Post-Buckling Analysis of an Elastically-Restrained Column

摘要

The nonlinear problem of the asymmetric snap-through buckling of a cantilever column that is restrained at its tip by a stiff, inclined wire, and loaded laterally by a tip force, admits an exact solution which was determined previously. The structure was found to be imperfection-sensitive if one considers combined extensional stiffnesses of the wire and of the column centerline to play the role of an imperfection. The same problem is now solved using the general Koiter method of analysis for the near post-buckling equilibrium. This present result for the post-buckling load vs. deflection relation for the 'perfect structure' (infinite extensional stiffnesses) is shown to be an asymptotic representation of the corresponding exact result for vanishingly small deflection. At positive deflection, the approximate values for load in the asymptotic representation are less than the exact values. A similar conclusion is drawn for the buckling load vs. imperfection amplitude relation for the imperfect structure (finite extensional stiffnesses). (Author)