Buckling analysis of thin-walled open members—A complementary energy variational principle

This first of two companion papers develops a new variational principle for the buckling analysis of thin-walled members based on the principle of stationary complementary energy. Some of the aspects of the Vlasov thin-walled beam theory (the rigid cross section assumption, and the stress expressions) are postulated to describe the behavior of members while other aspects of the theory (i.e., the zero shear strain assumption at mid-surface) are discarded. Koiterʹs formulation based on polar decomposition theory in finite elasticity is adopted to formulate expressions for statically admissible stress resultant fields. The stationarity conditions of the complementary energy expression are then evoked to yield the conditions of neutral stability and associated boundary conditions in which the rotation fields appear explicitly. The formulation seamlessly incorporates shear deformation effects and load position effects. Also, the Wagner effect and the mono-symmetry property which arise in displacement based formulations arise in the present formulation in a natural way.