Acknowledgement
Supported by : 경상대학교
References
- Babuska, I., Banerjee, U., & Osborn, J.E. (2004). Generalized finite element methods: main ideas, results, and perspective. Int. J. Compt. Meth., 1, 67-103. https://doi.org/10.1142/S0219876204000083
- Benson, D.J., Bazilevs, Y., De Luycker, E., Hsu, M.-C., Scott, M., Hughes, T.J.R., & Belytschko, T. (2010). A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM, Int. J. Numer. Meth. Eng., 83, 765-785. https://doi.org/10.1002/nme.2864
- Brebbia, J.C. Telles, C.A., & Wrobel, L.C. (1984). Boundary Element Techniques, Berlin, Springer.
- Cottrell, J.A., Bazilevs, Y., & Hughes, T.J.R. (2009). Isogeometric Analysis: Towards Integration of CAD and FEA, Wiley.
- Dai, K.Y., & Liu, G.R. (2007). Free and forced vibration analysis using the smoothed finite element method (SFEM), J. Sound Vib., 301, 803-820. https://doi.org/10.1016/j.jsv.2006.10.035
- De Boor, C. (1978). A Practical Guide to Splines, Springer.
- Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, R.M.N., Soares, C.M.M., & Liew, K.M. (2011). Buckling and vibration analysis of isotropic and laminated plates by radial basis functions, Composites Part B: Engineering, 42, 592-606. https://doi.org/10.1016/j.compositesb.2010.08.001
- Fries, T.-P., & Belytschko, T. (2010). The extended/generalized finite element method: An overview of the method and its applications, Int. J. Numer. Meth. Eng., 84, 253-304. https://doi.org/10.1002/nme.2914
- Hughes, T.J.R. (1987). The Finite Element Method-Linear Static and Dynamic Finite Element Analysis, New Jersey, Prentice-Hall.
- Hughes, T.J.R., & Cottrell, J.A. & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Meth. Appl. Mech., 194(39-41), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
- Hughes, T.J.R., & Evans, J.A. (2010). Isogeometric analysis, ICES Report 10-18, The Institute of Computational Engineering and Science, University of Texas Austin.
- Kolman, R. (2012). Isogeometric free vibration of an elastic block, J. Eng. Mech., 19(4), 279-291.
- Lee, S.J., & Park, K.S. (2011). Free vibration analysis of elastic bars using isogeometric approach, Architectural Research, 13, 41-47. https://doi.org/10.5659/AIKAR.2011.13.3.41
- Lee, S.J., & Kim, H.R. (2013). Vibration and buckling of thick plates using isogeometric approach, Architectural Research, 15, 35-42. https://doi.org/10.5659/AIKAR.2013.15.1.35
- Lee, S.J., & Park, K.S. (2013). Vibrations of Timoshenko beams with isogeometric approach, Appl. Math. Model., 37, 9174-9190. https://doi.org/10.1016/j.apm.2013.04.034
- Lee, S.J. (2014). Free vibrations of thin shell with isogeometric approach, Architectural Research, 13, 67-74. https://doi.org/10.5659/AIKAR.2014.16.2.67
- Lee, S.J. (2016). Free vibrations of plates and shells with an isogeometric RM shell element, Architectural Research, 18, 65-74. https://doi.org/10.5659/AIKAR.2016.18.2.65
- Leissa, A.W. (2005). The historical bases of the Rayleigh and Ritz method, J. Sound Vib., 287, 961-978. https://doi.org/10.1016/j.jsv.2004.12.021
- Liu, G.R., Nguyen-Xuan, H., Nguyen-Thoi, T., & Xu, X. (2009). A novel Galerkin-like weak form and a super convergent alpha finite element method (SaFEM) for mechanics problems using triangular meshes, J. Comput. Phys., 228, 4055-4087. https://doi.org/10.1016/j.jcp.2009.02.017
- Mazzochi, R., Garcia de Suarez, O.A., Rossi, R., & Morais da Silva Neto, J. (2013). Generalized finite element method to approach forced and free vibration in elastic 2D problems, The 22nd International Congress of Mechanical Engineering (COBEM 2013), Ribeirao Preto, SP, Brazil, November 3-7.
- Nagashima, T. (1999). Node-by-node meshless approach and its applications to structural analyses, Int. J. Numer. Meth. Eng., 46, 341-385. https://doi.org/10.1002/(SICI)1097-0207(19990930)46:3<341::AID-NME678>3.0.CO;2-T
- Piegl, L., & Tiller, W. (1997). The NURBS Book, Springer.
- Rauen, M., Machado, R.D., & Arndt, M. (2013). Isogeometric analysis of free vibration of bars, Proceedings of the 22nd International Congress of Mechanical Engineering, Ribeirao Preto SP, Brazil, November 3-7.
- Rauen, M., Machado, R.D., & Arndt, M. (2016). Isogeometric analysis applied to free vibration analysis of plane stress and plane strain structures, Proceedings of the XXXVII Iberian Latin-American Congress on Computational Methods in Engineering, Suzana Moreira Avila (Editor), ABMEC, Brasilia, DF, Brazil, November 6-9.
- Reali, A. (2004). An Isogeometric Analysis Approach for the Study of Structural Vibrations, ROSE School, European school for advanced studies in reduction of seismic risk.
- Shang, H.Y., Machado, R.D., Filho, J.E.A., & Arndt, M. (2017). Numerical analysis of plane stress free vibration in severely distorted mesh by generalized finite element method, European Journal of Mechanics A/Solids, 62, 50-66. https://doi.org/10.1016/j.euromechsol.2016.11.006
- Zhao, C., & Steven, G.P. (1995). Analytical solutions of mass transport problems for error estimation of finite/infinite element methods, Comm. Numer. Meth. Eng., 11, 13-23. https://doi.org/10.1002/cnm.1640110104
- Zhao, C., & Steven, G.P. (1996). Asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems in finite element analysis, Int. J. Numer. Meth. Eng., 39, 2821-2835. https://doi.org/10.1002/(SICI)1097-0207(19960830)39:16<2821::AID-NME979>3.0.CO;2-0
- Zienkiewicz, O.C., & Taylor, R.L. (2000). The Finite Element Method, fifth ed., Butterworth Heinemann, Oxford.