The Shanley model concept is used for simulating the elastic non-linear interaction between local buckling and overall buckling of thin-walled columns subjected to axial compression. The spring foundation is given a general macro material form for representing the local buckling response typical for thin walled cross-sections. For geometrically perfect columns, analytical post-buckling solutions are derived valid for any cross-sectional shape. For geometrical imperfect columns, a numerical procedure is proposed. The numerical method is based on a perturbation scheme with arc length control applied in an incremental procedure. It is demonstrated that the numerical method is able to trace unstable equilibrium paths with sharp peaks in the load-deflection space.
Further, a simplified two-degree of freedom macro material model is developed, applicable to panels with open thin-walled stiffener profiles. Included in the cross-sectional macro model is plate buckling interacting with sideways/torsional buckling of the free stiffener outstand and buckling of the stiffener web plate.
The present analytical and numerical study verifies that the recognised reduced modulus is an important parameter in the non-linear elastic interaction between local and overall buckling of stiffened panels.