Kolanek K, Jendo S (2008) Random field models of geometrically imperfect structures with "clamped" boundary conditions. Probab Eng Mech 23(2-3):219-226
24. Kolmogorov A (1956) Foundations of the theory of probability, 2nd edn. Chelsea Publishing Company, New York
25. Lazarov B, Schevenels M, Sigmund O (2011) Robust design of large-displacement compliant mechanisms. Mech Sci 2(2):175-182
26. Lazarov B, Schevenels M, Sigmund O (2012) Topology optimization using perturbation techniques taking into account geometric uncertainties. Int J Numer Methods Eng 90(11):1321-1336
27. Li C, Der Kiureghian A (1993) Optimal discretization of random fields. J Eng Mech 119(6):1136-1154 (Pubitemid 23670591)
28. Rozvany G, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Multidisc Optim 4:250-252
29. Schevenels M, Lazarov B, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Methods Appl Mech Eng 200(49-52):3613-3627
30. Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493-524 (Pubitemid 127608207)
31. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33(4-5):401-424 (Pubitemid 46362319)
32. Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sin 25:227-239
33. Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidisc Optim 16:68-75 (Pubitemid 128647652)
34. Smolyak S (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Sov Math, Dokl 4:240-243
35. Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964-979 (Pubitemid 351313888)
36. Sudret B, Der Kiureghian A (2000) Stochastic finite element methods and reliability - a state-of-the-art report. Report UCB/SEMM-2000/08, Department of Civil & Environmental Engineering, University of California, Berkeley
37. Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359-373 (Pubitemid 17525942)
38. Tootkaboni M, Asadpoure A, Guest J (2012) Topology optimization of continuum structures under uncertainty - a polynomial chaos approach. Comput Methods Appl Mech Eng 201-204(1):263-275
39. Wang F, Jensen J, Sigmund O (2011a) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. J Opt Soc Am B, Opt Phys 28(3):387-397
40. Wang F, Lazarov B, Sigmund O (2011b) On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim 43:767-784
41. Xiu D, Hesthaven JS (2005) High-order collocation methods for differential equations with random inputs. SIAM J Sci Comput 27(3):1118-1139
42. Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside functions. Struct Multidisc Optim 41:495-505