Secondary bifurcations and localisation in a three-dimensional buckling model

This paper revisits the effect of secondary bifurcations on the post-buckling response of a simple 3D system of elastically restrained beams, first discussed by Luongo in [19]. Our main objective is to show how to construct a uniform asymptotic expression for the localised buckling patterns experienced by this model. The governing equation is formulated as a fourth-order eigenvalue problem with non-constant coefficients and then a complex WKB technique is employed to yield the localised instability patterns. Numerical simulations supporting the analytical findings are included as well.