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Bending of Curvilinear and Rectilinear Polygonal Plates Symmetrically Loaded Over a Concentric Circle

Published online by Cambridge University Press:  24 October 2008

W. A. Bassali  and
N. O. M. Hanna
W. A. Bassali
Affiliation:
Faculty of Science University of AlexandriaAlexandria, Egypt
N. O. M. Hanna
Affiliation:
Faculty of Engineering Ain Shams UniversityCairo, Egypt
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Abstract

Complex variable methods are applied to obtain exact solutions for the complex potentials and deflexions of thin isotropic slabs bounded by regular curvilinear polygonal contours with n sides and subject to symmetrical loading distributed over a concentric circle. The supported boundary is either clamped or has equal boundary cross-couples. The plates taken in the z-plane are conformally mapped on the unit circle in the ζ-plane by the mapping function . Polynomial approximations to the Schwarz—Christoffel transformations are then used to discuss the bending of clamped and simply supported rectilinear plates symmetrically loaded over a concentric circle or acted upon by a central point load.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 166 - 179
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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