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Experimental Mechanics

, Volume 20, Issue 10, pp 365–368 | Cite as

The large deflection of thin plates with overhang

A special method of successive approximations is applied to the solution of a practically motivated, nonlinear problem of the bending of a uniformly loaded circular plate supported on a concentric circle
  • H. C. Lee
  • C. K. Lim
  • H. D. Conway
Article
  • 65 Downloads

Abstract

This investigation concerns the application of a special method of successive approximations to the solution of a practically motivated, nonlinear problem of the bending of a uniformly loaded circular plate supported on a concentric circle. Numerical results are obtained for a range of plate-radius/support-radius ratios, and the former are found to be in good agreement with the results of experiments.

Keywords

Mechanical Engineer Fluid Dynamics Nonlinear Problem Thin Plate Special Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a

outer radius of plate

b

support radius of plate

h

plate thickness

q

pressure on plate

r

arbitrary plate radius

w

plate deflection

w0

central plate deflection

x

(a2r2)/a2

D

flexural rigidityEh3/12(1−v2)

E

modulus of elasticity

Nr

radial membrane force per unit width

Nt

tangential membrane force per unit width

Q

[3(1−v2)]3/2qa4/4Eh4

S

3(1−v2)a2N r /Eh3

T

3(1−v2)a2N t /Eh3

W

\(\sqrt 3 \)(1 -v2)w/h

β

1−b2/a2

γ

b/a

v

Poisson's ratio

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References

  1. 1.
    Timoshenko, S. andWoinowski-Krieger, S., “Theory of Plates and Shells,”McGraw-Hill, New York, 2nd edition, 82 (1959).Google Scholar
  2. 2.
    Ibid., 398.Google Scholar
  3. 3.
    Way, S., “Bending of Circular Plates with Large Deflection,”Trans. ASME,56,627 (1934).Google Scholar
  4. 4.
    Timoshenko and Woinowsky-Krieger, 396.Google Scholar
  5. 5.
    Vei-Chan, T. andKai-Yoan, E., Acta Physica Sinica,10 (3),209 (1954).Google Scholar
  6. 6.
    Lim, C.K. and Kuklentz, R.J., “Application of the Digital Computer to an Accelerated Fatigue Model,” Use of Computers in the Fatigue Laboratory, ASTM STP 613, 126 (1976).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1980

Authors and Affiliations

  • H. C. Lee
    • 1
  • C. K. Lim
    • 1
  • H. D. Conway
    • 2
  1. 1.Systems Products DivisionIBM CorporationEndicott
  2. 2.Theoretical and Applied MechanicsCornell UniversityIthaca

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