### Analytical bending solution of fully clamped orthotropic rectangular plates resting on elastic foundations by the finite integral transform method

Document Type : Research Paper

Authors

1 Faculty of Mechanical Engineering, College of Engineering, University of Tehran, iran

2 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract

This study presents exact bending solution of fully clamped orthotropic rectangular plates subjected to arbitrary loads resting on elastic foundations, based on the finite integral transform method. In this method, it is not necessary to determine the deformation function because the basic governing equations of the classical plate theory for orthotropic plates have been used‌. A detailed parametric study is conducted to elucidate the influences of stiffness of elastic medium, plate length, flexural rigidities and distributed transverse load on the deflections. The applicability of the method is extensive since it can solve any plates with different loadings. Numerical results are presented to demonstrate the validity and accuracy of the approach, as it is totally in agreement with the other studies.

Keywords

Main Subjects

[1] Timoshenko, S. P. and Woinowsky-Krieger, S. W., Theory of Plates and Shell, McGraw-Hill, New York, 1959.
[2] Li, R., Zhong, Y., Tian, B., Liu, Y., “On the finite integral transform method for exact bending solutions of fully clamped orthotropic rectangular thin plates”, Applied Mathematics Letters, Vol. 22, pp. 1821–1827, 2009.
[3] Pan, B., Li, R., Su, Y., Wang, B., Zhong, Y., “Analytical bending solutions of clamped rectangular thin plates resting on elastic foundations by the symplectic superposition method”, Applied Mathematics Letters, Vol. 26, pp. 355–361, 2013.
[4] Chang, F. V., “Bending of a cantilever rectangular plate loaded discontinuously”, Applied Mathematics and Mechanics, Vol. 2, pp. 403–410, 1981.
[5] Lim, C. W., Cui, S., Yao, W. A., “On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported”, International Journal of Solids and Structures, Vol. 44, pp. 5396–5411, 2007.
[6] Lim, C. W., Yao, W. A., Cui, S., “Benchmarks of analytical symplectic solutions for bending of corner supported rectangular thin plates”, IES Journal Part A: Civil & Structural Engineering, Vol. 1, pp. 106–115, 2008.
[7] Vallabhan, C. V. G., Straughan, W. T., Das, Y. C., “Refined model for analysis of plates on elastic foundations”, Journal of Engineering Mechanics-ASCE, Vol. 117, pp. 2830-2844, 1991.
[8] Huang, M. H., Thambiratnam, D. P., “Analysis of plate resting on elastic supports and elastic foundation by finite strip method”, Computers & Structures, Vol. 79, pp. 2547-2557, 2001.
[9] Civalek, Ö., Ulker, M., “Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates”, Structural Engineering and Mechanics, Vol. 17, pp. 1–14, 2004.
[10] Barton, M. V., “Finite difference equations for the analysis of thin rectangular plates with combinations of fixed and free edges”, Defense Research Lab. Rep. No. 175, Univ. of Texas, 1948.
[11] Civalek, O., “Three dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method”, International Journal of Mechanical Sciences, Vol. 49, pp. 752–765, 2007.
[12] Shao, W., Wu, X., “Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation”, Engineering Analysis with Boundary Elements, Vol. 35, pp. 389-394, 2011.
[13] Zenkour, A. M., Allam, M. N. M., Sobhy, M., “Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations”, Archive of Applied Mechanics, Vol. 81, pp. 77–96, 2011.
[14] Sneddon, I. N., The Use of Integral Transforms, McGraw-Hill, New York, 1972.
[15] Sneddon, I. N., Application of Integral Transforms in the Theory of Elasticity, McGraw-Hill, New York, 1975.
[16] Li, R., Zhong, Y., Tian, B., Du, J., “Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads”, International Applied Mechanics, Vol. 47, pp. 107-119, 2011.
[17] Li, R., Tian, B., Zhong, Y., “Analytical bending solutions of free orthotropic rectangular thin plates under arbitrary loading”, Meccanica, Vol. 48, pp. 2497-2510, 2013.