Domain dependence of elastic green's, Hadamard's and Bergmann's functions

Abstract

T he variation of the three-dimensional anisotropic elastic Green's function induced by an infinitesimal perturbation of the shape of an elastically homogeneous body is expressed in terms of the Green's function for the unperturbed body. These variational derivatives are given for both Neumann's and Green's functions, which solve the problem of prescribed boundary tractions and displacements, respectively. Hadamard's function, being defined on the surface of the body, is obtained by letting both arguments of the Green's function tend to the surface. Together with the Green's function for the infinite body it suffices to solve the elastic Dirichlet problem, with the displacement prescribed at the surface of the body. It is also shown how from Bergmann's kernel function (the difference of Neumann's and Green's functions) either of them can be obtained.