In this paper the author discusses mathematically problems concerning the pressures and deformations that arise when a very rigid die or punch is pressed against a comparatively elastic material, and also in the case where column footings rest on an elastic soil foundation. The author considers (1) the case where the axial section of the die is given and the resulting distribution of pressure along the curved contact surface is required; and (2) where the distribution of pressure over the contact surface is prescribed and the proper curvature of the surface to give such a distribution of pressure is required. Solutions of each of these cases are given for two types of die; namely, when the die is a body of revolution, and when it has a rectangular cross-section the dimension of which perpendicular to the plane of the figure is either very large or very small.

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