On generalized Kelvin solutions in a multilayered elastic medium (Q1904622)

An elastic layer of finite thickness made of \(n\) dissimilar homogeneous isotropic elastic layers adheres two dissimilar homogeneous isotropic elastic half-spaces. The interfacial conditions are assumed to be fully bonded (continuity of the displacement and traction vector fields), and an elastostatic state (displacement, strain and stress) is produced either by a concentrated force acting on an internal point of the \(k\)-th layer \((k = 0, 1, 2, \dots, n)\), or by a force uniformly concentrated on a circle situated in the \(k\)-th layer in parallels to the interface planes. The elastostatic state for such an infinite layered body is obtained in the form of double improper integrals, by combining a Fourier-Hankel transform method with a backward transfer matrix technique, and the integrals are analysed with regard to their convergence and singular properties. Numerical results obtained by computer programs for the integral solutions are included. The reviewer notes a number of misprints, e.g. (i) the definitions of symbols \(R\) and \(R_a\) below (24a) and (26), respectively, have little to do with eqs. (24a) and (26); (ii) the reference item [45] on pages 11, 18 and 21 should read [46].