Evaluation of non-linear buckling loads of geometrically imperfect composite cylinders and cones with the Ritz method

A semi-analytical model to predict the non-linear behavior of unstiffened cylinders and cones considering initial geometric imperfections and various loads and boundary conditions is presented. The formulation is developed using the Classical Laminated Plate Theory (CLPT) and Donnell's equations, solving for the complete displacement field. The non-linear static problem is solved using a modified Newton-Raphson algorithm with line-search. A numerical integration scheme for the non-linear matrices is proposed and details regarding the implementation of the proposed method are given. Two methods to include measured imperfections into the analyses are presented and for one method the effect of using different approximation levels for the imperfection field on the non-linear response is investigated, and a minimum approximation accuracy that should be used is determined. The semi-analytical results are verified using finite elements and previous models from the literature. The implemented routines are distributed on-line and are based on a matrix notation simply applicable to other problems.