Loading paths for an elastic rod in contact with a flat inclined surface

This paper computes stationary profiles of an isotropic, homogeneous, linearly elastic rod with its endpoint locations and tangents specified. One end of the rod is clamped and the other end makes contact with a flat, rigid, impenetrable surface, which is displaced towards the clamped end. This boundary value problem has applications to biomechanical sensory devices such as mammal whiskers. The paper gives exact analytical solutions to the boundary value problem, embracing the planar equilibrium configurations for both point contact and line contact with the wall. Plots of loading paths for different inclinations of the wall provide an insight into the force-displacement relationship appertaining to real world slender rods under this type of loading. This report is complemented by data obtained from corresponding experimental studies which shed light on the differences between the model, which is based on the mathematical theory of elasticity, and the mechanics of real world long slender bodies, such as mammalian vibrissal systems.