Softening Branches of A Two-degree-of-freedom System Induced By Spatial Buckling

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.