Post-buckling analysis of space frames using concept of hybrid arc-length methods

Hybrid arc-length methods have been used for tracing the post-buckling equilibrium path of semirigid elastoplastic space frames. For example, the original implicit arc-length method uses the implicit Newton–Raphson method in both the predictor and the corrector steps, while the explicit arc-length method uses the explicit dynamic relaxation method in both the steps. The explicit and implicit arc-length methods have a clear disadvantage in that both require an excessive number of iterations, and the matrices are often singular. In this study, algorithms for implicit–explicit and explicit–implicit hybrid arc-length methods are developed for use in the predictor and corrector steps, to improve the accuracy and efficiency of the said method. The accuracy and applicability of the proposed methods are investigated by solving examples.