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The Quarterly Journal of Mechanics and Applied Mathematics 1965 18(1):11-24; doi:10.1093/qjmam/18.1.11
© 1965 by Oxford University Press
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AXISYMMETRICAL BENDING OF A HIGHLY STRETCHED ANNULAR PLATE

W. H. WITTRICK {dagger}

( Department of Aeronautical Engineering, University of Sydney )

This paper is concerned with a thin annular plate bounded by two concentric circular edges. Radial tensions of different magnitudes are applied uniformly at both edges. At one edge the tension lies in the middle plane of the plate, but at the other edge it is applied with an eccentricity of the order of the thickness of the plate. An asymptotic solution is obtained for large values of a parameter P which depends upon the magnitude of the eccentrically applied tension. It is shown that the bending is confined to a narrow boundary layer, and explicit expressions are given for the stresses and displacements at the edges. By an appropriate choice of sign, the results are valid for both of the two possible cases where the eccentric tension is applied at the inner or at the outer edge. The solution for a disk loaded by an eccentrically applied radial tension at its outer edge is deduced from the equations for an annular plate.


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