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Circular plates partially resting on an elastic foundation

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Summary

The axisymmetric problem of a circular plate partially resting on a smooth elastic foundation and subjected to uniform load distribution has been studied in view ofReissner's thick plate theory. Various edge loadings have been considered. The results contain the case of rigid foundation and those predicted by classical theory, in the limiting case. Numerical results are given in the form of graphs and tables.

Zusammenfassung

Das rotationssymmetrische Problem einer teilweise elastisch aufliegenden Kreisplatte unter gleichförmiger Last und verschiedenen Randbedingungen wird mittels derReissnerschen Theorie dicker Platten studiert. Die Ergebnisse beinhalten die starre Auflagerung und die klassische Theorie als Grenzfälle. Numerische Ergebnisse werden in Kurvenform und Tabellen angegeben.

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Abbreviations

a :

radius of plate

b :

radius of the region of foundation

h :

plate thickness

D :

Eh 3/12(1−Eh 2), flexural rigidity of plate

ν:

Poisson's ratio

k :

Modulus of the elastic foundation

p 0 :

uniform load distribution

w :

lateral deflection of plate

r, θ:

cylindrical coordinates

M r, M0 :

radial and tangential bending moments of plate

V r :

shear stress resultant

α r :

slope of the plate

q 2 :

reaction due to elastic foundation

i :

\(\sqrt { - 1} \)

J n, Yn :

Bessel function of first and second kind, and of ordern

References

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, India

    N. Gajendar

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  1. N. Gajendar
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With 2 Figures

The contents of this paper form a part of author's Ph. D. thesis submitted to Indian Institute of Technology, Kharagpur in 1965.

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Gajendar, N. Circular plates partially resting on an elastic foundation. Acta Mechanica 4, 336–348 (1967). https://doi.org/10.1007/BF01591576

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  • DOI: https://doi.org/10.1007/BF01591576

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