An approximate analysis of the large deflection elastic behaviour of clamped, uniformly loaded, rectangular plates is carried out using a perturbation method. The solutions obtained are presented in a general form which allows the behaviour of a plate having any particular value of aspect ratio to be predicted. The predictions of the present solutions are compared with those of existing solutions where these are available.
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References
1.
BoobnoffI. G.‘On the stresses in ship's bottom plating due to water pressure’, Trans. Instn nav. Archit.190244, 15.
2.
FopplA.FopplL.Drang und Zwang1920, 230–232 (R. Oldenbourg).
3.
HenckyH.‘Die Berechnung dunner rechteckiger Platten mit verschwindender Biegungsteifigkeit’, Z. angew. Math. Mech.19211, 81.
WayS.‘Uniformly loaded, clamped, rectangular plates with large deflections’, Proc. 5th Int. Congr. Appl. Mech., Cambridge, Mass., 1938, 123.
6.
LevyS.‘Square plate with clamped edges under normal pressure producing large deflections’, N.A.C.A. Report No. 740, 1942.
7.
GreenJ. R.SouthwellR. V.‘Problems relating to large transverse displacements of thin elastic plates’, Phil. Trans. R. Soc.1940–46239, (Series A), 539.
8.
WangC. T.‘Bending of rectangular plates with large deflections’, N.A.C.A. Tech. Note No. 1462, 1948.
9.
BergerH. M.‘A new approach to the analysis of large deflections of plates’, J. appl. Mech.195522, 465.
10.
ChienW. Z.YehK. Y.‘On the large deflection of rectangular plates’, Proc. 9th Int. Congr. appl. Mech., Brussels, 19576, 403.
11.
BalachandraM.GopalacharyuluS.‘Large deflections of clamped plate by modified Fourier series’, J. appl. Mech.196532, 943.
12.
MansfieldE. H.The bending and stretching of plates1964 (Pergamon Press).
13.
TimoshenkoS.Woinowsky-KriegerS.Theory of plates and shells1959 (McGraw-Hill).
14.
ClarksonJ.‘Strength of approximately flat long rectangular plates under lateral pressure’, Trans. N.E. Cst Instn Engrs Shipbldrs1957–5874, 21.
15.
HookeR.RawlingsB.‘An experimental investigation of the behaviour of clamped, rectangular, mild steel plates subjected to uniform transverse pressure’, Proc. Instn civ. Engrs196942, (January), 75.