Rectangular Thick Plate with Free Edges on Pasternak Foundation
Publication: Journal of Engineering Mechanics
Volume 120, Issue 5
Abstract
In this paper the work on the thick‐plate equations and their solution for the problem concerning the bending of a rectangular plate with four free edges resting on the Pasternak foundation are described. The basic equations are those obtained from Reissner's 1945 theory, and are modified to include the Pasternak foundation. The solutions of the basic equations are arrived at by superposing the solutions of three elemental plates, one with four guided support edges; the other two with two guided support edges and two free edges acted upon by an unknown bending moment. Finally, numerical examples are also presented to examine the solution for convergence and validation. It shows that the presented solution can be used as a good mechanical model for the analysis of the plate structures supported by elastic foundation, where the transverse shear deformation and the local effects in the plates and the transverse connection in the foundation must be considered.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chou, Y. T. (1983). “Subgrade contact pressures under rigid pavements.” J. Trans. Engrg., ASCE, 109(3), 363–379.
2.
Henwood, D. J., Whiteman, J. R., and Yettram, A. L. (1981). “Finite difference solution of a system of first order partial differential equations.” Int. J. Numerical Methods Engrg., 17(9), 1385–1395.
3.
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. Numerical Methods Engrg., 18(12), 1801–1820.
4.
Huang, Y. H. (1974). “Finite element analysis of slabs on elastic solids.” J. Trans. Engrg., ASCE, 100(2).
5.
Li, J. (1986). “Analysis of a concrete slab system,” M.S. thesis, Tongji University, (in Chinese).
6.
Mindlin, R. D. (1951). “Influence of rotatory inertia and shear on flexural motions of isotopic, elastic plates.” J. Appl. Mech., 18, 31–38.
7.
Pasternak, P. L. (1954). “On a new method of analysis of an elastic foundation by means of two foundation constants.” Gps. Izd. Lit. po Strait. i Arkh. (in Russian).
8.
Reissner, E. (1945). “Effect of transverse shear deformation on elastic plates.” J. Appl. Mech., 12, 69–77.
9.
Reissner, E. (1950). “On a variational theorem in elasticity.” J. Math. and Physics, (Jul.), 90–95.
10.
Shi, X., and Yao, Z. (1986). “The solution of a rectangular thick plate with four free edges resting on an elastic foundation.” J. Mech. Practice, 18(2) (in Chinese).
11.
Westergaard, H. M. (1926). “Stresses in concrete pavements computed by theoretical analysis.” Public Roads, 7(2), 23–35.
12.
Woinowsky‐Krieger, S. (1931). “The state of stress in thick elastic plates.” Ingenieur‐Archiv, 4, 305–331 (in German).
13.
Yao, Z. (1981). “The experimental verification of the theoretical stresses in concrete pavements.” J. Tongji Univ., 9(1), 68–77 (in Chinese).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 120 • Issue 5 • May 1994
Pages: 971 - 988
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Apr 27, 1992
Published online: May 1, 1994
Published in print: May 1994
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.