A simple method to follow post-buckling paths in finite element analysis

Abstract

A simple method to follow the postbuckling paths in the finite element analysis is presented. During a standard path-following by means of arc-length method, the signs of diagonal elements in the triangularized tangent stiffness matrix are monitored to determine the existence of singular points between two adjacent solution points on paths. A simple approach to identify limit or bifurcation points is developed using the definition of limit points and the idea of generalized deflections. Instead of the exact bifurcation points, the approximate bifurcation points on the secants of the solution paths are solved. In order to follow the required postbuckling branches at bifurcation points, the asymptotic postbuckling solution at the approximate bifurcation points, and the initial postbuckling behavior based on Koiter's theory are given and used for the branch-switching. Some numerical examples of postbuckling behavior of metallic as well as laminated composite structures are computed using a “quasi-conforming” triangular shell element to demonstrate the proposed method.