A beam contact benchmark with analytic solution

This paper presents a test case to help validate simulation codes for contact problems involving beams. A closed form solution is derived and the comparison made with finite element (FE) implementation that uses mortar method enforcing constraints. The consists of semi-infinite cantilever beam subjected constant distributed load experiencing frictionless straight rigid substrate. Both an Euler-Bernoulli Timoshenko model are considered influence differing kinematic hypotheses analyzed. In force equal along region except at boundary where point appears. On contrary, substrate exerts fully on which decays exponentially from first tends towards applied load. rate decay depends relative shear deformability. Moreover, whereas in transverse discontinuous, it becomes continuous when allowing deformation. An example benchmarking given particular FE code. error respect exact can be computed shown numerical converges analytic mesh refined.