Geometrically nonlinear finite element behaviour using buckling mode superposition

Within the context of finite element analysis a method is presented for analysing the geometrically nonlinear static behaviour of thin-type structures under one-parametric, conservative loading. The method is applicable in cases of mild geometrical nonlinearities, which are characterized by the existence of a linear bifurcation situation which is “close” to the considered situation. In this case the true nonlinear behaviour in the initial loading range can be quite well approximated by a linear combination of the eigenvectors of the linear buckling problem where the coefficients of combination are nonlinear functions of the load parameter and are easily computable from the eigenvalues, eigenvectors and the applied loading. A comprehensive treatment of this method of linear buckling mode superposition is given, including theoretical derivations, physical interpretation, software implementation, computational considerations and selected application examples which illustrate the basic nature of the method.