A nonlinear beam finite element for the post-buckling analysis of plane frames by Koiterʹs perturbation approach Original Research Article

A nonlinear finite element of plane beam oriented to Koiterʹs perturbation analysis of frames is presented. The locking problem arising in the calculation of the post-critical curvature is thoroughly examined and solved at the continuum level, by means of a suitable definition of the kinematic settings. The proposed strain measures are Lagrangian and rationally founded (geometrically exact). The exact solutions of the critical problem have been chosen as shape functions of the finite element, so obtaining an immediately convergent finite element in the calculation of the critical load and of the post-critical slope.