The M Integral Operator: An Application of the Cauchy-Hobson Theory to the Semiinfinite Medium

摘要

A classical problem in the theory of elasticity for which a general solution has been found is that of the semiinfinite elastic solid. Cerruti and Boussinesq were the first to consider a problem where such a region was employed as the vehicle for exposing the boundary value problems of this theory. Specifically, it is assumed that all of the space on one side of a plane is occupied by an ideal elastic continuum, and either the surface displacements or the surface tractions on the bounding plane are prescribed. Since the problem can be formulated in terms of displacements for either case of prescribed surface loading, the problem reduces to finding functions to represent the displacements, and which satisfy the equations of equilibrium at all points within the medium and known conditions on the bounding surface.