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Erschienen in: Meccanica 6/2018

08.11.2017 | Novel Computational Approaches to Old and New Problems in Mechanics

Reinforced concrete seismically-excited frame design with a new mixed \(\varvec{H}_2/\varvec{H}_{\infty }\) optimization approach

verfasst von: Paolo Venini, Carlo Cinquini

Erschienen in: Meccanica | Ausgabe 6/2018

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Abstract

A new approach is proposed for the optimal design of seismically excited reinforced concrete frames. Unlike most existing methods that do not exploit the input/output relationship between the base acceleration and the structural response, the main feature of the presented approach is to directly shape the input/output transfer function so as to reduce the dynamic amplification factors that govern the structural response. The approach is general with respect to distinctive issues: on the one side the structural output may encompass different quantities of engineering interest such as the overall compliance, the lateral displacement of a representative point (typically the averaged top-storey displacement) and the interstorey drift vector, on the other two system norms may be considered (or a combination thereof) as to the transfer-function amplitude to be minimized, namely the \(H_{\infty }\)-norm and the \(H_2\)-norm. The former allows to reduce the peak-gain response whereas the latter the squared power energy of the response. By cleverly combining the two, typically by means of a convex combination, one may end up with significant peak gain as well as power response reduction. A numerical investigation on a 2D frame is conducted to validate the theoretical framework that is modeled following Eurocode 8 (CEN in Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Brussels (2004)) in medium ductility class (DCM) but the method applies to any regulations including modern displacement based codes such as the fib Model Code 2010 (Bulletins Nos. 65/66, Federation Internationale du Beton, Lausanne 2012).

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Literatur
1.
Zurück zum Zitat ProSap RY2017(a). 2S.I. Software e Servizi per l’Ingegneria S.r.l., Ferrara, Italy ProSap RY2017(a). 2S.I. Software e Servizi per l’Ingegneria S.r.l., Ferrara, Italy
2.
Zurück zum Zitat CEN (2004) Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Brussels, Belgium CEN (2004) Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Brussels, Belgium
3.
Zurück zum Zitat fib. Model Code 2010. Bulletins Nos. 65/66. Federation Internationale du Beton, Lausanne (2012) fib. Model Code 2010. Bulletins Nos. 65/66. Federation Internationale du Beton, Lausanne (2012)
4.
Zurück zum Zitat Acun B, Athanasopoulou A, Pinto A, Carvalho E, Fardis M (2012) Eurocode 8: seismic design of buildings worked examples. JRC Scientific and Tecnical Reports, Luxenbourg Acun B, Athanasopoulou A, Pinto A, Carvalho E, Fardis M (2012) Eurocode 8: seismic design of buildings worked examples. JRC Scientific and Tecnical Reports, Luxenbourg
5.
Zurück zum Zitat Baji H, Ronagh H, Melchers R (2016) Reliability of ductility requirements in concrete design codes. Struct Saf 62:76–87CrossRef Baji H, Ronagh H, Melchers R (2016) Reliability of ductility requirements in concrete design codes. Struct Saf 62:76–87CrossRef
6.
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
7.
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
8.
Zurück zum Zitat Benner P, Sima V, Voigt M (2012) Robust and efficient algorithms for \(\cal{L}_{\infty }\)-norm computation for descriptor systems. In: 7th IFAC Symposium on Robust Control Design, ROCOND’12, vol 45. Aalborg, Denmark, pp 195–200 Benner P, Sima V, Voigt M (2012) Robust and efficient algorithms for \(\cal{L}_{\infty }\)-norm computation for descriptor systems. In: 7th IFAC Symposium on Robust Control Design, ROCOND’12, vol 45. Aalborg, Denmark, pp 195–200
9.
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 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 2(3):207–219MathSciNetCrossRef
10.
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
11.
Zurück zum Zitat Curtis F, Mitchell T, Overton M (2017) A BFGS-SQP method for nonsmooth, nonconvex, constrained optimization and its evaluation using relative minimization profiles. Optim Methods Softw 32(1):148–181MathSciNetCrossRefMATH Curtis F, Mitchell T, Overton M (2017) A BFGS-SQP method for nonsmooth, nonconvex, constrained optimization and its evaluation using relative minimization profiles. Optim Methods Softw 32(1):148–181MathSciNetCrossRefMATH
12.
Zurück zum Zitat Fardis M (2013) Performance- and displacement-based seismic design and assessment of concrete structures in fib model code 2010. Struct Concr 14(3):215–229CrossRef Fardis M (2013) Performance- and displacement-based seismic design and assessment of concrete structures in fib model code 2010. Struct Concr 14(3):215–229CrossRef
13.
Zurück zum Zitat Fardis M, Carvalho E, Fajfar P, Pecker A (2014) Seismic design of concrete buildings to Eurocode 8. CRC Press, New York Fardis M, Carvalho E, Fajfar P, Pecker A (2014) Seismic design of concrete buildings to Eurocode 8. CRC Press, New York
14.
Zurück zum Zitat Francis B (1987) A course in \(H_{\infty }\) control theory. Lecture notes in control and information sciences, vol 88 Springer, Berlin Francis B (1987) A course in \(H_{\infty }\) control theory. Lecture notes in control and information sciences, vol 88 Springer, Berlin
15.
Zurück zum Zitat Giesy DP, Lim KB (1993) H\(_{\infty }\) norm sensitivity formula with control system design applications. J Guid Control Dyn 16(6):1138–1145ADSCrossRefMATH Giesy DP, Lim KB (1993) H\(_{\infty }\) norm sensitivity formula with control system design applications. J Guid Control Dyn 16(6):1138–1145ADSCrossRefMATH
16.
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
17.
Zurück zum Zitat Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. N.J. Prentice-Hall International, Englewood CliffsMATH Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. N.J. Prentice-Hall International, Englewood CliffsMATH
18.
Zurück zum Zitat Lagaros N, Papadrakakis M (2007) Seismic design of RC structures: a critical assessment in the framework of multi-objective optimization. Earthq Eng Struct Dyn 36:1623–1639CrossRef Lagaros N, Papadrakakis M (2007) Seismic design of RC structures: a critical assessment in the framework of multi-objective optimization. Earthq Eng Struct Dyn 36:1623–1639CrossRef
19.
Zurück zum Zitat Mergos P (2017) Optimum seismic design of reinforced concrete frames according to Eurocode 8 and fib Model Code 2010. Earthq Eng Struct Dyn doi:10.1002/eqe.2851 Mergos P (2017) Optimum seismic design of reinforced concrete frames according to Eurocode 8 and fib Model Code 2010. Earthq Eng Struct Dyn doi:10.​1002/​eqe.​2851
20.
Zurück zum Zitat Ning N, Qu W, Ma J (2016) Design recommendations for achieving “strong column-weak beam” in RC frames. Eng Struct 126:343–352CrossRef Ning N, Qu W, Ma J (2016) Design recommendations for achieving “strong column-weak beam” in RC frames. Eng Struct 126:343–352CrossRef
21.
Zurück zum Zitat SeismoArtif: SeismoSoft. Earthquake Engineering Software Solutions, SeismoArtif, Seismosoft Ltd., Piazza Castello 19, Pavia, Italy SeismoArtif: SeismoSoft. Earthquake Engineering Software Solutions, SeismoArtif, Seismosoft Ltd., Piazza Castello 19, Pavia, Italy
22.
Zurück zum Zitat Skogestad A, Postlethwaite I (2005) Multivariable feedback control: analysis and design, 2nd edn. John Wiley, ChichesterMATH Skogestad A, Postlethwaite I (2005) Multivariable feedback control: analysis and design, 2nd edn. John Wiley, ChichesterMATH
23.
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
24.
Zurück zum Zitat Venini P (2017) A new simple viscoelastic frame element: dynamic response and structural optimization. Computers and Structures (submitted) Venini P (2017) A new simple viscoelastic frame element: dynamic response and structural optimization. Computers and Structures (submitted)
25.
Zurück zum Zitat Venini P: A rational \(H_{\infty }\)–norm based approach for the optimal design of seismically excited reinforced concrete frames. Earthquake Engineering and Structural Dynamics (submitted) Venini P: A rational \(H_{\infty }\)–norm based approach for the optimal design of seismically excited reinforced concrete frames. Earthquake Engineering and Structural Dynamics (submitted)
26.
Zurück zum Zitat Venini P, Pingaro M (2016) An innovative \(H_{\infty }\)-norm based worst case scenario approach for dynamic compliance optimization with applications to viscoelastic beams. Struct Multidiscip Optim . doi:10.1007/s00158-016-1605-0 Venini P, Pingaro M (2016) An innovative \(H_{\infty }\)-norm based worst case scenario approach for dynamic compliance optimization with applications to viscoelastic beams. Struct Multidiscip Optim . doi:10.​1007/​s00158-016-1605-0
27.
Zurück zum Zitat Venini P, Pingaro M (2016) A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function \(H_{\infty }\)-norm. Struct Multidiscip Optim . doi:10.1007/s00158-016-1600-5 Venini P, Pingaro M (2016) A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function \(H_{\infty }\)-norm. Struct Multidiscip Optim . doi:10.​1007/​s00158-016-1600-5
28.
Zurück zum Zitat Žižmond J, Dolšek M (2016) Evaluation of factors influencing the earthquake-resistant design of reinforced concrete frames according to Eurocode 8. Struct Infrastruct Eng 12(10):1323–1341CrossRef Žižmond J, Dolšek M (2016) Evaluation of factors influencing the earthquake-resistant design of reinforced concrete frames according to Eurocode 8. Struct Infrastruct Eng 12(10):1323–1341CrossRef
29.
Zurück zum Zitat Zou X, Chan CM (2005) An optimal resizing technique for seismic drift design of concrete buildings subjected to response spectrum and time history loadings. Comput Struct 83:1689–1704CrossRef Zou X, Chan CM (2005) An optimal resizing technique for seismic drift design of concrete buildings subjected to response spectrum and time history loadings. Comput Struct 83:1689–1704CrossRef
Metadaten
Titel
Reinforced concrete seismically-excited frame design with a new mixed optimization approach
verfasst von
Paolo Venini
Carlo Cinquini
Publikationsdatum
08.11.2017
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 6/2018
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-017-0781-3

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