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Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
art. no. 2023117
Opis fizyczny
Bibliogr. 16 poz., rys., wykr.
Twórcy
autor
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland
autor
- Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland
autor
- Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland
autor
- Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland
Bibliografia
- 1. S.J. Oh, B.K. Lee, I.W. Lee; Natural frequencies of non-circular arches with rotatory inertia and shear deformation; J Sound Vib, 1999, 219(1), 23-33; DOI: 10.1006/jsvi.1998.1822
- 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
- 5. J.S. Wu, L.K. Chiang; Free vibration analysis of arches using curved beam elements; Int J Numer Methods Eng, 2003, 58, 1907-1936; DOI: 10.1002/nme.837
- 6. T.J.R. Hughes, J.A. Cottrell, Y. Bazilev; Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement; Comput Methods Appl Mech Eng, 2005, 194, 4135-4195; DOI: 10.1016/j.cma.2004.10.008
- 7. J.A. Cottrell, A. Reali, Bazilevs, T.J.R. Hughes; Isogeometric analysis of structural vibrations; Comput Methods Appl Mech Eng, 2006, 195, 5257-5296; DOI: 10.1016/j.cma.2005.09.027
- 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
- 9. A.T. Luu, N.I. Kim, J. Lee; Isogeometric vibration analysis of free-form Timoshenko curved beams; Meccanica, 2015, 50, 169-187; DOI: 10.1007/s11012-014-0062-3
- 10. B.S. Gan; An Isogeometric approach to beam structures; Springer, 2018; DOI: 10.1007/978-3-319-56493-7
- 11. C. De Boor; A practical guide to splines; Springer, New York, 1978
- 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).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-99948b54-b20d-480c-b6ce-e2773f51ac97