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Erschienen in: Structural and Multidisciplinary Optimization 4/2016

20.11.2015 | RESEARCH PAPER

An efficient approach to reliability-based topology optimization for continua under material uncertainty

verfasst von: Mehdi Jalalpour, Mazdak Tootkaboni

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2016

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Abstract

This contribution presents a computationally efficient method for reliability-based topology optimization for continuum domains under material properties uncertainty. Material Young’s modulus is assumed to be lognormally distributed and correlated within the domain. The computational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribution that follows the empirical distribution of the response, and employing an efficient gradient-based optimizer. Two widely-studied topology optimization problems are examined and the changes in the optimized topology is discussed for various levels of target reliability and correlation strength. Accuracy of the proposed algorithm is verified using Monte Carlo simulation.

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Literatur
Zurück zum Zitat Agarwal H (2004) Reliability based design optimization: formulations and methodologies. PhD thesis Agarwal H (2004) Reliability based design optimization: formulations and methodologies. PhD thesis
Zurück zum Zitat Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidiscip Optim 33(3):217–227CrossRef Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidiscip Optim 33(3):217–227CrossRef
Zurück zum Zitat Agarwal H, Renaud J (2004) Reliability based design optimization using response surfaces in application to multidisciplinary systems. Eng Optim 36(3):291–311CrossRef Agarwal H, Renaud J (2004) Reliability based design optimization using response surfaces in application to multidisciplinary systems. Eng Optim 36(3):291–311CrossRef
Zurück zum Zitat Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidiscip Optim 43(1):1–16CrossRefMATH Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidiscip Optim 43(1):1–16CrossRefMATH
Zurück zum Zitat Asadpoure A, Guest J, Igusa T (2010) Structural topology optimization considering correlated uncertainties in elastic modulus. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference Asadpoure A, Guest J, Igusa T (2010) Structural topology optimization considering correlated uncertainties in elastic modulus. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Zurück zum Zitat 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 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
Zurück zum Zitat Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86(19):1904–1917CrossRef Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86(19):1904–1917CrossRef
Zurück zum Zitat Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRef Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRef
Zurück zum Zitat Bendsoe MP, Sigmund O (2004) Topology optimization: theory, methods and applications. Springer Bendsoe MP, Sigmund O (2004) Topology optimization: theory, methods and applications. Springer
Zurück zum Zitat Chen S, Chen W, Lee S (2010) Level set based robust shape and topology optimization under random field uncertainties. Struct Multidiscip Optim 41(4):507–524MathSciNetCrossRefMATH Chen S, Chen W, Lee S (2010) Level set based robust shape and topology optimization under random field uncertainties. Struct Multidiscip Optim 41(4):507–524MathSciNetCrossRefMATH
Zurück zum Zitat Chen X, Hasselman T K, Neill DJ (1997) Reliability based structural design optimization for practical applications. In: Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp 2724–2732 Chen X, Hasselman T K, Neill DJ (1997) Reliability based structural design optimization for practical applications. In: Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp 2724–2732
Zurück zum Zitat Der Kiureghian A, Lin H, Hwang S (1987) Second-order reliability approximations. J Eng Mech 113 (8):1208–1225CrossRef Der Kiureghian A, Lin H, Hwang S (1987) Second-order reliability approximations. J Eng Mech 113 (8):1208–1225CrossRef
Zurück zum Zitat Ditlevsen O (1979) Generalized second moment reliability index. J Struct Mech 7(4):435–451CrossRef Ditlevsen O (1979) Generalized second moment reliability index. J Struct Mech 7(4):435–451CrossRef
Zurück zum Zitat Ditlevsen O, Madsen HO (1996) Structural reliability methods, vol 178. Wiley, New York Ditlevsen O, Madsen HO (1996) Structural reliability methods, vol 178. Wiley, New York
Zurück zum Zitat Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15 (3):169–196CrossRef Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15 (3):169–196CrossRef
Zurück zum Zitat Guest J, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Meth Appl Mech Eng 198(1):116–124MathSciNetCrossRefMATH Guest J, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Meth Appl Mech Eng 198(1):116–124MathSciNetCrossRefMATH
Zurück zum Zitat Guest JK, Asadpoure A, Ha SH (2011) Eliminating beta-continuation from heaviside projection and density filter algorithms. Struct Multidiscip Optim 44(4):443–453MathSciNetCrossRefMATH Guest JK, Asadpoure A, Ha SH (2011) Eliminating beta-continuation from heaviside projection and density filter algorithms. Struct Multidiscip Optim 44(4):443–453MathSciNetCrossRefMATH
Zurück zum Zitat Guest JK, Prévost JH, 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– 254MathSciNetCrossRefMATH Guest JK, Prévost JH, 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– 254MathSciNetCrossRefMATH
Zurück zum Zitat Hisada T, Nakagiri S (1981) Stochastic finite element method developed for structural safety and reliability. In: Proceedings of the 3rd international conference on structural safety and reliability, pp 395–408 Hisada T, Nakagiri S (1981) Stochastic finite element method developed for structural safety and reliability. In: Proceedings of the 3rd international conference on structural safety and reliability, pp 395–408
Zurück zum Zitat Jalalpour M, Guest JK, Igusa T (2013) Reliability-based topology optimization of trusses with stochastic stiffness. Struct Saf 43(0):41–49CrossRef Jalalpour M, Guest JK, Igusa T (2013) Reliability-based topology optimization of trusses with stochastic stiffness. Struct Saf 43(0):41–49CrossRef
Zurück zum Zitat Jalalpour M, Igusa T, Guest J (2011) Optimal design of trusses with geometric imperfections: Accounting for global instability. Int J Solids Struct 48(21):3011–3019CrossRef Jalalpour M, Igusa T, Guest J (2011) Optimal design of trusses with geometric imperfections: Accounting for global instability. Int J Solids Struct 48(21):3011–3019CrossRef
Zurück zum Zitat Jang G-W, Dijk NP, Keulen F (2012) Topology optimization of mems considering etching uncertainties using the level-set method. Int J Numer Methods Eng 92(6):571–588MathSciNetCrossRef Jang G-W, Dijk NP, Keulen F (2012) Topology optimization of mems considering etching uncertainties using the level-set method. Int J Numer Methods Eng 92(6):571–588MathSciNetCrossRef
Zurück zum Zitat Jansen M, Lombaert G, Diehl M, Lazarov BS, Sigmund O, Schevenels M (2013) Robust topology optimization accounting for misplacement of material. Struct Multidiscip Optim 47(3):317–333MathSciNetCrossRefMATH Jansen M, Lombaert G, Diehl M, Lazarov BS, Sigmund O, Schevenels M (2013) Robust topology optimization accounting for misplacement of material. Struct Multidiscip Optim 47(3):317–333MathSciNetCrossRefMATH
Zurück zum Zitat Jung H-S, Cho S (2004) Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties. Finite Elem Anal Des 41(3):311–331MathSciNetCrossRef Jung H-S, Cho S (2004) Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties. Finite Elem Anal Des 41(3):311–331MathSciNetCrossRef
Zurück zum Zitat Kang J, Kim C, Wang S (2004) Reliability-based topology optimization for electromagnetic systems. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 23 (3):715–723MathSciNetCrossRefMATH Kang J, Kim C, Wang S (2004) Reliability-based topology optimization for electromagnetic systems. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 23 (3):715–723MathSciNetCrossRefMATH
Zurück zum Zitat Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidiscip Optim 24(3):233–245CrossRef Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidiscip Optim 24(3):233–245CrossRef
Zurück zum Zitat Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscip Optim 26(5):295–307CrossRef Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscip Optim 26(5):295–307CrossRef
Zurück zum Zitat Kim C, Choi KK (2008) Reliability-based design optimization using response surface method with prediction interval estimation. Journal of Mechanical Design 130(12):121401CrossRef Kim C, Choi KK (2008) Reliability-based design optimization using response surface method with prediction interval estimation. Journal of Mechanical Design 130(12):121401CrossRef
Zurück zum Zitat Kleiber M, Hien TD (1992) The stochastic finite element method: basic perturbation technique and computer implementation. Wiley, New YorkMATH Kleiber M, Hien TD (1992) The stochastic finite element method: basic perturbation technique and computer implementation. Wiley, New YorkMATH
Zurück zum Zitat Kogiso N, Hirano Y, Nishiwaki S, Izui K, Yoshimura M, Min S (2010) Reliability-based topology optimization of frame structures for multiple criteria using slsv method. Journal of Computational Science and Technology 4:172–184CrossRef Kogiso N, Hirano Y, Nishiwaki S, Izui K, Yoshimura M, Min S (2010) Reliability-based topology optimization of frame structures for multiple criteria using slsv method. Journal of Computational Science and Technology 4:172–184CrossRef
Zurück zum Zitat Kuschel N, Rackwitz R (2000) A new approach for structural optimization of series systems. Applications of Statistics and Probability 2(8):987–994MATH Kuschel N, Rackwitz R (2000) A new approach for structural optimization of series systems. Applications of Statistics and Probability 2(8):987–994MATH
Zurück zum Zitat Lazarov BS, Schevenels M, Sigmund O (2012a) Topology optimization considering material and geometric uncertainties using stochastic collocation methods. Struct Multidiscip Optim 46(4): 597–612MathSciNetCrossRefMATH Lazarov BS, Schevenels M, Sigmund O (2012a) Topology optimization considering material and geometric uncertainties using stochastic collocation methods. Struct Multidiscip Optim 46(4): 597–612MathSciNetCrossRefMATH
Zurück zum Zitat Lazarov BS, Schevenels M, Sigmund O (2012b) Topology optimization with geometric uncertainties by perturbation techniques. Int J Numer Methods Eng 90(11):1321–1336CrossRefMATH Lazarov BS, Schevenels M, Sigmund O (2012b) Topology optimization with geometric uncertainties by perturbation techniques. Int J Numer Methods Eng 90(11):1321–1336CrossRefMATH
Zurück zum Zitat Liang J, Mourelatos ZP, Tu J (2004) A single-loop method for reliability-based design optimization. In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp 419–430. American Society of Mechanical Engineers Liang J, Mourelatos ZP, Tu J (2004) A single-loop method for reliability-based design optimization. In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp 419–430. American Society of Mechanical Engineers
Zurück zum Zitat Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probabilistic Engineering Mechanics 1(2):105–112CrossRef Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probabilistic Engineering Mechanics 1(2):105–112CrossRef
Zurück zum Zitat Liu WK, Belytschko T, Mani A (1986) Probabilistic finite elements for nonlinear structural dynamics. Comput Methods Appl Mech Eng 56(1):61–81CrossRefMATH Liu WK, Belytschko T, Mani A (1986) Probabilistic finite elements for nonlinear structural dynamics. Comput Methods Appl Mech Eng 56(1):61–81CrossRefMATH
Zurück zum Zitat Maute K (2014) Topology optimization under uncertainty. In: Topology Optimization in Structural and Continuum Mechanics, pp 457–471. Springer Maute K (2014) Topology optimization under uncertainty. In: Topology Optimization in Structural and Continuum Mechanics, pp 457–471. Springer
Zurück zum Zitat Maute K, Frangopol DM (2003) Reliability-based design of mems mechanisms by topology optimization. Comput Struct 81(8-11):813–824. K.J Bathe 60th Anniversary IssueCrossRef Maute K, Frangopol DM (2003) Reliability-based design of mems mechanisms by topology optimization. Comput Struct 81(8-11):813–824. K.J Bathe 60th Anniversary IssueCrossRef
Zurück zum Zitat Mlejnek H (1992) Some aspects of the genesis of structures. Structural Optimization 5(1-2):64–69CrossRef Mlejnek H (1992) Some aspects of the genesis of structures. Structural Optimization 5(1-2):64–69CrossRef
Zurück zum Zitat Mogami K, Nishiwaki S, Izui K, Yoshimura M, Kogiso N (2006) Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques. Struct Multi Optim 32:299–311CrossRef Mogami K, Nishiwaki S, Izui K, Yoshimura M, Kogiso N (2006) Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques. Struct Multi Optim 32:299–311CrossRef
Zurück zum Zitat Nguyen TH, Song J, Paulino GH (2011) Single-loop system reliability-based topology optimization considering statistical dependence between limit-states. Struct Multi Optim 44(5):593–611MathSciNetCrossRefMATH Nguyen TH, Song J, Paulino GH (2011) Single-loop system reliability-based topology optimization considering statistical dependence between limit-states. Struct Multi Optim 44(5):593–611MathSciNetCrossRefMATH
Zurück zum Zitat Patel J, Choi S-K (2012) Classification approach for reliability-based topology optimization using probabilistic neural networks. Struct Multi Optim 45(4):529–543MathSciNetCrossRefMATH Patel J, Choi S-K (2012) Classification approach for reliability-based topology optimization using probabilistic neural networks. Struct Multi Optim 45(4):529–543MathSciNetCrossRefMATH
Zurück zum Zitat Rackwitz R (2001) Reliability analysisa review and some perspectives. Struct Saf 23(4):365–395CrossRef Rackwitz R (2001) Reliability analysisa review and some perspectives. Struct Saf 23(4):365–395CrossRef
Zurück zum Zitat Rackwitz R, Flessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):489–494CrossRefMATH Rackwitz R, Flessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):489–494CrossRefMATH
Zurück zum Zitat Rozvany GI, Maute K (2011) Analytical and numerical solutions for a reliability-based benchmark example. Struct Multidiscip Optim 43(6):745–753CrossRefMATH Rozvany GI, Maute K (2011) Analytical and numerical solutions for a reliability-based benchmark example. Struct Multidiscip Optim 43(6):745–753CrossRefMATH
Zurück zum Zitat Schevenels M, Lazarov BS, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Meth Appl Mech Eng 200:3613–3627CrossRefMATH Schevenels M, Lazarov BS, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Meth Appl Mech Eng 200:3613–3627CrossRefMATH
Zurück zum Zitat Schuëller G, Jensen H (2008) Computational methods in optimization considering uncertainties- an overview. Comput Meth Appl Mech Eng 198(1):2–13CrossRefMATH Schuëller G, Jensen H (2008) Computational methods in optimization considering uncertainties- an overview. Comput Meth Appl Mech Eng 198(1):2–13CrossRefMATH
Zurück zum Zitat Schuëller G, Pradlwarter H, Koutsourelakis P (2004) A critical appraisal of reliability estimation procedures for high dimensions. Probab Eng Mech 19(4):463–474CrossRef Schuëller G, Pradlwarter H, Koutsourelakis P (2004) A critical appraisal of reliability estimation procedures for high dimensions. Probab Eng Mech 19(4):463–474CrossRef
Zurück zum Zitat Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multi Optim 33(4-5):401–424CrossRef Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multi Optim 33(4-5):401–424CrossRef
Zurück zum Zitat Sigmund O (2011) On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim 43(5):589–596MathSciNetCrossRefMATH Sigmund O (2011) On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim 43(5):589–596MathSciNetCrossRefMATH
Zurück zum Zitat Silva M, Tortorelli D, Norato J, Ha C, Bae H-R (2010) Component and system reliability-based topology optimization using a single-loop method. Struct Multi Optim 41:87–106MathSciNetCrossRefMATH Silva M, Tortorelli D, Norato J, Ha C, Bae H-R (2010) Component and system reliability-based topology optimization using a single-loop method. Struct Multi Optim 41:87–106MathSciNetCrossRefMATH
Zurück zum Zitat Svanberg K (1987) The method of moving asymptotesa new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH Svanberg K (1987) The method of moving asymptotesa new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH
Zurück zum Zitat Taflanidis A, Beck J (2008) Stochastic subset optimization for optimal reliability problems. Probabilistic Engineering Mechanics 23(2):324–338CrossRef Taflanidis A, Beck J (2008) Stochastic subset optimization for optimal reliability problems. Probabilistic Engineering Mechanics 23(2):324–338CrossRef
Zurück zum Zitat Tootkaboni M, Asadpoure A, Guest JK (2012) Topology optimization of continuum structures under uncertainty : A polynomial chaos approach. Comput Meth Appl Mech Eng 201:204(0):263– 275MathSciNetCrossRefMATH Tootkaboni M, Asadpoure A, Guest JK (2012) Topology optimization of continuum structures under uncertainty : A polynomial chaos approach. Comput Meth Appl Mech Eng 201:204(0):263– 275MathSciNetCrossRefMATH
Zurück zum Zitat Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564CrossRef Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564CrossRef
Zurück zum Zitat Valdebenito MA, Schuëller GI (2010) A survey on approaches for reliability-based optimization. Struct Multidiscip Optim 42(5): 645–663MathSciNetCrossRefMATH Valdebenito MA, Schuëller GI (2010) A survey on approaches for reliability-based optimization. Struct Multidiscip Optim 42(5): 645–663MathSciNetCrossRefMATH
Zurück zum Zitat Valdebenito MA, Schuëller GI (2011) Efficient strategies for reliability-based optimization involving non-linear, dynamical structures. Comput Struct 89(19):1797–1811CrossRef Valdebenito MA, Schuëller GI (2011) Efficient strategies for reliability-based optimization involving non-linear, dynamical structures. Comput Struct 89(19):1797–1811CrossRef
Zurück zum Zitat Wang S, Moon H, Kim C, Kang J, Choi KK (2006) Reliability-based topology optimization (rbto). In IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, pp 493–504. Springer Wang S, Moon H, Kim C, Kang J, Choi KK (2006) Reliability-based topology optimization (rbto). In IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, pp 493–504. Springer
Zurück zum Zitat Xu L, Cheng G (2003) Discussion on: moment methods for structural reliability. Struct Saf 25(2):193–199CrossRef Xu L, Cheng G (2003) Discussion on: moment methods for structural reliability. Struct Saf 25(2):193–199CrossRef
Zurück zum Zitat Youn BD, Choi KK (2004) A new response surface methodology for reliability-based design optimization. Comput Struct 82(2):241–256CrossRef Youn BD, Choi KK (2004) A new response surface methodology for reliability-based design optimization. Comput Struct 82(2):241–256CrossRef
Zurück zum Zitat Zhao Q, Chen X, Lin Y (2013) Reliability-based topology optimization of control arm of suspension for lightweight design. In: Proceedings of the FISITA 2012 World Automotive Congress, pp 1129–1138. Springer Zhao Q, Chen X, Lin Y (2013) Reliability-based topology optimization of control arm of suspension for lightweight design. In: Proceedings of the FISITA 2012 World Automotive Congress, pp 1129–1138. Springer
Zurück zum Zitat Zhao Y-G, Ono T (2001) Moment methods for structural reliability. Struct Saf 23(1):47–75CrossRef Zhao Y-G, Ono T (2001) Moment methods for structural reliability. Struct Saf 23(1):47–75CrossRef
Zurück zum Zitat Zhou M, Rozvany G (1991) The COC algorithm, part ii: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1):309–336CrossRef Zhou M, Rozvany G (1991) The COC algorithm, part ii: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1):309–336CrossRef
Metadaten
Titel
An efficient approach to reliability-based topology optimization for continua under material uncertainty
verfasst von
Mehdi Jalalpour
Mazdak Tootkaboni
Publikationsdatum
20.11.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 4/2016
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-015-1360-7

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