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Structural and Multidisciplinary Optimization
Erschienen in: Structural and Multidisciplinary Optimization 4/2012

01.10.2012 | Research Paper

Topology optimization considering material and geometric uncertainties using stochastic collocation methods

verfasst von: Boyan S. Lazarov, Mattias Schevenels, Ole Sigmund

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2012

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Abstract

The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties. The random variations are modeled by a memory-less transformation of spatially varying Gaussian random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is discussed in details and solutions to decrease it, like sparse grids and discretization refinement are proposed and demonstrated as well. The method is utilized in the design of compliant mechanisms.
Vorheriger Artikel Enhanced analysis of design sensitivities in topology optimization
Nächster Artikel Hydroelastic optimization of a keel fin of a sailing boat: a multidisciplinary robust formulation for ship design

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Fußnoten
1
Figures 12, 20 and 21 in Wang et al. (2011) show the normalized length scale as a function of the projection threshold η, In these figures the vertical axis is erroneously labeled as b/2R. The correct label is b/R, where b is the length scale and R is the filter radius.
 
Literatur
Asadpoure A, Tootkaboni M, Guest JK (2011) Robust topology optimization of structures with uncertainties in stiffness—application to truss structures. Comput Struct 89(11–12):1131–1141CrossRef
Bendsøe MP, Sigmund O (2004) Topology optimization—theory, methods and applications. Springer, BerlinMATH
Beyer HG, Sendhoff B (2007) Robust optimization—a comprehensive survey. Comput Methods Appl Mech Eng 196(33–34):3190–3218MathSciNetMATHCrossRef
Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190:3443–3459MATHCrossRef
Chen S, Chen W (2011) A new level-set based approach to shape and topology optimization under geometric uncertainty. Struct Multidisc Optim 44:1–18CrossRef
Chen S, Chen W, Lee S (2010) Level set based robust shape and topology optimization under random field uncertainties. Structural and Multidisciplinary Optimization 41:507–524MathSciNetCrossRef
Ditlevsen O (1996) Dimension reduction and discretization in stochastic problems by regression method. In: Casciati F, Roberts B (eds) Mathematical models for structural reliability analysis. CRS Press, Boca Raton
Elesin Y, Lazarov B, Jensen J, Sigmund O (2012) Design of robust and efficient photonic switches using topology optimization. Photonics Nanostruct Fundam Appl 10(1):153–165CrossRef
Field Jr R, Grigoriu M (2009) Model selection for a class of stochastic processes or random fields with bounded range. Probab Eng Mech 24(3):331–342CrossRef
Ghanem R, Spanos P (2003) Stochastic finite elements—a spectral approach. Dover, New York
Grigoriu M (1998) Simulation of stationary non-Gaussian translation processes. J Eng Mech - ASCE 124(2):121–126CrossRef
Guest J, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Methods Appl Mech Eng 198(1):116–124MathSciNetMATHCrossRef
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):238–254MathSciNetMATHCrossRef
Karhunen K (1947) Über lineare methoden in der wahrscheinlichkeitsrechnung. Amer Acad Sci, Fennicade, Ser A 37:3–79
Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2011) Heaviside projection based topology optimization by a pde-filtered scalar function. Struct Multidisc Optim 44(1):19–24CrossRef
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
Lazarov BS, Sigmund O (2011) Filters in topology optimizat ion based on Helmholtz type differential equations. Int J Numer Methods Eng 86(6):765–781MathSciNetMATHCrossRef
Lazarov BS, Schevenels M, Sigmund O (2011) Robust design of large-displacement compliant mechanisms. Mech Sci 2(2):175–182CrossRef
Lazarov BS, Schevenels M, Sigmund O (2012) Topology optimization with geometric uncertainties by perturbation techniques. Int J Numer Methods Eng (in print). doi:10.​1002/​nme.​3361
Li CC, Kiureghian AD (1993) Optimal discretization of random fields. J Eng Mech - ASCE 119:1136–1154CrossRef
Loève M (1955) Probability theory. Van Nostrand, PrincetonMATH
Logo J, Ghaemi M, Rad M (2009) Optimal topologies in case of probabilistic loading: the influence of load correlation. Mech Based Des Struct Mach 37(3):327–348CrossRef
Maitre OPL, Knio OM (2010) Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer, BerlinMATHCrossRef
Schevenels M, Lazarov B, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Methods Appl Mech Eng 200(49–52):3613–3627MATHCrossRef
Schueller GI, Jensen HA (2008) Computational methods im optimization considering uncertainties—an overview. Comput Methods Appl Mech Eng 198:2–13MathSciNetMATHCrossRef
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25:493–524CrossRef
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424CrossRef
Smolyak S (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl Akad Nauk USSR 4:240–243
Stefanou G (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198(9–12):1031–1051MATHCrossRef
Sudret B, Der Kiureghian A (2000) Stochastic finite elements and reliability—a state-of-the-art report report n ucb/semm-2000/08. Tech. rep., University of California, Berkeley
Tsompanakis Y, Lagaros ND, Papadrakakis M (eds) (2008) Structural design optimization considering uncertainties, structures & infrastructures series, vol 1. Taylor & Francis, New York
Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim 43(6):767–784CrossRef
Xiu D (2007) Efficient collocational approach for parametric uncertainty analysis. Commun Comput Phys 2:293–309MathSciNetMATH
Xiu D (2010) Numerical methods for stochastic computations: a spectral method approach. Princeton University Press, PrincetonMATH
Xiu D, Hesthaven JS (2005) High-order collocation methods for differential equations with random inputs. SIAM J Sci Comput 27(3):1118–1139MathSciNetMATHCrossRef
Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside functions. Struct Multidisc Optim 41:1615–1488MathSciNet
Zhang J, Ellingwood B (1994) Orthogonal series expansions of random fields in first-order reliability analysis. J Eng Mech - ASCE 120(12):2660–2677CrossRef
Metadaten
Titel
Topology optimization considering material and geometric uncertainties using stochastic collocation methods
verfasst von
Boyan S. Lazarov
Mattias Schevenels
Ole Sigmund
Publikationsdatum
01.10.2012
Verlag
Springer-Verlag
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 4/2012
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-012-0791-7

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