Summary
The influence of elastic support on the centre deflections and maximum centre and edge moments in clamped parallelogram shaped plates is examined. A polynomial series is assumed for the deflection function, and by applying Galerkin's process, an approximate solution to the governing differential equation is obtained. Convergence of the results were verified. Results for various skew angles and aspect ratios are presented graphically.
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Abbreviations
- 2a, 2b :
-
lengths of the sides of the parallelogram
- a mn :
-
undetermined parameter in series representing the deflection W
- c :
-
= cosine θ
- D :
-
flexural rigidity of plate =Eh 3/[12(1−ν 2)]
- E :
-
Young's modulus
- h :
-
thickness of plate
- k, l, m, n, M, N :
-
positive integers
- p :
-
aspect ratio = b/a
- q :
-
intensity of uniform load
- s :
-
= sine θ
- u, v :
-
oblique co-ordinates
- W :
-
lateral deflection
- x, y :
-
Cartesian co-ordinates
- β :
-
reaction of foundation per unit area for unit deflection
- γ :
-
adjustable constant, zero or one
- ζ :
-
outwardly drawn normal
- η, ξ :
-
dimensionless oblique co-ordinates equal to v/b and u/a respectively
- θ :
-
skew angle
- ν :
-
Poisson's ratio
References
Timoshenko, S. P. and S. Woinowsky-Krieger, Theory of Plates and Shells, p. 259, McGraw-Hill, New York, 1959.
Sinha, S. N., J. Eng. Mech. Div., ASCE 89 (1963) 1.
Ng. S. and J. B. Kennedy, Trans. E.I.C. 9, No. A-5 (1966).
Duncan, W. J., Galerkin's method in mechanics and differential equations, Report and Memoranda No. 1798, Aug. 1937.
Kennedy, J. B., J. Roy. Aero. Soc. 69 (1965) 352.
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Kennedy, J.B. Influence of elastic support on the bending of parallelogram plates. Appl. Sci. Res. 18, 68–80 (1968). https://doi.org/10.1007/BF00382337
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DOI: https://doi.org/10.1007/BF00382337