Large‐Deformation Analysis of Plates on Unilateral Elastic Foundation
Publication: Journal of Engineering Mechanics
Volume 120, Issue 8
Abstract
In this technical note, the effect of large deformation on the contact of an axisymmetric circular plate that rests unilaterally on an elastic foundation is investigated. Von Karman's equations for large deformation of a thin plate are modified to include the effect of the unilateral elastic foundation. The coupled equations in terms of the plate vertical displacement and the stress function are discretized using the finite‐difference method, and then solved using an incremental‐iterative algorithm. Results for a circular plate with a central point load are reported for different cases. Unlike the behavior observed in small‐deformation analysis, in which the contact area remains constant, the large‐deformation analysis shows that as the load increases, the contact area tends to expand until full contact is reached. The effects of the foundation modulus and the level of loading on the size of the contact zone and the plate displacement are also investigated.
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References
1.
Celep, A. (1988). “Circular plates on tensionless Winkler foundation.” J. Engrg. Mech. Div., ASCE, 104(10), 1723–1739.
2.
Chia, C. (1980). Nonlinear analysis of plates. McGraw‐Hill, New York, N.Y.
3.
Datta, S. (1975). “Large deflection of a circular plate on elastic foundation under a concentrated load at the center.” J. Appl. Mech., 503–505.
4.
Gladwell, G., and Iyer, K. (1974). “Unbonded contact between a circular plate and an elastic half‐space.” J. of Elasticity, 4(2), 115–130.
5.
Griffiths, D., and Smith, M. (1991). Numerical methods of engineers. Blackwell Scientific Publications, Oxford, England.
6.
Khathlan, A. (1991). “Partial uplift of axisymmetric plates on tensionless elastic foundations.” Azhar 2nd Int. Conf., Al‐Azhar Engineering University, Cairo, 17–26.
7.
Lewandowski, R., and Switka, R. (1991). “Unilateral plate contact with the elastic‐plastic Winkler‐type foundations.” Comp. & Struct., 39(6), 641–651.
8.
Li, H., and Dempsey, J. (1988). “Unbonded contact of a square plate on an elastic half‐space or a Winkler foundation.” J. Appl. Mech., Vol. 55, 430–436.
9.
Ongmahutmongkol, S., and Kawaguchi, M. (1982). “Analysis of circular plate resting on nontension foundation.” Proc. of Japanese Soc. Civ. Engrg., Vol. 318, 167–170.
10.
Sinha, S. (1963). “Large deflection of plates on elastic foundations.” J. Engrg. Mech., ASCE 89, 1–24.
11.
Sokol‐Supel, J. (1989). “Elastoplastic circular plates resting unilaterally on elastic subgrade.” Mech. Struct. & Machines, 16(3), 335–357.
12.
Svec, O. (1974). “The unbonded contact problem of a plate on the elastic half‐space.” Comp. Methods in Appl. Mech. & Engrg., Vol. 3, 105–113.
13.
Villagio, P. (1983). “A free boundary value problem in plate theory.” J. Appl. Mech., Vol. 50, 297–302.
14.
Weitsman, Y. (1970). “On foundations that react in compression only.” J. Appl. Mech., Vol. 37, 1019–1030.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 120 • Issue 8 • August 1994
Pages: 1820 - 1827
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jun 23, 1993
Published online: Aug 1, 1994
Published in print: Aug 1994
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