Contact Stresses On A Thin Plate After Large Displacements To A Half Parabolic Surface

ABSTRACT:
In a previous report a solution was obtained for the determination of all loads necessary to hold an initially flat, thin, elastic plate in the shape of a prescribed parabolic surface, following large displacement. These loads include spatially varying normal tractions distributed over

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the back surface of the plate, and a uniform shear force and bending moment applied along the opposing edges which become the rims of the parabola after deformation. In actual practice the edge loads are not present and, as a result, local displacement and stress variations arise creating what is known as an edge effect. Furthermore, if the full parabola is separated into two equal halves at the vertex another edge effect occurs. The analysis used to compute the local displacement and stress variations arising near the rim is repeated here to treat the absence of edge loads at the vertex. In addition to the normal stresses which arise, shear stresses result from the absence of the membrane reaction at the vertex, which was present in the case of the full parabolic surface. Correlation between the present theory and data from laser ray trace experiments is also presented.

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