Constrained Euler buckling: an interplay of computation and analysis

We consider elastic buckling of an inextensible beam with hinged ends and f ixed 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 se arch and path-following algorithms to find equilibria in various classes sa tisfying different contact patterns and hence boundary conditions. We deriv e complete analytical results for the case of line contacts with the sidewa lls, and partial results for point contact and mixed cases. The analysis is essential to understanding the numerical results, for in contrast to the u nconstrained problem, we find a very rich bifurcation structure, with the c ardinality of branches growing exponentially with mode number. (C) 1999 Els evier Science S.A. All rights reserved.