Unilaterally Supported Beam by an Elastic Obstacle

Abstract

We study a simple model of a spring or beam in ID given by a second order ODE and homogeneous Dirichlet boundary conditions. We assume that the spring/beam is unilaterally supported from below on a part of the domain by a soft/elastic obstacle. We focus on the dependence of the critical forces (which stress the beam and cause its buckling) on the strength/elasticity parameter of the obstacle. We present both analytical and numerical results.