Asymptotic formula for the flexible bar

Abstract The postbuckling of an elastica bar is studied through an eigenvalue perturbation about the bifurcation point. The 4-term series is found to be highly accurate, valid up to the complete collapse of the bar. The result is particularly useful for analyzing systems containing flexible pinned–pinned elements. Two examples using such elastica links are illustrated. The present method is much more simpler than using elliptic functions or direct numerical integration.