Solution to the Incorrect Benchmark Shell-Buckling Problem

Abstract

A benchmark, geometrically nonlinear, shell-buckling problem is reviewed and the correct solution is identified and discussed vis-a-vis the incorrect solution from the open literature. The problem is that of a hinged, thin, isotropic cylindrical shell section, point-loaded transversely at the center, undergoing large deformations (5 x thickness). This benchmark problem and solution were introduced in 1972 and have been reproduced in at least 30 journal articles and books in the more than three decades since that time. The benchmark problem is of interest because it demonstrates many features possible in shell buckling, including a load-limit point (snap-through buckling) and a deflection-limit point (snap-down, or snap-back). The benchmark problem is typically used to demonstrate the capability of commercial/private finite element codes to traverse such complicated nonlinear load paths. The existing incorrect benchmark solution involves the nonlinear growth of only symmetric deformation modes. The correct solution to this benchmark problem involves bifurcation from the nonlinear load path into a simple asymmetric deformation mode. Experimental data do not exist for verification of the calculated benchmark response, and so a similar problem using a laminated composite shell is suggested as an alternative benchmark problem for shell stability analysis.