Love's rectangular contact problem revisited: A complete solution

• A complete set of elementary solutions presented in explicit closed-form.
• A novel notation proposed for capturing the special structure of the formulae.
• Optimized primitives suggested for better continuity and numerical stability.
• Connections with Green's function and computational contact analyses noted.

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.

The present work may be utilized as elementary solution for computational contact analyses. This figure shows discretization of the computation domain using a uniform rectangular mesh, with an enlarged view of a typical element loading patch (|x1−x1′|≤∆1/2, |x2−x2′|≤∆2/2) shown at the right.Figure optionsDownload high-quality image (246 K)Download as PowerPoint slide