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Erschienen in: Structural and Multidisciplinary Optimization 5/2017

03.10.2016 | RESEARCH PAPER

A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function \(\boldsymbol {H}_{\infty }\)-norm

verfasst von: Paolo Venini, Marco Pingaro

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 5/2017

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Abstract

A new approach to structural optimization in dynamic regime is presented that is based on the minimization of the \(H_{\infty }\) norm of the transfer function between the external loads and the structural response. The method is successfully applied to the sizing optimization of viscoelastic beams as shown by extensive numerical investigations that are presented in much detail. The abstract nature of the proposed approach makes it applicable to a wide class of dynamical systems including 2D and 3D systems within general topology optimization frameworks that are object of ongoing analysis.

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Literatur
Zurück zum Zitat Bendsoe M, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654MATH Bendsoe M, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654MATH
Zurück zum Zitat Bendsoe M, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinMATH Bendsoe M, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinMATH
Zurück zum Zitat Boyd S, Balakrishnan V, Kabamb P (1989) A bisection method for computing the h\(_{\infty }\) norm of a transfer matrix and related problems. Math Control Signals Syst (MCSS) 2(3):207–219MathSciNetCrossRef Boyd S, Balakrishnan V, Kabamb P (1989) A bisection method for computing the h\(_{\infty }\) norm of a transfer matrix and related problems. Math Control Signals Syst (MCSS) 2(3):207–219MathSciNetCrossRef
Zurück zum Zitat Bruisma N, Steinbuch M (1990) A fast algorithm to compute the \(H_{\infty }\)-norm of a transfer function matrix. Syst Control Lett 14:287–293MathSciNetCrossRef Bruisma N, Steinbuch M (1990) A fast algorithm to compute the \(H_{\infty }\)-norm of a transfer function matrix. Syst Control Lett 14:287–293MathSciNetCrossRef
Zurück zum Zitat Dahl J, Jensen JS, Sigmund O (2008) Topology optimization of transient wave propagation problems in one dimension. Struct Multidiscip Optim 36:585–595MathSciNetCrossRefMATH Dahl J, Jensen JS, Sigmund O (2008) Topology optimization of transient wave propagation problems in one dimension. Struct Multidiscip Optim 36:585–595MathSciNetCrossRefMATH
Zurück zum Zitat DenHartog J (1934) Mechanical vibrations. McGraw-Hill, New York DenHartog J (1934) Mechanical vibrations. McGraw-Hill, New York
Zurück zum Zitat Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim 34:91–110MathSciNetCrossRefMATH Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim 34:91–110MathSciNetCrossRefMATH
Zurück zum Zitat Filipov ET, Chun J, Paulino GH (2015) Polygonal multiresolution topology optimization (polymtop) for structural dynamics. Struct Multidiscip Optim. doi:10.1007/s00158-015-1309-x Filipov ET, Chun J, Paulino GH (2015) Polygonal multiresolution topology optimization (polymtop) for structural dynamics. Struct Multidiscip Optim. doi:10.​1007/​s00158-015-1309-x
Zurück zum Zitat Francis B (1987) A course in \(H_{\infty }\) control theory, Lecture notes in control and information sciences, vol 88. Springer-Verlag, Berlin, Heidelberg Francis B (1987) A course in \(H_{\infty }\) control theory, Lecture notes in control and information sciences, vol 88. Springer-Verlag, Berlin, Heidelberg
Zurück zum Zitat García-Barruetabeña J, Cortés F, Abete J, Fernández P, Lamela M, Fernández-Cantel A (2013) Relaxation modulus-complex modulus interconversion for linear viscoelastic materials. Mech Time-Depend Mater:465–479 García-Barruetabeña J, Cortés F, Abete J, Fernández P, Lamela M, Fernández-Cantel A (2013) Relaxation modulus-complex modulus interconversion for linear viscoelastic materials. Mech Time-Depend Mater:465–479
Zurück zum Zitat Giesy DP, Lim KB (1993) H\(_{\infty }\) norm sensitivity formula with control system design applications. J Guid Control Dyn 16(6):1138–1145CrossRefMATH Giesy DP, Lim KB (1993) H\(_{\infty }\) norm sensitivity formula with control system design applications. J Guid Control Dyn 16(6):1138–1145CrossRefMATH
Zurück zum Zitat Guglielmi N, Gurbuzabaln M, Overton M (2013) Fast approximation of the \(H_{\infty }\) norm via optimization over spectral value sets. SIAM J Matrix Anal Appl 34(2):709–737MathSciNetCrossRefMATH Guglielmi N, Gurbuzabaln M, Overton M (2013) Fast approximation of the \(H_{\infty }\) norm via optimization over spectral value sets. SIAM J Matrix Anal Appl 34(2):709–737MathSciNetCrossRefMATH
Zurück zum Zitat Jensen JS (2007) Topology optimization of dynamics problems with padé approximants. Int J Numer Methods Eng 72:1605–1630CrossRefMATH Jensen JS (2007) Topology optimization of dynamics problems with padé approximants. Int J Numer Methods Eng 72:1605–1630CrossRefMATH
Zurück zum Zitat Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef
Zurück zum Zitat Jung J, Hyun J, Goo S, Wang S (2015) An efficient design sensitivity analysis using element energies for topology optimization of a frequency response problem. Comput Methods Appl Mech Eng 296:196–2010MathSciNetCrossRef Jung J, Hyun J, Goo S, Wang S (2015) An efficient design sensitivity analysis using element energies for topology optimization of a frequency response problem. Comput Methods Appl Mech Eng 296:196–2010MathSciNetCrossRef
Zurück zum Zitat Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management. J Mech Phys Solids 60:351–378MathSciNetCrossRefMATH Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management. J Mech Phys Solids 60:351–378MathSciNetCrossRefMATH
Zurück zum Zitat Lee HA, Park GJ (2015) Nonlinear dynamic response topology optimization using the equivalent static loads method. Comput Methods Appl Mech Eng 283:956–970MathSciNetCrossRef Lee HA, Park GJ (2015) Nonlinear dynamic response topology optimization using the equivalent static loads method. Comput Methods Appl Mech Eng 283:956–970MathSciNetCrossRef
Zurück zum Zitat The Mathworks Inc. (2015) Natick, Massachusetts: MATLAB version 8.5.0.197613 (R2015a) The Mathworks Inc. (2015) Natick, Massachusetts: MATLAB version 8.5.0.197613 (R2015a)
Zurück zum Zitat Min S, Kikuchi N, Park YC, Kim S, S C (1999) Optimal topology design of structures under dynamic loads. Struct Multidiscip Optim 17:208–218 Min S, Kikuchi N, Park YC, Kim S, S C (1999) Optimal topology design of structures under dynamic loads. Struct Multidiscip Optim 17:208–218
Zurück zum Zitat Olhoff N (1989) Multicriterion structural optimization via bound formulation and mathematical programming. Struct Optim 1:11–17CrossRef Olhoff N (1989) Multicriterion structural optimization via bound formulation and mathematical programming. Struct Optim 1:11–17CrossRef
Zurück zum Zitat Olhoff N, Du J (2014) Topological design of continuum structures subjected to forced vibration. In: Topology optimization in structural and continuum mechanics. Springer, pp 325–339 Olhoff N, Du J (2014) Topological design of continuum structures subjected to forced vibration. In: Topology optimization in structural and continuum mechanics. Springer, pp 325–339
Zurück zum Zitat Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49:3158–3169CrossRef Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49:3158–3169CrossRef
Zurück zum Zitat Pingaro M, Venini P (2016) A fast approach to analysis and optimization of viscoelastic beams. Comput Struct 168:46–55CrossRef Pingaro M, Venini P (2016) A fast approach to analysis and optimization of viscoelastic beams. Comput Struct 168:46–55CrossRef
Zurück zum Zitat Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Optim 8(4):207– 227CrossRef Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Optim 8(4):207– 227CrossRef
Zurück zum Zitat Shu L, Wang MY, Fang Z, Ma Z, Wei P (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330(24):5820–5834CrossRef Shu L, Wang MY, Fang Z, Ma Z, Wei P (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330(24):5820–5834CrossRef
Zurück zum Zitat Skogestad S, Postlethwaite I (1996) Multivariable feedback control - analysis and design. Wiley, ChichesterMATH Skogestad S, Postlethwaite I (1996) Multivariable feedback control - analysis and design. Wiley, ChichesterMATH
Zurück zum Zitat Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefMATH Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefMATH
Zurück zum Zitat Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199(25):1744–1763MathSciNetCrossRefMATH Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199(25):1744–1763MathSciNetCrossRefMATH
Zurück zum Zitat Yu Y, Jang IG, M KB (2013) Topology optimization for a frequency response and its application to a violin bridge. Struct Multidisc Optim 48(3):627–636MathSciNetCrossRef Yu Y, Jang IG, M KB (2013) Topology optimization for a frequency response and its application to a violin bridge. Struct Multidisc Optim 48(3):627–636MathSciNetCrossRef
Metadaten
Titel
A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function -norm
verfasst von
Paolo Venini
Marco Pingaro
Publikationsdatum
03.10.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 5/2017
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-016-1600-5

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