On the Kelvin, Boussinesq, and Mindlin problems

Three fundamental three-dimensional axisymmetric problems of elasticity are revisited: the Kelvin problem of a concentrated force in an infinite space, the Boussinesq problem of a vertical concentrated force at the boundary of a half-space, and the Mindlin problem of a vertical concentrated force in the interior of a half-space. New elements of the derivation of the solution to each of these problems are included to make the presentation more appealing for the coverage of the topic in graduate courses of solid mechanics. Two approaches are employed and compared, one based on the Galerkin method and Love’s potential function, and the other based on the Papkovich–Neuber displacement representation and Boussinesq’s potential functions. A historical perspective and a referral to more recent contributions in the field are also given.