Buckling and postbuckling behaviors of symmetric/asymmetric double-beam systems

Abstract

Double-beam systems composed of two interconnected parallel beams have become basic mechanical components of modern engineering structures. Focusing on the asymmetric features in boundary conditions and other structural parameters, this paper studies the buckling and postbuckling behaviors of a double-beam system supported on an elastic foundation. The nonlinear governing differential equations of the system are derived by using the Hamilton's principle, and discretized via the differential quadrature method. Then the pseudo-arc length algorithm is adopted to overcome difficulties of numerical continuation around bifurcation points. Compared with single beam systems, double-beam systems exhibit some peculiarities like multivalued critical buckling loads, in-phase and out-of-phase postbuckling paths. Based on the proposed procedures, these buckling and postbuckling behaviors are investigated in detail. For symmetric boundary cases of the two sub-beams, the multivalued critical buckling loads of the system compose a cluster of critical curves that intersect at a point determined only by the critical loads of single beams. Hence a simple criterion based on single beam critical loads is proposed to quickly estimate whether or not the axial loads would trigger the buckling of the system. However for asymmetric boundary cases, the cluster of critical curves locate in a region that depends on the intrinsic double-beam characteristics, and the criterion is revised accordingly. Also for asymmetric systems, some unique features of the out-of-phase postbuckling paths are detected. It is found that their stabilities are quite different from those of symmetric systems, and that strengthening the system stiffness may even trigger the out-of-phase buckling more easily.