Love's rectangular contact problem revisited: A complete solution

Love's rectangular contact solution was recognized as the key ingredient in developing fast Fourier Transform related algorithms for computational contact analyses. This paper proposes an effective notation to simplify the analytical derivations, which are only carried out on the primitive functions. The complete solution of the stresses and displacements, together with the surface deflection, produced by the both uniform normal and tangential loadings over a rectangular patch are solved in a more compact and consistent way, with explicit closed-form solutions optimized for computational efficiency and numerical stability. The correlation to the Green's functions due to Boussinesq and Cerruti is also noted. The present work complements the existing literature and provides a complete reference to the classical contact solution.