A free boundary problem and stability for the nonlinear beam

摘要

AbstractThe stability bound for the classical nonlinear Euler beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a forceP>P0, whereP0denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.