TABLE OF CONTENTS The Kelvin problem concerns a point force F x in an infinite plane. The solution possesses an apparent similarity to the problem of loading of a wedge apex with a concentrated force (and the Flamant problem), because the stresses must vary as 1/ r to allow the force balance condition to be satisfied on a circle of arbitrary radius.
The first step towards constructing the Kelvin solution is to select the case of axial concentrated force applied at the apex of an elastic wedge with the half-angle ?= ?, which conforms to the general Airy stress function form A=k 1 r ?sin.
We next note that the application of the IntegrateStrain procedure to the strain field arising from this solution leads to the displacement field
It is apparent that the displacement field contains a discontinuity in the displacement component u ? on the line ?=0, i.e., the positive half of the x-axis. Furthermore, the magnitude of this discontinuity is constant along this half-axis and is equal to
We have already encountered a different Airy stress function solution that contained a constant discontinuity of displacement component u ? along the positive half of the x-axis, namely, the dislocation b y solution (5.40) that has the general Airy stress function form k 2 r log r cos ?. It follows that a superposition of these two solutions can be found such...
