An accurate and efficient implementation of initial geometrical imperfections in the predictor–corrector reduced-order modeling method

Abstract

A predictor–corrector reduced-order modeling method based on Koiter theory is proposed for nonlinear buckling analysis of thin-walled structures with initial geometric imperfections. The imperfections are implemented into the von Kármán kinematics and are considered using an a priori and a posteriori manners, respectively, in buckling analysis. Since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path-tracing, the a priori account of imperfections still shows advantages in computational efficiency. The advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections, which means building once and for all, by simply adding some independent imperfection terms in the reduced system. The a posteriori accounts of imperfections with the first/second-order accuracies, are developed, respectively, to deal with the linear/nonlinear prebuckling behaviors and small/large imperfection amplitudes. The good performance of the proposed method in terms of reliability, accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole-field geometric imperfections.