Buckling of Unilaterally Constrained Infinite Plates
Publication: Journal of Engineering Mechanics
Volume 124, Issue 2
Abstract
The problem of finding the buckling load of unilaterally constrained infinite plates is considered. The plates are modeled along the lines of classical plate theory employing Kirchhoff-Love hypotheses. The condition of contact at buckling, which renders the problem to be of the nonlinear eigenvalue type, is resolved by modeling the plate as having two distinct regions, a contacted and an uncontacted region. This results in a problem of the linear eigenvalue type. Simply supported and clamped-free boundary conditions on the unloaded edges are considered. An exact solution for the case of a simply supported plate resting on a rigid foundation is derived. Plates made up of isotropic as well as different orthotropic materials are examined. Due to the constraint on the deformation being one-sided, an increase in the buckling load of approximately 30% over the unconstrained situation is obtained. This study clearly shows that the neglect of unilateral constraints in a plate buckling problem can lead to inaccurate results, which in turn will lead to poor estimates, for example, in assessing the residual compressive stiffness of delaminated plates.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Allan, T.(1968). “One-way buckling of a compressed strip under lateral loading.”J. Mech. Engrg. Sci., 10(2), 173–181.
2.
Celep, Z.(1988). “Rectangular plates resting on tensionless elastic foundations.”J. Engrg. Mech., ASCE, 114(12), 2083–2092.
3.
Chai, H., Babcock, C., and Knauss, W.(1981). “One dimensional modeling of failure in laminated plates by delamination buckling.”Int. J. Solids and Struct., 17(11), 1069–1083.
4.
Civelek, M. B., and Erdogan, F. (1976). “Interface separation in a frictionless contact problem for an elastic layer.”J. Appl. Mech., (March), 175–177.
5.
Fung, Y. C. (1965). Foundations of solid mechanics. Prentice-Hall, Inc., Englewood Cliffs, N.J.
6.
Gladwell, G. M. L. (1976). “On some unbonded contact problems in plane elasticity theory.”J. Appl. Mech., (June), 263–267.
7.
Kooi, B. W.(1985). “A unilateral contact problem with the heavy elastica solved by use of finite elements.”Comp. and Struct., 21(1/2), 95–103.
8.
Roorda, J. (1988). “Buckles, bulges and blow-ups.”Applied solid mechanics, A. S. Tooth and J. Spence, eds., Elsevier Applied Science, New York, N.Y., 347–380.
9.
Seide, P. (1958). “Compressive buckling of a long simply supported plate on an elastic foundation.”J. Aeronautical Sci., (June), 382–392.
10.
Shahwan, K. W. (1995). “Buckling, postbuckling and non-self-similar decohesion along a finite interface of unilaterally constrained delaminations in composites,” PhD dissertation, Dept. of Aerosp. Engrg., The Univ. of Michigan, Ann Arbor, Mich.
11.
Shahwan, K., and Waas, A. (1991). “Elastic buckling of infinitely long specially orthotropic plates on tensionless foundations.”J. Engrg. Mat. and Technol., (October), 396–403.
12.
Soong, T. C., and Choi, I.(1986). “An elastica that involves continuous and multiple discrete contacts with a boundary.”Int. J. Mech. Sci., 28(1), 1–10.
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Feb 1, 1998
Published in print: Feb 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.