References
- Bellman, R. and Casti, J. (1971), 'Differential quadrature and long-term integration', J. Mathematics Analytic Applications, 34,235-238 https://doi.org/10.1016/0022-247X(71)90110-7
- Bellman, R, Kashef, Rand Casti, J. (1972), 'Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations', J. of Computational Physics, 10(1),40-52 https://doi.org/10.1016/0021-9991(72)90089-7
- Bellomo, N. (1997), 'Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods', Mathematical and Computer Modelling, 26(4), 13-34 https://doi.org/10.1016/S0895-7177(97)00142-8
- Bert, C.W. and Malik, M. (1996), 'Differential quadrature method in computational mechanics: a review', Appl. Mech. Rev., 49, 1-27 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. of Pressure Vessel Technology, 118, 1-12 https://doi.org/10.1115/1.2842156
- Gould, P.L. (1999), Analysis of Shells and Plates, Upper Saddle River, Prentice Hall
- Gould, P.L. and Sen, S.K. (1971), 'Refined mixed method finite elements for shells of revolution', Proc. Air Force third Conference on matrix methods in structural mechanics, AFB Ohio
- Jiang, W. and Redekop, D. (2002), 'Polar axisymmetric vibration of a hollow toroid using the differential quadrature method', J. Sound Vib., 251(4), 761-765 https://doi.org/10.1006/jsvi.2001.3865
- Kim, J.G. and Kim, Y.Y. (2000), 'A higher-order hybrid-mixed harmonic shell-of-revolution element', Comput. Meth. Appl. Mech. Eng., 182, 1-16 https://doi.org/10.1016/S0045-7825(99)00082-1
- KIysl, P. and Belytschko, T. (1996), 'Analysis of thin shells by the element-free Galerkin method', Int. J Solids Struct., 33(20-22), 3057-3080 https://doi.org/10.1016/0020-7683(95)00023-4
- Kunieda, H. (1984), 'Flexural axisymmetric free vibrations of a spherical dome: exact results and approximate solutions', J. Sound Vib., 92(1), 1-10 https://doi.org/10.1016/0022-460X(84)90368-7
- Liu, Y. (1998), 'Analysis of shell-like structures by the boundary element method based on 3-D elasticity: Formulation and verification', Int. J Numer. Meth. Eng., 41,541-558 https://doi.org/10.1002/(SICI)1097-0207(19980215)41:3<541::AID-NME298>3.0.CO;2-K
- Luah, M.H. and Fan, S.C. (1990), 'New spline finite element for analysis of shells of revolution', J. Eng. Mech., ASCE, 116(3), 709-725 https://doi.org/10.1061/(ASCE)0733-9399(1990)116:3(709)
- Mirfakhraei, P. and Redekop, D. (1998), 'Buckling of circular cylindrical shells by the Differential Quadrature Method', Int. J of Pressure Vessels and Piping, 75,347-353 https://doi.org/10.1016/S0308-0161(98)00032-5
- Mizusawa, T. (1988), 'Application of spline strip method to analyse vibration of open cylindrical shells', Int. J. Numer. Meth. Eng., 26, 663-676 https://doi.org/10.1002/nme.1620260310
- Prato, C. (1969), 'Shell finite element method via Reissner's principle', Int. J Solids Struct., 5, 1119-1133 https://doi.org/10.1016/0020-7683(69)90007-9
- Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wiley & Sons
- Redekop, D. and Xu, R (1999), 'Vibration analysis of toroidal panels using the differential quadrature method', Thin Walled Structures, 34,217-231 https://doi.org/10.1016/S0263-8231(99)00010-5
- Reissner, E. (1946), 'Stresses and small displacements of shallow spherical shells - Part II', J. Mathematics Physics, 25, 80-85 https://doi.org/10.1002/sapm194625180
- Shu, C. and Richards, B.E. (1992), 'Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations', Int. J. Numer. Meth. Eng., 15, 791-798 https://doi.org/10.1002/fld.1650150704
- Viola, E. and Artioli, E. (2004), 'The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements', Structural Engineering and Mechanics, 17(6),789-817 https://doi.org/10.12989/sem.2004.17.6.789
- Viola, E., Sgallari, F. and Artioli, E. (2003), 'Computational efficiency of the Generalized Differential Quadrature method in the elastic analysis of shells of revolution', Technical Report, DISTART, University of Bologna, Italy
- Wu, C.P. and Lee, C.Y. (2001), 'Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffuess', Int. J Mech. Sci., 43, 1853-1869 https://doi.org/10.1016/S0020-7403(01)00010-8
- Yang, H.T.Y., Saigal, S., Masud, A. and Kapania, R.K. (2000), 'A survey of recent shell finite elements', Int. J. Numer. Meth. Eng., 47, 101-127 https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<101::AID-NME763>3.0.CO;2-C
Cited by
- Free vibration of four-parameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions vol.42, 2017, https://doi.org/10.1016/j.apm.2016.10.047
- Free vibration analysis of functionally graded panels and shells of revolution vol.44, pp.3, 2009, https://doi.org/10.1007/s11012-008-9167-x
- Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution vol.28, pp.5, 2009, https://doi.org/10.1016/j.euromechsol.2009.04.005
- General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian vol.331, pp.22, 2012, https://doi.org/10.1016/j.jsv.2012.05.036
- 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures vol.328, pp.3, 2009, https://doi.org/10.1016/j.jsv.2009.07.031
- RETRACTED: Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method vol.200, pp.9-12, 2011, https://doi.org/10.1016/j.cma.2010.11.017
- Generalized stress–strain recovery formulation applied to functionally graded spherical shells and panels under static loading vol.156, 2016, https://doi.org/10.1016/j.compstruct.2015.12.060
- Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution vol.198, pp.37-40, 2009, https://doi.org/10.1016/j.cma.2009.04.011
- Free vibration of moderately thick functionally graded parabolic and circular panels and shells of revolution with general boundary conditions vol.34, pp.5, 2017, https://doi.org/10.1108/EC-06-2016-0218
- 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution vol.93, pp.7, 2011, https://doi.org/10.1016/j.compstruct.2011.02.006
- Transport–diffusion models with nonlinear boundary conditions and solution by generalized collocation methods vol.58, pp.3, 2009, https://doi.org/10.1016/j.camwa.2009.02.034
- FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations vol.53, pp.6, 2011, https://doi.org/10.1016/j.ijmecsci.2011.03.007
- NURBS-Based Collocation Methods for the Structural Analysis of Shells of Revolution vol.6, pp.12, 2016, https://doi.org/10.3390/met6030068
- Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery vol.112, 2014, https://doi.org/10.1016/j.compstruct.2014.01.039
- Generalized collocation method for two-dimensional reaction-diffusion problems with homogeneous Neumann boundary conditions vol.56, pp.9, 2008, https://doi.org/10.1016/j.camwa.2008.05.041
- Free vibration of FG-GPLRC spherical shell on two parameter elastic foundation vol.36, pp.6, 2005, https://doi.org/10.12989/scs.2020.36.6.711