Large Deflection of Reissner-Mindlin Plates on Elastic Foundations
Publication: Journal of Engineering Mechanics
Volume 124, Issue 10
Abstract
A large deflection analysis is presented for a rectangular Reissner-Mindlin plate with free edges exposed to a stationary temperature field, subjected to a transverse partially distributed load, and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner-Mindlin plate theory, considering the first-order shear deformation effect and including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of moderately thick plates with free edges subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. In this study, the influence is affected by the foundation stiffness, transverse shear deformation, loaded area, plate aspect ratio, and initial thermal bending stress. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ariman, T. (1967). “On thick elastic plates on an elastic foundation subjected to steady temperature distribution.”Recent advances in engineering science, Vol. 2, Gordon & Breach Science Publishers, Inc., New York, N.Y., 353–369.
2.
Frederick, D.(1957). “Thick rectangular plates on elastic foundation.”Trans. ASCE, 122, 1069–1085.
3.
Ghosh, P. K.(1977). “Large deflection of a rectangular plate resting on a Pasternak-type elastic foundation.”J. Appl. Mech., 44(3), 509–511.
4.
Harik, I. E., Jianping, P., Southgate, H., and Allen, D.(1994). “Temperature effects on rigid pavements.”J. Transp. Engrg., ASCE, 120(1), 127–143.
5.
Henwood, D. J., Whiteman, J. R., and Yettram, A. L.(1982). “Fourier series solution for a rectangular thick plate with free edges on an elastic foundation.”Int. J. Numer. Methods Engrg., 18(12), 1801–1820.
6.
Katsikadelis, J. T., and Kallivokas, L. F.(1988). “Plates on biparameter elastic foundation by BDIE method.”J. Engrg. Mech., ASCE, 114(5), 847–875.
7.
Mindlin, R. D.(1951). “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates.”J. Appl. Mech., 18(1), 31–38.
8.
Mirambell, E. (1990). “Temperature and stress distributions in plane concrete pavements under thermal and mechanical loads.”Proc., 2nd Int. Workshop on Des. and Rehabilitation of Concrete Pavements, 121–135.
9.
Qu, Q., and Liang, X. (1995). “Nonlinear bending of rectangular plates with four free edges on elastic foundation.”China Civ. Engrg. J., China, 28(1), 46–54 (in Chinese).
10.
Reissner, E. (1945). “The effect of transverse shear deformation on the bending of elastic plates.”J. Appl. Mech., 12(2), A69–A77.
11.
Reissner, E.(1950). “On a variational theorem in elasticity.”J. Math. Phys., 29, 90–95.
12.
Shen, H. S.(1995). “Postbuckling analysis of moderately thick rectangular plates on two-parameter elastic foundations.”Engrg. Struct., 17(7), 523–529.
13.
Shen, H. S.(1996). “Thermomechanical postbuckling of imperfect moderately thick plates on two-parameter elastic foundations.”Struct. Engrg. and Mech., 4(2), 149–162.
14.
Shen, H. S.(1997). “Thermal post-buckling analysis of imperfect shear-deformable plates on two-parameter elastic foundations.”Comp. and Struct., 63(6), 1187–1193.
15.
Shi, X. P., Tan, S. A., and Fwa, T. F.(1994). “Rectangular thick plate with free edges on Pasternak foundation.”J. Engrg. Mech., ASCE, 120(5), 971–988.
16.
Sinha, S. N.(1963). “Large deflections of plates on elastic foundations.”J. Engrg. Mech. Div., ASCE, 89(1), 1–24.
17.
Vallabhan, C. V. G., Straughan, W. T., and Das, Y. C.(1991). “Refined model for analysis of plates on elastic foundations.”J. Engrg. Mech., ASCE, 117(12), 2830–2844.
18.
Yang, H. T. Y.(1970). “Flexible plate finite element on elastic foundation.”J. Struct. Div., ASCE, 96(10), 2083–2101.
19.
Yang, T. Y.(1972). “A finite element analysis of plates on a two parameter foundation model.”Comp. and Struct., 2(4), 593–641.
20.
Yettram, A. L., Whiteman, J. R., and Henwood, D. J.(1984). “Effect of thickness on the behaviour of plates on foundations.”Comp. and Struct., 19(4), 501–509.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 10 • October 1998
Pages: 1080 - 1089
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Oct 1, 1998
Published in print: Oct 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.