Abstract
The standard finite elements approach for the dynamics of curved beam is usually based on the same energy functional used for straight beam, in other words an energy form that is essentially derived from de Saint–Venant’s theory. In case of strongly curved elements this approximation yields to not negligible errors, in particular for stress assessments. For this reason, in this work a different formulation, based on the Winkler’s simple kinematic assumptions, is adopted. In this way a non diagonal constitutive matrix is obtained and the computational efficiency of NURBS (Non Uniform Rational B–Splines) shape functions is added to an accurate representation of the constitutive relations. In this paper the natural frequencies and mode shapes of plane curved concrete beams are obtained. Computational cost and results accuracy is assessed with respect to closed form solutions and literature results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aristodemo M, Turco E (1994) Boundary element discretization of plane elasticity and plate bending problems. Int J Numer Meth Eng 37(6):965–987
Buffa F, Causin A, Cazzani A, Poppi S, Sanna G, Solci M, Stochino F, Turco E (2015) The sardinia radio telescope: a comparison between close-range photogrammetry and finite element models. Math Mech Solids 22:1005–1026. https://doi.org/10.1177/1081286515616227
Bilotta A, Formica G, Turco E (2010) Performance of a high-continuity finite element in three-dimensional elasticity. Int J Numer Meth Biomed Eng 26(9):1155–1175
Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New York
Cazzani A, Wagner N, Ruge P, Stochino F (2016a) Continuous transition between traveling mass and traveling oscillator using mixed variables. Int J Non-Linear Mech 80:82–95
Cazzani A, Malagù M, Turco E (2016b) Isogeometric analysis of plane-curved beams. Math Mech Solids 21(5):562–577
Cazzani A, Stochino F, Turco E (2016c) On the whole spectrum of Timoshenko beams Part I: a theoretical revisitation. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 67(24):1–30
Cazzani A, Stochino F, Turco E (2016d) On the whole spectrum of Timoshenko beams Part II: further applications. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 67(25):1–21
Cazzani A, Stochino F, Turco E (2016e) An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams. J Appl Math Mech Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 96(10):1220–1244. https://doi.org/10.1002/zamm.201500280
Cazzani A, Malagù M, Turco E, Stochino F (2016f) Constitutive models for strongly curved beams in the frame of isogeometric analysis. Math Mech Solids 21(2):182–209
Sevim B, Atamturktur S, Altunişik AC, Bayraktar A (2016) Ambient vibration testing and seismic behavior of historical arch bridges under near and far fault ground motions. Bull Earthq Eng 14(1):241–259
Kadkhodayan V, Aghajanzadeh M, Mirzabozorg H (2016) Seismic assessment of arch dams using fragility curves. Civ Eng J 1(2):14–20
Li Y, Cai CS, Liu Y, Chen Y, Liu J (2016) Dynamic analysis of a large span specially shaped hybrid girder bridge with concrete-filled steel tube arches. Eng Struct 106:243–260
Luu AT, Kim NI, Lee J (2015) Isogeometric vibration analysis of free-form Timoshenko curved beams. Meccanica 50(1):169–187
Stochino F, Cazzani A, Poppi S, Turco E (2018) Sardinia radio telescope finite element model updating by means of photogrammetric measurements. Math Mech Solids 22(4):885–901. https://doi.org/10.1177/1081286515616046
Stochino F, Carta G (2014) SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects. Nucl Eng Des 276:74–86
Stochino F (2016) RC beams under blast load: reliability and sensitivity analysis. Eng Fail Anal 66:544–565
Tüfekçi E, Arpaci A (1998) Exact solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects. J Sound Vib 209(5):845–856
Zong Z, Xia Z, Liu H, Li Y, Huang X (2016) Collapse failure of prestressed concrete continuous rigid-frame bridge under strong earthquake excitation: testing and simulation. J Bridge Eng 21:04016047
Winkler E (1858) Formänderung und festigkeit gekrümmter körper, insbesondere der ringe. Der Civilingenieur 4:232–246
Acknowledgements
The financial support of MIUR, the Italian Ministry of Education, University and Research, under grant PRIN 2010–2011 (project 2010MBJK5B—Dynamic, Stability and Control of Flexible Structures) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Stochino, F., Cazzani, A., Giaccu, G.F., Turco, E. (2018). Dynamics of Strongly Curved Concrete Beams by Isogeometric Finite Elements. In: di Prisco, M., Menegotto, M. (eds) Proceedings of Italian Concrete Days 2016. ICD 2016. Lecture Notes in Civil Engineering , vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-78936-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-78936-1_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78935-4
Online ISBN: 978-3-319-78936-1
eBook Packages: EngineeringEngineering (R0)