A general solution of equations of equilibrium in linear elasticity

A general solution of equations of equilibrium in linear elasticity is presented in cylindrical coordinates in terms of three harmonic functions describing an arbitrary displacement field. The structure of this solution is similar to the general solution given by Love (Kelvin’s solution) in spherical coordinates. Galerkin vector representation of our solution leads to an integral connecting the harmonic functions. The connections to Papkovich–Neuber and Muki’s general representations are also provided. Suitable choices of the harmonic functions in our new representation yield general solutions for axisymmetric deformations due to Love, Boussinesq and Michell. Some unbounded deformations induced by singular forces are tabulated in terms of the scalar harmonic functions to justify the simple nature of our representation. Exact solution of the half-space boundary value problem is also provided to demonstrate the power of our approach. The stress components computed via our solution are also listed (see the Appendix).