Some Elementary Distributions of Stress in Three Dimensions

A force is applied to an isotropic elastic solid, either at an internal point, or on a plane boundary, or at the vertex of a cone, and it is required to find the distribution of stress.If we make the assumption that the stresses vary inversely as the square of the distance from the point of application of the force, we arrive at a series of elementary solutions of which those suitable for the present problems are here communicated.These elementary solutions must of course include those at the base of the classical works of Thomson and Tait,* Boussinesq,f and Cerruti on the infinite solid and the solid with an infinite plane boundary. The General Equations.Introducing the polar components of force X, Y, Z, these equations are known to be equivalent to z = o, * Love, Elasticity, $161.