Post-critical analysis of structures with a nonlinear pre-buckling state in the presence of imperfections

摘要

In the context of the geometrically nonlinear analysis of structures by continuation methods, a technique for the determination of the imperfection sensitivity is carried out. The technique is based on Galerkin's reduction of equilibrium equations in the subspace of extrapolation branches emanating from the bifurcation points. The pre- and post-critical behaviour in the neighbourhood of bifurcation points, however, is well approximated provided that ex- trapolations have a large convergence domain. To this end an efficient asymptotic representation of the primary and secondary equilibrium paths and procedures that overcome the ill-conditioning of the systems defined in the critical points is used here.