Differential correction and arc-length continuation applied to boundary value problems: Examples based on snap-through of circular arches

Inspired by the application of differential correction to initial-value problems find periodic orbits in both autonomous and non-autonomous dynamical systems, here is applied boundary-value problems. As a numerical demonstration, snap-through buckling circular arches structural mechanics are selected as examples. Due complicated geometrical nonlinearity such problems, limit points turning might exist. In this case, typical Newton–Raphson method commonly used algorithms will fail cross points. current study, an arc-length continuation introduced enable algorithm capture load-deflection paths. We present rigorous mathematical derivations inside algorithm, for continuation. To show accuracy efficiency correction, we also compare results with software package COCO. The obtained proposed COCO agree well each other, suggesting validity robustness