Abstract

This paper contains an exact solution for the stress distribution in an elastic sphere under two equal and opposite concentrated loads, applied at the end points of a diameter. The solution is based on the Boussinesq stress-function approach to axisymmetric problems and is represented as a sum of two solutions: A singular solution in closed form, and a series solution corresponding to surface tractions which are finite and continuous throughout the surface of the sphere. It is shown that the singularity at the points of application of the loads is not identical with that arising at a concentrated load acting normal to a plane boundary. The existence of pseudosolutions to the problem under consideration, as well as to concentrated-force problems in general, is illustrated, and the validity of the present solution is confirmed through a limit process applied to the case of tractions uniformly distributed over a portion of the boundary. The numerical results for the normal stress on the plane of symmetry perpendicular to the load axis, are compared with the corresponding stress values obtained in a recent three-dimensional photoelastic investigation of the same problem by Frocht and Guernsey (1).

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