Buckling of Elastic Columns Using Convex Model of Uncertain Springs

Abstract

A procedure is described for evaluating the buckling load of weightless prismatic columns with uncertain rotational spring elements. The uncertainty in the spring elements is expressed in terms of a nonprobabilistic convex model. An ellipsoidal bound is used that defines the uncertainty in terms of a size parameter and the deviations of the spring constants from their nominal values. The size parameter represents the size of the ellipsoid and is analogous to the standard deviation magnitude in probabilistic analyses. The semiaxes of the ellipsoid are the deviations of the spring constants from their nominal values and they determine the shape of the ellipsoid. A first-order analysis shows that the reduction in the buckling load when uncertainty in the spring stiffnesses is present, is a linear function of the size parameter and a nonlinear function of the semiaxes of the uncertainty ellipsoid. For columns for which more than one buckling mode is possible, different reductions in the value of the buckling load result in each mode for the same uncertainty in the spring element stiffnesses.