참고문헌
- Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Englewood Cliffs. NJ: Prentice-Hall
- Bellman, R., Kashef, B.G. and Casti, J. (1972), 'Differential quadrature: A technique for the rapid solution of nonlinear partial differential equation', J. of Computational Physics, 10, 40-52 https://doi.org/10.1016/0021-9991(72)90089-7
- Bert, C.W. and Malik, M. (1996), 'Differential quadrature method in computational mechanics: A review', Appl. Mech. Rev., 49(1), 1-28 https://doi.org/10.1115/1.3101882
- Bert, C.W. and Malik, M. (1996), 'Free vibration analysis of thin cylindrical shells by the differential quadrature method', J. Press. Vessel Tech., 118, 1-12 https://doi.org/10.1115/1.2842156
- Celia, M.A. and Gray, W.G. (1992), Numerical Methods for Differential Equations, Fundamental Concepts for Scientific and Engineering Applications. NJ, Prentice Hall
- Chia, C.Y. (1980), Nonlinear Analysis of Plates, Mc-Graw Book Co., New York, N.Y.
- Civalek, O. (2002), Differential Quadrature (DQ) for Static and Dynamic Analysis of Structures, (in Turkish), Firat University
- Civalek, O. (2004), 'Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns', Eng. Struct., An Int. J., 26(2), 171-186 https://doi.org/10.1016/j.engstruct.2003.09.005
- Civalek, O. and Ulker, M. (2004), 'Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates', Struct. Eng. Mech., Int. J., 17(1), 1-14 https://doi.org/10.12989/sem.2004.17.1.001
- Civalek, O. and Ulker, M. (2004), 'Free vibration analysis of elastic beams using harmonic differential quadrature (HDQ)', Mathematical and Computational Applications, 9(2), 257-264 https://doi.org/10.3390/mca9020257
- Civalek, O. and Catal, H.H. (2003), 'Linear static and vibration analysis of circular and annular plates by the harmonic differential quadrature (HDQ) method', J. of Eng. and Arthitecture Faculty of Osmangazi University, 16(1), 45-76
- Civalek, O. and Catal, H.H. (2002), 'Dynamic analysis of one and two dimensional structures by the method of generalized differential quadrature', Turkish Bulletin of Engineering, 417, 39-46
- Civalek, O. (2003), 'Linear and nonlinear dynamic response of multi-degree-of freedom-systems by the method of harmonic differential quadrature (HDQ)', PhD. Thesis, Dokuz Eyliil University, Izmir, (in Turkish)
- Civalek, O. (1998), Finite Element Analysis of Plates and Shells, Elazig: FIrat University, (in Turkish)
- Civalek, O. (2004), 'Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)', PhD. Thesis, Firat University, (in Turkish), Elazig
- Civalek, O. (2004), 'Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ- FD methods', Int. J. ofP ressure Vessels and Piping, (in press)
- Civalek, O. (2001), 'Static, dynamic and buckling analysis of elastic bars using differential quadrature', XVI. National Technical Engineering Symposium, Paper No: 5, Ankara: METU
- Civalek, O. (2004), 'Differential quadrature methods in vibration analysis', J of Engineer and Machine, Turkish Chamber of Mechanical Eng., 45, 530, 27-36
- Hua, L. and Lam, K.Y. (2000), 'The generalized differential quadrature method for frequency analysis of a rotating conical shell with initial pressure', Int. J. Numer. Meth. Engng, 48, 1703-1722 https://doi.org/10.1002/1097-0207(20000830)48:12<1703::AID-NME961>3.0.CO;2-X
- Leissa, A.W., Lee, J.K. and Wang, A.J. (1983), 'Vibration of cantilevered doubly curved shallow shells', Int. J. Solids Struct., 19, 411-424 https://doi.org/10.1016/0020-7683(83)90052-5
- Leissa, A.W., and Kadi, A.S. (1971), 'Curvature effects on shallow shell vibration', J. Sound Vib., 16, 173-187 https://doi.org/10.1016/0022-460X(71)90482-2
- Leissa, A.W. and Nariata, Y. (1984), 'Vibrations of completely free shallow shells of rectangular planform', J. Sound Vib., 96, 207-218 https://doi.org/10.1016/0022-460X(84)90579-0
- Leissa, A.W. (1973), Vibration of Shells, NASA, SP-288
- Lim, C.W. and Liew, K.M. (1994), 'A pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform', J. Sound Vib., 173(3), 343-375 https://doi.org/10.1006/jsvi.1994.1235
- Liew, K.M. and Lim, C.W. (1995), 'A Ritz vibration analysis of doubly curved rectangular shallow shells using a refilled first-order theory', Comput. Meth. Appl. Mech. Eng., 127, 145-162 https://doi.org/10.1016/0045-7825(95)00837-1
- Liew, K.M., Lim, C.M. and Kitipomchai, S. (1997), 'Vibration of shallow shells: A review with bibliography', Trans. ASME Appl. Meeh. Rev., 50(8), 431-444 https://doi.org/10.1115/1.3101731
- Liew, K.M. and Lim, C.M. (1996), 'A higher order theory for vibration of doubly curved shallow shells', J. Appl. Mech., 63, 587-593 https://doi.org/10.1115/1.2823338
- Liew, K.M., Lim, M.K., Lim, C.W., Li, D.B. and Zhang, Y.R. (1995a), 'Effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells', J. Sound Vib., 180(2), 272-296
- Liew, K.M., Han, J-B, Xiao, Z.M. and Du, H. (1996), 'Differential quadrature method for Mindlin plates on Winkler foundations', Int. J. Mech. Sci., 38(4), 405-421 https://doi.org/10.1016/0020-7403(95)00062-3
- Liew, K.M., Teo, T.M. and Han, J.B. (1999), 'Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates', Int. J. Numer. Meth. Eng., 45, 1831-1848 https://doi.org/10.1002/(SICI)1097-0207(19990830)45:12<1831::AID-NME656>3.0.CO;2-W
- Liew, K.M., Teo, T.M. and Han, J.B. (2001), 'Three-dimensional static solutions of rectangular plates by variant differential quadrature method', Int. J. Mech. Sci., 43, 1611-1628 https://doi.org/10.1016/S0020-7403(00)00098-9
- Liew, K.M. and Lim, C.W. (1995b), 'Vibratory behavior of doubly curved shallow shells of curvilinear planform', J. Eng. Mech., ASCE, 121(2), 1277-1283 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:12(1277)
- Markus, S. (1988), The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York
- Matsunaga, H. (1999), 'Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses', J. Sound Vib., 225(1), 41-60 https://doi.org/10.1006/jsvi.1999.2234
- Nath, Y, Mahrenholtz, O. and Varma, K.K. (1987), 'Nonlinear dynamic response of a doubly curved shallow shell on an elastic foundation', J. Sound Vib., 112(1), 53-61 https://doi.org/10.1016/S0022-460X(87)80093-7
- Nath, Y. and Jain, R.K (1983), 'Nonlinear dynamic analysis of shallow spherical shells on elastic foundation', Int. J. Mech. Sci., 25(6), 409-419 https://doi.org/10.1016/0020-7403(83)90055-3
- Nath, Y. and Kumar, S. (1995), 'Chebyshev series solution to non-linear boundary value problems in rectangular domain', Comput. Meth. Appl. Mech. Eng., 125, 41-52 https://doi.org/10.1016/0045-7825(95)00801-7
- Nath, Y. and Sandeep, K. (2000), 'Nonlinear analysis of doubly curved shells: An analytical approach', Sadhana, 25(4), 343-352 https://doi.org/10.1007/BF03029719
- Nath, Y., Dumir, P.C. and Gandhi, M.L. (1983), 'Choice of collocation points for axisymmertric nonlinear two point boundary value problems in statics of shallow shells', Engineering Transaction, 31(3), 331-340
- Shu, C. and Xue, H. (1997), 'Explicit computations of weighting coefficients in the harmonic differential quadrature', J. Sound Vib., 204(3), 549-555 https://doi.org/10.1006/jsvi.1996.0894
- Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, London
- Shu, C. (1996), 'Free vibration analysis of composite laminated conical shells by generalized differential quadrature', J. Sound Vib., 194(4), 587-604 https://doi.org/10.1006/jsvi.1996.0379
- Shu, C. and Richards, B.E. (1992), 'Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations', Int. J. Numer. Meth. Fluids, 15, 791-798 https://doi.org/10.1002/fld.1650150704
- Soedel, W. (1996), Vibrations of Shells and Plates, Second Edition, Revised and Expanded, Marcal Dekker, Inc., New York
- Striz, A.G., Wang, X. and Bert, C.W. (1995), 'Harmonic differential quadrature method and applications to analysis of structural components', Acta Mechanica, 111, 85-94 https://doi.org/10.1007/BF01187729
- Striz, A.G., Jang, S.K. and Bert, C.W. (1988), ''Nonlinear bending analysis of thin circular plates by differential quadrature', Thin-Walled Structures, 6, 51-62 https://doi.org/10.1016/0263-8231(88)90025-0
- Timoshenko, S. and Woinowski-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill, NewYork
- Wu, T.Y. and Liu, G.R. (2000), 'Axisymmetric bending solution of shells of revolution by the generalized differential quadrature rule', Int. J. Press. Vessel and Piping, 77, 149-157 https://doi.org/10.1016/S0308-0161(00)00006-5
- Wu, T.Y. and Liu, G.R. (2001), 'Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule', Int. J. Solids Struct., 38, 7967-7980 https://doi.org/10.1016/S0020-7683(01)00077-4
- Wu, T.Y., Wang, Y.Y. and Liu, G.R. (2002), 'Free vibration analysis of circular plates using generalized differential quadrature rule', Comput. Meth. Appl. Mech. Eng., 191, 5365-5380 https://doi.org/10.1016/S0045-7825(02)00463-2
- Zienkiewicz, O.C. (1977), The Finite Element Method in Engineering Science. (3rd ed.). London, McGraw-Hill
피인용 문헌
- Nonlinear free vibration of spherical shell panel using higher order shear deformation theory – A finite element approach vol.86, pp.6, 2009, https://doi.org/10.1016/j.ijpvp.2008.11.023
- Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method vol.186, 2018, https://doi.org/10.1016/j.compstruct.2017.12.008
- Vibration analysis of conical panels using the method of discrete singular convolution vol.24, pp.3, 2006, https://doi.org/10.1002/cnm.961
- Vibration of laminated composite panels and curved plates with different types of FGM composite constituent vol.122, 2017, https://doi.org/10.1016/j.compositesb.2017.04.012
- The determination of frequencies of laminated conical shells via the discrete singular convolution method vol.1, pp.1, 2006, https://doi.org/10.2140/jomms.2006.1.163
- Analysis of non-homogeneous orthotropic plates using EDQM vol.61, pp.2, 2005, https://doi.org/10.12989/sem.2017.61.2.295
- Large Displacement Static Analysis of Composite Elliptic Panels of Revolution having Variable Thickness and Resting on Winkler-Pasternak Elastic Foundation vol.16, pp.9, 2019, https://doi.org/10.1590/1679-78255842