References
- Akbarov, S.D. and Kocaturk, T. (1997), 'On the bending problems of anisotropic plates resting on elastic foundations that react in compression only', Int. J. Solids Struct., 34(8),3673-3689 https://doi.org/10.1016/S0020-7683(96)00227-2
- Beaufait, F.W and Hoadley, P.W (1980), 'Analysis of elastic beams on nonlinear foundation', Comput. Struct., 12(5), 669-676 https://doi.org/10.1016/0045-7949(80)90168-6
- Bellman, R. and Casti, J. (1971), 'Differential quadrature and long-term integration', J. Mathematical Analysis and Application, 34, 235-238 https://doi.org/10.1016/0022-247X(71)90110-7
- Bellman, R.E., Kashef, B.G and Casti, J. (1972), 'Differential quadrature: A technique for rapid solution of nonlinear partial differential equations', J. Computational Physics, 10, 40-52 https://doi.org/10.1016/0021-9991(72)90089-7
- Bert, C.W and Malik, M. (1996a), 'Free vibration analysis of tapered rectangular plates by differential quadrature method: A semi-analytical approach', J. Sound Vib., 190(1), 41-63 https://doi.org/10.1006/jsvi.1996.0046
- Bert, C.W and Malik, M. (1996b), 'Differential quadrature method in computational mechanics', Appl. Mech. Review, 49(1), 1-28 https://doi.org/10.1115/1.3101882
- Bert, C.W., Jang, S.K. and Striz, A.G (1988), 'Two new approximate methods for analyzing free vibration of structural components', Int. J. Numer. Meth. Eng., 28, 561-577
- Bert, C.W, Wang, X. and Striz, A.G (1993), 'Differential quadrature for static and free vibration analysis of anisotropic plates', Int. J. Solids Struct., 30, 1737-1744 https://doi.org/10.1016/0020-7683(93)90230-5
- Bert, C.W, Wang, X. and Striz, A.G (1994a), 'Static and free vibration analysis of beams and plates by differential quadrature method', Acta Mechanica, 102, 11-24 https://doi.org/10.1007/BF01178514
- Bert, C.W., Wang, X. and Striz, A.G (1994b), 'Convergence of the DQ method in the analysis of anisotropic plates', J. Sound Vib., 170, 140-144 https://doi.org/10.1006/jsvi.1994.1051
- Celep, Z. (1998a), 'Circular plate on tensionless Winkler foundations', J. Eng. Mech., 114(10), 1723-1739
- Celep, Z. (1998b), 'Rectangular plates resting on tensionless elastic foundation', J. Eng. Mech., 114(12), 2083-2092
- Chen, C.N. (1998), 'Solution of beam on elastic foundation by DEQM', J. Eng. Mech., 124(12), 1381-1384 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1381)
- Chen, W and Zhong, T. (1997), 'The study on the nonlinear computations of the DQ and DC methods', Numerical Methods for Partial Differential Equations, 13, 57-75 https://doi.org/10.1002/(SICI)1098-2426(199701)13:1<57::AID-NUM5>3.0.CO;2-L
- Chen, W, Shu, C., He, W and Zhong, T. (2000), 'The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates', Comput. Struct., 74, 65-76 https://doi.org/10.1016/S0045-7949(98)00320-4
- Du, H., Liew, K.M. and Lim, M.K. (1996), 'Generalized differential quadrature method for buckling analysis', J. Eng. Mech., 122(2), 95-100 https://doi.org/10.1061/(ASCE)0733-9399(1996)122:2(95)
- Feng, Y. and Bert, C.W. (1992), 'Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam', Nonlinear Dynamics, 3, 13-18 https://doi.org/10.1007/BF00045468
- Hong, T., Teng, J.G and Luo, Y.F. (1999), 'Axisymmetric shells and plates on tensionless elastic foundations', Int. J. Solids Struct, 25, 4166-4299
- Jang, S.K, Bert, C.W. and Striz, A.G (1989), 'Application of differential quadrature to static analysis of structural components', Int. J. Numer. Meth. Eng., 28, 561-577 https://doi.org/10.1002/nme.1620280306
- Kuo, Y.H. and Lee, S.Y. (1994), 'Deflection of nonuniform beams resting on a nonlinear elastic foundation', Comput. Struct., 51(5),513-519 https://doi.org/10.1016/0045-7949(94)90058-2
- Li, H. and Dempsey, J.P. (1988), 'Unbonded contact of a square plate on an elastic half-space or a Winkler foundation', J. Appl. Mech., 55, 430-436 https://doi.org/10.1115/1.3173694
- Lin, L. and Adams, G.G (1987), 'Beam on tensionless elastic foundation', J. Eng. Mech. Div., 113, 542-553 https://doi.org/10.1061/(ASCE)0733-9399(1987)113:4(542)
- Ma, T.F. (2004), 'Positive solutions for a beam equation on a nonlinear elastic foundation', Mathematical and Computer Modelling, 39, 1195-1201 https://doi.org/10.1016/j.mcm.2004.06.001
- Malik, M. and Bert, C.W. (1995), 'Differential quadrature solutions for steady state incompressible and compressible lubrication problems', J. of Tribology, 116, 296-302
- Malik, M. and Bert, C.W. (1996), 'Implementing multiple boundary conditions in the DQ solution of higherorder PDE's application to free vibration of plates', Int. J. Numer. Meth. Eng., 39, 1237-1258 https://doi.org/10.1002/(SICI)1097-0207(19960415)39:7<1237::AID-NME904>3.0.CO;2-2
- Mishra, R.C. and Chakrabarti, S.K. (1996), 'Rectangular plates resting on tensionless elastic foundation: Some new results', J. Eng. Mech., 122(4), 287-385
- Quan, J.R. and Chang, C.T. (1989a), 'New insights in solving distributed system equations by the quadrature method-I. Analysis', Computers in Chemical Engineering, 13, 779-788 https://doi.org/10.1016/0098-1354(89)85051-3
- Quan, J.R. and Chang, C.T. (1989b), 'New insights in solving distributed system equations by the quadrature method-II. Numerical experiments', Computers in Chemical Engineering, 13, 1017-1024 https://doi.org/10.1016/0098-1354(89)87043-7
- Sharma, S.P. and DasGupta, S. (1975), 'Bending problem of axially constrained beams on nonlinear elastic foundations', Int. J. Solids Struct., 11(7-8), 853-859 https://doi.org/10.1016/0020-7683(75)90007-4
- Shen, H.S. and Yu, L. (2004), 'Nonlinear bending behavior of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations', Int. J. Solids Struct, 41, 4809-4825 https://doi.org/10.1016/j.ijsolstr.2004.02.013
- Sherbourne, A.N. and Pandey, M.D. (1991), 'Differential quadrature method in the buckling analysis of beams and composite plates', Comput. Struct., 40, 903-913 https://doi.org/10.1016/0045-7949(91)90320-L
- Silva, A.R.D., Silveira, R.A.M. and Goncalves, P.B. (2001), 'Numerical methods for analysis of plates on tensionless elastic foundations', Int. J. Solids Struct, 38(10-13),2083-2100 https://doi.org/10.1016/S0020-7683(00)00154-2
- Striz, A.G, Chen, W. and Bert, C.W. (1994), 'Static analysis of structures by the quadrature element method (QEM)', Int. J. Solids Struct, 31, 2807-2818 https://doi.org/10.1016/0020-7683(94)90070-1
- Tomasiello, S. (1998), 'Differential quadrature method: Application to initial-boundary-value problems', J. Sound Vib., 218(4), 573-585 https://doi.org/10.1006/jsvi.1998.1833
- Tsai, N.C. and Westmann, R.E. (1967), 'Beams on tensionless foundation', J. Eng. Mech. Div., 93, 1-12
- Weitsman, Y. (1970), 'On foundations that react in compression only', J. Appl. Mech., 37, 1019-1030 https://doi.org/10.1115/1.3408653
- Weitsman, Y. (1972), 'A tensionless contact between a beam and an elastic half-space', Int. J. Eng. Sci., 10, 73-81 https://doi.org/10.1016/0020-7225(72)90075-4
- Xiao, J.R. (2001), 'Boundary element analysis of unilateral supported Reissner plates on elastic foundations', Comput. Mech., 27(1), 1-10 https://doi.org/10.1007/s004660000207
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