The plane problem for a nonhomogeneous elastic circular domain: PMM Vol. 37, N°1, 1973, pp. 106–113

Abstract

We consider the problem of a layered-nonhomogeneous body such that the elastic constants of the isotropic medium depend exponentially on the Cartesian coordinates. Poisson's ratio is assumed to be constant. Making use of the Airy stress function and of expansions with respect to a small parameter, we construct the solution of the first fundamental boundary value problem of the plane elasticity theory for a circular domain when the circumference we are given the radial stresses as continuous functions of bounded variation of the polar angle. This problem has been investigated in [1] by the method of successive approximations with the aid of the complex representations given by the authors of [2–4]. The convergence of the successive approximation process has not been proved. In problems with nonhomogeneous elasticity the complex representation present no advantage, therefore we will apply the Airy function method in that version in which it was used in [5], in conjunction with expansions with respect to a small parameter, characterizing the nonhomogeneity. We give a recursion process in order to compute the functions which are the coefficients of the power series and we prove the convergence of this series. An example is given.