Buckling and post-buckling in a two-bar frame: a qualitative approach

A direct one-dimensional beam model has the kinematics described by the axis displacement, the rotation of the cross-sections and an average measure of warping. Mechanical actions on the beam are the dual of the velocities. Balancing external and internal power yields local balance equations for the mechanical actions. Shear indeformability and a linear relationship between twist and warping are assumed as inner constraints; non-linear hyperelastic constitutive relations are formulated. Field equations in terms of displacements are obtained, and the possibilities of buckling in a two-bar frame are examined. The critical load is found for both the in- and the out-of-plane bifurcation. In the latter case, the post-buckling path is investigated.