Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a posteriori the effects of the imperfections in the reduced nonlinear equations. The state-of-art treatment of geometrical imperfections is accurate only for small imperfection amplitudes and linear pre-critical behaviour. This work enlarges the validity of the method to a wider range of practical problems through a new approach, which accurately takes into account the imperfection without losing the benefits of the a posteriori treatment. A mixed solid-shell finite element is used to build the discrete model. A large number of numerical tests, regarding nonlinear buckling problems, modal interaction, unstable post-critical and imperfection sensitive structures, validates the proposal. Copyright © 2017 John Wiley & Sons, Ltd.