Buckling and Sensitivity to Imperfection of Conical Shells Under Dynamic Step-Loading

Abstract

A general nonlinear dynamic analysis, based on Donnell’s shell-type theory, is developed for an arbitrary imperfect isotropic conical shell. It is used for studying dynamic stability and imperfection sensitivity under dynamic step loading. The nonlinear dynamic time history and the sensitivity behavior are examined in parametric terms over a wide range of aspect ratios. A general symbolic code (using the MAPLE compiler) was programmed to create the differential operators. By this means the Newmark discretization, Galerkin procedure, Newton-Raphson iteration, and finite difference scheme are applied for automatic development of an efficient FORTRAN code for the parametric study, and for examining the correlation of the sensitivity behavior between two different dynamic stability criteria. An extensive parametric study of the effect of the cone semi-vertex angle on the stability and sensitivity to imperfection under dynamic step loading was carried out. It was found that the dynamic buckling can indeed be derived from the nonlinear static solution.