A new perspective on variational methods for stability analysis of columns

Summary

The classical linear stability equations for columns take the form of equilibrium equations in terms of displacements. From a variational point of view these equations emerge as conditions of extremum from an energy or virtual work functionals. In principle it should be possible to arrive at the governing equations for stability of columns from a complementary energy or complementary virtual work functional involving force quantities alone. This is rarely done. Both the energy and the complementary energy approaches depend upon the relevant constitutive equations. In this study a formulation is employed wherein focus is maintained on the constitutive equations. It is shown that under certain admissibility conditions a least squares functional, forcing the satisfaction of the constitutive equations, yields the energy and the so-called pure complementary energy functionals as subsets.

By way of illustration, a number of examples of conservative and non conservative column buckling problems are analysed by the procedures outlined.