Asymptotics for thin elastic fibers in unilateral contact
Abstract
What is the contact condition in a 1D beam‐model and is it possible to obtain the frictional moments and forces from the 3D traction? If it is possible does the cross‐section of the beams influence these values? These questions motivate to study the dimension reduction of a 3D contact problem for beams. This paper is a continuation of [1]. In [1] the asymptotic dimension reduction of a Robin‐type elasticity boundary value problem was presented. In this work the explicit relation between a 3D contact problem and a 3D Robin‐type elasticity boundary value problem are established and the 1D equations derived in [1] are interpreted as 1D contact conditions, further some numerical examples are shown.
