How to cite this paper
Dehghan, M., Nejad, M & Moosaie, A. (2016). An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation.Engineering Solid Mechanics, 4(4), 201-218.
Refrences
Bellman, R., Kashef, B. G., & Casti, J. (1972). Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations.Journal of computational physics, 10(1), 40-52.
Bert, C. W., & Malik, M. (1996). Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews, 49(1), 1-28.
Dehghan, M., & Baradaran, G. H. (2011). Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method. Applied Mathematics and Computation, 218(6), 2772-2784.
Du, H., Lim, M. K., & Lin, R. M. (1994). Application of generalized differential quadrature method to structural problems. International Journal for Numerical Methods in Engineering, 37(11), 1881-1896.
Gupta, U., Sharma, S., & Singhal, P. (2016). DQM modeling of rectangular plate resting on two parameter foundation. Engineering Solid Mechanics,4(1), 33-44.
Lam, K. Y., Wang, C. M., & He, X. Q. (2000). Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions.Engineering Structures, 22(4), 364-378.
Leissa, A. W. (1973). The free vibration of rectangular plates. Journal of Sound and vibration, 31(3), 257-293.
Liew, K. M., & Teo, T. M. (1998). Modeling via differential quadrature method: three-dimensional solutions for rectangular plates. Computer Methods in Applied Mechanics and Engineering, 159(3), 369-381.
Liew, K. M., & Teo, T. M. (1999). Three-dimensional vibration analysis of rectangular plates based on differential quadrature method. Journal of Sound and Vibration, 220(4), 577-599.
Lim, C. W. (1999). Three-dimensional vibration analysis of a cantilevered parallelepiped: exact and approximate solutions. The Journal of the Acoustical Society of America, 106(6), 3375-3383.
Matsunaga, H. (2000). Vibration and stability of thick plates on elastic foundations. Journal of engineering mechanics, 126(1), 27-34.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. ASME Journal of Applied Mechanics, 18, 1031-1036.
Motaghian, S., Mofid, M., & Akin, J. E. (2012). On the free vibration response of rectangular plates, partially supported on elastic foundation.Applied Mathematical Modelling, 36(9), 4473-4482.
Omurtag, M. H., Ozutok, A. & Akoz, A. (1997). Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential. International Journal for Numerical Methods in Engineering, 40(2), 295–317.
Pan, B., Li, R., Su, Y., Wang, B., & Zhong, Y. (2013). Analytical bending solutions of clamped rectangular thin plates resting on elastic foundations by the symplectic superposition method. Applied Mathematics Letters, 26(3), 355-361.
Pasternak, P. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants (in Russian). Gosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Takahashi, K. & Sonoda, T. (1992). Dynamic stability of a rectangular plate on Pasternak foundation subjected to sinusoidally time-varying in-plane load. Theoretical and Applied Mechanics, 7, 55–62.
Teo, T. M., & Liew, K. M. (1999). A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates. International journal of solids and structures, 36(8), 1149-1168.
Thai, H. T. & Choi, D.H. (2014). Zeroth-order shear deformation theory for functionally graded plates resting on elastic foundation. International Journal of Mechanical Sciences, 78, 35–43.
Thai, H. T., Park, M. & Choi, D. H. (2013). A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation. International Journal of Mechanical Sciences, 73, 40–52.
Timoshenko, S. P. & Woinowsky-Krieger, W. (1970). Theory of Plates and Shells. New York: McGraw-Hill.
Ventsel, E. (2001). Thin plates and shells: Theory, Analysis, and Applications. Marcel Dekker Incorporated, New York, USA.
Vimal, J., Srivastava, R., Bhatt, A., & Sharma, A. (2014). Free vibration analysis of moderately thick functionally graded skew plates. Engineering Solid Mechanics, 2(3), 229-238.
Winkler, E. (1867). Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus.
Xiang, Y. (2003). Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations. International journal of mechanical sciences, 45(6), 1229-1244.
Xiang, Y., Wang, C. M., & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International journal of mechanical sciences, 36(4), 311-316.
Zhou, D., Cheung, Y. K., Lo, S. H., & Au, F. T. K. (2004). Three‐dimensional vibration analysis of rectangular thick plates on Pasternak foundation.International journal for numerical methods in engineering, 59(10), 1313-1334.
Bert, C. W., & Malik, M. (1996). Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews, 49(1), 1-28.
Dehghan, M., & Baradaran, G. H. (2011). Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method. Applied Mathematics and Computation, 218(6), 2772-2784.
Du, H., Lim, M. K., & Lin, R. M. (1994). Application of generalized differential quadrature method to structural problems. International Journal for Numerical Methods in Engineering, 37(11), 1881-1896.
Gupta, U., Sharma, S., & Singhal, P. (2016). DQM modeling of rectangular plate resting on two parameter foundation. Engineering Solid Mechanics,4(1), 33-44.
Lam, K. Y., Wang, C. M., & He, X. Q. (2000). Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions.Engineering Structures, 22(4), 364-378.
Leissa, A. W. (1973). The free vibration of rectangular plates. Journal of Sound and vibration, 31(3), 257-293.
Liew, K. M., & Teo, T. M. (1998). Modeling via differential quadrature method: three-dimensional solutions for rectangular plates. Computer Methods in Applied Mechanics and Engineering, 159(3), 369-381.
Liew, K. M., & Teo, T. M. (1999). Three-dimensional vibration analysis of rectangular plates based on differential quadrature method. Journal of Sound and Vibration, 220(4), 577-599.
Lim, C. W. (1999). Three-dimensional vibration analysis of a cantilevered parallelepiped: exact and approximate solutions. The Journal of the Acoustical Society of America, 106(6), 3375-3383.
Matsunaga, H. (2000). Vibration and stability of thick plates on elastic foundations. Journal of engineering mechanics, 126(1), 27-34.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. ASME Journal of Applied Mechanics, 18, 1031-1036.
Motaghian, S., Mofid, M., & Akin, J. E. (2012). On the free vibration response of rectangular plates, partially supported on elastic foundation.Applied Mathematical Modelling, 36(9), 4473-4482.
Omurtag, M. H., Ozutok, A. & Akoz, A. (1997). Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential. International Journal for Numerical Methods in Engineering, 40(2), 295–317.
Pan, B., Li, R., Su, Y., Wang, B., & Zhong, Y. (2013). Analytical bending solutions of clamped rectangular thin plates resting on elastic foundations by the symplectic superposition method. Applied Mathematics Letters, 26(3), 355-361.
Pasternak, P. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants (in Russian). Gosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Takahashi, K. & Sonoda, T. (1992). Dynamic stability of a rectangular plate on Pasternak foundation subjected to sinusoidally time-varying in-plane load. Theoretical and Applied Mechanics, 7, 55–62.
Teo, T. M., & Liew, K. M. (1999). A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates. International journal of solids and structures, 36(8), 1149-1168.
Thai, H. T. & Choi, D.H. (2014). Zeroth-order shear deformation theory for functionally graded plates resting on elastic foundation. International Journal of Mechanical Sciences, 78, 35–43.
Thai, H. T., Park, M. & Choi, D. H. (2013). A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation. International Journal of Mechanical Sciences, 73, 40–52.
Timoshenko, S. P. & Woinowsky-Krieger, W. (1970). Theory of Plates and Shells. New York: McGraw-Hill.
Ventsel, E. (2001). Thin plates and shells: Theory, Analysis, and Applications. Marcel Dekker Incorporated, New York, USA.
Vimal, J., Srivastava, R., Bhatt, A., & Sharma, A. (2014). Free vibration analysis of moderately thick functionally graded skew plates. Engineering Solid Mechanics, 2(3), 229-238.
Winkler, E. (1867). Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus.
Xiang, Y. (2003). Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations. International journal of mechanical sciences, 45(6), 1229-1244.
Xiang, Y., Wang, C. M., & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International journal of mechanical sciences, 36(4), 311-316.
Zhou, D., Cheung, Y. K., Lo, S. H., & Au, F. T. K. (2004). Three‐dimensional vibration analysis of rectangular thick plates on Pasternak foundation.International journal for numerical methods in engineering, 59(10), 1313-1334.