Green's functions for torsional body force problems of an elastic layer on an elastic half space.

Abstract

Green's functions in a closed form are shown for axisymmetric torsional body force problems of m elastic layer on an elastic half space. A Green's function is defined as a solution to the problem of an elastic layer on an elastic half space subjected to a torsional body force acting on a circle in he interior of the layer. As a special case for Green's functions, we can obtain Green's functions for torsional body force problems of (i) an elastic half space, (ii) an elastic thick plate, and (iii) an elastic layer on a rigid foundation. A general method of solution is presented for torsional body force problems of an elastic layer on an elastic foundation. Green's functions, mentioned above, are obtained by applying the general method of solution. As an example of the application of Green's functions we consider torsion of a hemispherical rigid body embedded in an elastic layer on an elastic foundation. Numerical results for the problem are shown.