Constrained Euler buckling: an interplay of computation and analysis Original Research Article

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 develop global search and path-following algorithms to find equilibria in various classes satisfying different contact patterns and hence boundary conditions. We derive complete analytical results for the case of line contacts with the sidewalls, and partial results for point contact and mixed cases. The analysis is essential to understanding the numerical results, for in contrast to the unconstrained problem, we find a very rich bifurcation structure, with the cardinality of branches growing exponentially with mode number.