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The Quarterly Journal of Mechanics and Applied Mathematics 1960 13(4):462-471; doi:10.1093/qjmam/13.4.462
© 1960 by Oxford University Press
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UNIFORMLY STRETCHED PLATES SUBJECTED TO CONCENTRATED TRANSVERSE FORCES

ARNOLD D. KERR

( Institute of Mathematical Sciences, New York University )

This paper contains a study of the behaviour of isotropic elastic plates of various shapes subjected to uniform tension in the plane of the plate and loaded transversely by concentrated forces.

The deflexion w of the plate is governed by the partial differential equation {Delta}{Delta}w— (N/D){Delta}w= O, where N is the tension intensity per unit length and D is the flexural rigidity of the plate. The fundamental deflexion function (Green's function for an unbounded domain) is determined and used in connexion with the method of images to construct solutions for plates of various shapes, simply supported along their boundaries.

Solutions are obtained for (a) the wedge-shaped plate with opening angle {alpha} = {pi}/m (m = 1, 2, 3,...) and (b) the rectangular plate. It is shown that the rectangular corner plate, the infinite and semi-infinite strip, can be obtained as special cases. The rectangular corner plate is discussed in more detail.


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