Abstract
For problems of non-uniform compression, stability analysis is complicated because it requires the solution for the in-plane force field as a preliminary step. It is the purpose of the present chapter to illustrate this two-step procedure with specific reference to uniaxially compressed rectangular plates.
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Notes
- 1.
These results, as well as the mathematical procedure itself, have been reproduced here with copyright permission from: Prasun Jana, K. Bhaskar, Stability analysis of simply supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane-stress solutions, Thin-Walled Structures, 44, 2006, 507–516 © Elsevier Ltd.
- 2.
Thus, in the absence of body forces, the governing equation in terms of is the same for both plane stress and plane strain problems; the implications of this may be found in any standard book on the theory of elasticity.
- 3.
R. W. Little, Elasticity, Prentice-Hall, 1973.
- 4.
J. H. Kang, A. W. Leissa, Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges, International Jl. of Solids and Structures, 42, 2005, 4220–4238.
- 5.
S. P. Timoshenko, J. M. Gere, Theory of Elastic Stability, McGraw-Hill, 1963.
- 6.
For other possible interpretations of this functional, see: N. A. Alfutov, Stability of Elastic Structures, Springer, 2000.
- 7.
A. W. Leissa, E. F. Ayoub, Vibration and buckling of a simply supported rectangular plate subjected to a pair of in-plane concentrated forces, Jl. of Sound and Vibration, 127, 1988, 155–171.
- 8.
N. A. Alfutov, L. I. Balabukh, On the possibility of solving plate stability problems without a preliminary determination of the initial state of stress, Jl. of Applied Mathematics and Mechanics (PMM), 31(4), 1967, 730–736.
- 9.
H. H. Spencer, H. Surjanhata, The simplified buckling criterion applied to plates with partial edge loading, Applied Scientific Research, 43, 1986, 79–90.
- 10.
Prasun Jana, K.Bhaskar, Analytical solutions for buckling of rectangular plates under non-uniform biaxial compression or uniaxial compression with in-plane lateral restraint, International Jl. of Mechanical Sciences, 49, 2007, 1104–1112.
- 11.
J. Bharat Kalyan, K. Bhaskar, An analytical parametric study on buckling of non-uniformly compressed orthotropic rectangular plates, Composite Structures, 82, 2008, 10–18.
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Bhaskar, K., Varadan, T.K. (2021). Plate Buckling Due to Non-uniform Compression. In: Plates. Springer, Cham. https://doi.org/10.1007/978-3-030-69424-1_13
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DOI: https://doi.org/10.1007/978-3-030-69424-1_13
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