Buckling analysis of thin-walled open members—A finite element formulation

In a companion paper, a variational principle based on the principle of stationary complementary energy was developed for the buckling analysis of thin-walled members with open cross-sections. In this paper, the variational principle is adopted to formulate a finite element buckling solution. The formulation successfully incorporates shear deformation effects, a feature that is neglected in most available buckling solutions. By adopting a non-orthogonal coordinate system, the solution successfully captures the transverse load position effect relative to the shear center. A series of examples demonstrate the validity of the finite elements formulated and their applicability to a wide variety of buckling problems. Examples include column flexural and torsional buckling, lateral torsional buckling of beams with a variety of end conditions and subjected to a variety of moment gradients. The formulation is shown to be applicable to beams with mono-symmetric sections. In all cases, the validity of the new solution is assessed and established through comparisons to well-established closed-form and/or numerical solutions.