Symmetric bifurcation of plane frames through a modified potential energy approach

Abstract The modified potential energy approach to the nonlinear analysis of slender elastic beams is employed to investigate the buckling and postbuckling behavior of two symmetric plane frames, namely a hinged portal frame and a hinged two-bar frame, The beams are assumed to be inextensible and shear undeformable. The “hybrid” functional on which the present analysis is based according to a Koiter-type energy approach is obtained from the total potential energy functional by adding extra terms which account for the nonlinear energy associated with the internal forces applied at the beam ends. Thus the nonlinear constraints on the potential energy (expressed in terms of the cross-section rotation φ only), which are associated with the continuity condition relative to the axial and lateral displacement across the joints, are accounted for by introducing the corresponding joint forces as Lagrangian multipliers. The inherent simplicity of the proposed beam model facilitates the postbuckling analysis of the ...