Application of isogeometric approach to dynamics of curved beam

• Autorzy: Łasecka-Plura Magdalena , Białasik Jan , Kuczma Mieczysław , Tabrizikahou Alireza

Identyfikatory

DOI

10.21008/j.0860-6897.2023.1.17

• Języki publikacji: EN

Abstrakty

EN

In the paper dynamics of a free-form Timoshenko curved beam is investigated. The considered problem is solved using isogeometric analysis. Non-uniform rational B-spline (NURBS) basis functions are applied to describe both geometry and displacement field of the considered beam. The Timoshenko beam theory is used to derive the element stiffness and mass matrices. The application of the presented method is shown in numerical examples. The correctness of the presented approach is proved by comparing the obtained results to those available in the literature and calculated by the finite element method. Analysis of convergence is presented for different orders of NURBS basis functions.

Słowa kluczowe

EN

isogeometric analysis; free-form curved beam; Timoshenko beam theory; vibration analysis

PL

analiza izogeometryczna; belka zakrzywiona; teoria Timoshenki; analiza drgań

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2023
• Tom: Vol. 34, nr 1
• Strony: art. no. 2023117
• Opis fizyczny: Bibliogr. 16 poz., rys., wykr.

Twórcy

autor

Łasecka-Plura Magdalena

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland

• https://orcid.org/0000-0002-5229-9361

autor

Białasik Jan

• Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland

autor

Kuczma Mieczysław

• Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland

• https://orcid.org/0000-0001-7427-3675

autor

Tabrizikahou Alireza

• Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland

• https://orcid.org/0000-0002-3161-2224

Bibliografia

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• 2. Y.P. Tseng, C.S. Huang, M.S. Kao; In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis; Compos Struct, 2000, 50, 103-114; DOI: 10.1016/S0263-8223(00)00003-9
• 3. K.Y. Nieh, C.S. Huang, Y.P. Tseng; An analytical solution for in-plane free vibration and stability of loaded elliptic arches; Comput Struct, 2003, 81, 1311-1327; DOI: 10.1016/S0045-7949(03)00057-9
• 4. F. Yang, R. Sedaghati, E. Esmailzadeh; Free in plane vibration of general curved beams using finite element method; J Sound Vib, 2008, 318, 850-867; DOI: 10.1016/j.jsv.2008.04.041
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• 8. S.J. Lee, K.S. Park; Vibrations of Timoshenko beams with isogeometric approach; Appl Math Model, 2013, 37, 9174-9190; DOI: 10.1016/j.apm.2013.04.034
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• 12. J.A. Cottrell, T.J.R. Hughes, Y. Bazilevs; Isogeometric analysis. Toward integration of CAD and FEA; John Wiley & Sons, 2009
• 13. L. Piegl, W. Tiller; The NURBS Book; Springer, New York, 1997
• 14. E. Marino, S.F. Hosseini, A. Hashemian, A. Reali; Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion; Comput Math Appl, 2020, 80, 2563-2585; DOI: 10.1016/j.camwa.2020.06.006
• 15. P. Rareendranath, G. Singh, G.V. Rao; A three-noded shear-flexible curved beam element based on coupled displacement field interpolations; Int J Numer Methods Eng, 2001, 51, 85-101; DOI: 10.1002/nme.160
• 16. P. Litewka, J. Rakowski; Free vibrations of shear-flexible and compressible arches by FEM; Int J Numer Methods Eng, 2001, 52, 273-286; DOI: 10.1002/nme.249

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).