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In this paper we consider a thin circular elastic plate of thickness t and radius R subjected either to a uniform lateral pressure, p, or to a uniform edge thrust, f. The first loading situation is referred to as a bending problem and the second as a buckling problem. In both cases only rotationally symmetric deformations will be considered so that all deflections and stresses are functions of a single radial coordinate, r.
It is well known that the classical linear theory of plates yields solutions of these problems which are valid only for a limited range of low loads. For larger values of p and f it is necessary to apply non-linear plate theories which allow for finite deflections and account for the interaction of membrane and bending stresses. Thus we employ the von Karman equations [1] which are based on a non-linear theory of elasticity with infinitesimal strains and are valid for flat plates undergoing small but finite displacements. For rotationally symmetric deformations of circular plates these equations reduce to two coupled second order non - linear ordinary differential equations.
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