Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges
- Authors
- Kang, JH; Leissa, AW
- Issue Date
- Jul-2005
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- Keywords
- buckling; rectangular plate; exact solution; frobenius method; in-plane buckling load; linearly varying in-plane load
- Citation
- INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, v.42, no.14, pp 4220 - 4238
- Pages
- 19
- Journal Title
- INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
- Volume
- 42
- Number
- 14
- Start Page
- 4220
- End Page
- 4238
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/24576
- DOI
- 10.1016/j.ijsolstr.2004.12.011
- ISSN
- 0020-7683
1879-2146
- Abstract
- An exact solution procedure is formulated for the buckling analysis of rectangular plates having two opposite edges (x = 0 and a) simply supported when these edges are subjected to linearly varying normal stresses sigma(x) = -N-0[1 - alpha(y/b)]/h, where It is the plate thickness. The other two edges (y = 0 and b) may be clamped, simply supported or free, or they may be elastically supported. By assuming the transverse displacement (w) to vary as, sin(m pi x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients, for which an exact solution is obtained as a power series (i.e., the method of Frobenius). Applying the boundary conditions at y = 0 and b yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to retain sufficient terms in the power series in calculating accurate buckling loads, as is demonstrated by a convergence table for all nine possible combinations of unloaded clamped, simply supported or free edges at y 0 and b. Buckling loads are presented for all nine possible edge combinations over the range of aspect ratios 0.5 <= a/b <= 3 for loading parameters a = 0, 0.5, 1, 1.5, 2, for which alpha = 2 is a pure in-plane bending moment. Some interesting contour plots of their mode shapes are presented for a variety of edge conditions and in-plane moment loadings. Because the nondimensional buckling parameters depend upon the Poisson's ratio (v) for five of the nine edge combinations, results are shown for them for the complete range, 0 <= v <= 0.5 valid for isotropic materials. Comparisons are made with results available in the published literature. (c) 2004 Elsevier Ltd. All rights reserved.
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