Constrained euler buckling: line contact solution

摘要

We consider elastic buckling of an inextensible beam with hinged ends and fixed end displacements, confined to the plane, and in the presence of rigid, frictionless sidewalls which constrain overall lateral displacements. We formulate the geometrically nonlinear (Euler) problem, and derive complete analytical results for the case of line contacts with the sidewalls. In contrast to the unconstrained problem, we find a rich bifurcation structure, with multiple branches.