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http://dx.doi.org/10.5659/AIKAR.2016.18.2.65

Free Vibrations of Plates and Shells with an Isogeometric RM Shell Element  

LEE, Sang Jin (ADOPT Research Group, Department of Architectural Engineering, Gyeongsang National University)
Publication Information
Architectural research / v.18, no.2, 2016 , pp. 65-74 More about this Journal
Abstract
Free vibration analysis of plates and shells is carried out by using isogeometric approach. For this purpose, an isogeometric shell element based on Reissner-Mindlin (RM) shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and it is also used to derive all terms required in the isogeometric element formulation. New anchor positions are proposed to calculate the shell normal vector. Gauss integration rule is used for the formation of stiffness and mass matrices. The proposed shell element is then used to examine vibrational behaviours of plate and shell structures. From numerical results, it is found to be that reliable natural frequencies and associated mode shapes can be predicted by the present isogeometric RM shell element.
Keywords
Reissner-Mindlin; Shell element; Isogeometric Analysis; Free Vibration; NURBS;
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  • Reference
1 BAQUS manual, Theory and Users Manuals. Hibbit, Karlson and Sorensen, Inc., Version 5.7.
2 Cottrell, J.A., Bazilevs, Y. and Hughes, T.J.R. (2009). Isogeometric Analysis: Towards Integration of CAD and FEA. Wiley.
3 De Boor, C. (1978) A Practical Guide to Splines. Springer.
4 Flugge, W. (1934) Statik und Dynamik der Schalen. Springer-Verlag, Berlin, Germany.
5 Huang, H.C. and Hinton, E. (1986) A new nine node degenerated shell element with enhanced membrane and shear interpolation. Int. J. Num. Meth. Engng., 22, pp.73-92.   DOI
6 Hughes, T.J.R. (1987) The Finite Element Method- Linear Static and Dynamic Finite Element Analysis. New Jersey: Prentice-Hall.
7 Hughes, T.J.R., Cottrell, J. A. and Bazilevs, Y. (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng., 194(39-41), pp.4135-4195.   DOI
8 Hughes, T.J.R. and Evans J.A. (2010). Isogeometric analysis. ICES Report 10-18, The Institute of Computational Engineering and Science, University of Texas Austin.
9 Kanok-nukulchai, W. (1979) A simple and efficient finite element for general shell element. Int. J. Num. Meth. Engng. 14, pp.179-200.   DOI
10 Lee, J.K., Leissa, A.W. and Wang, A.J. (1981) Vibrations of cantilevered shallow cylindrical shells of rectangular planform. J. Sound and Vibration, 78, pp.311-328.   DOI
11 Lee, S.J. and Kim, H.R. (2012) Vibration and buckling of thick plates using isogeometric approach. Architectural Research, 15, pp. 35-42.
12 Lee, S.J. and Han, S.E. (2001) Free-vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element. Journal of Sound and Vibration, 241, pp.605-633.   DOI
13 Lee, S.J. and Park, K.S. (2013) Vibrations of Timoshenko beams with isogeometric approach. Applied Mathematical Modelling. 37(22), pp.9174-9190.   DOI
14 Leissa, A.W. (1969) Vibrations of plates. NASA SP-160, Washington D.C.
15 Leissa, A.W. (1973) Vibrations of shells. NASA SP-288, Washington D.C.
16 Liew, K.M. (1992) Use of two-dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates. J. Sound and Vibration, 154, pp.261-269.   DOI
17 Liew, K.M. (1995) Research on thick plate vibration: a literature survey. J. Sound and Vibration, 180, pp.163-176.   DOI
18 Lim, C.W. and Liew, K.M. (1994) A ph-z Ritz formulation for flexural vibration of shallow cylindrical shell of rectangular planform. J. Sound and Vibration, 173, pp.343-375.   DOI
19 Love, A.E.H. (1888) The small free vibrations and deformation of a thin elastic shell, Philosophical transactions of royal society of London A, 179, pp.491-549.   DOI
20 Qatu, M.S. (1992) Review of shallow shell vibration research, Shock Vibration Digest, 24, pp.3-15.
21 Piegl, Les and Tiller, Wayne (1997) The NURBS Book, Springer
22 Rayleigh, J.W.S. (1894), Theory of sound. MacMillan Inc., London, England