A simple method to follow the postbuckling paths in the finite element
analysis is presented. During a standard path-following by means of a
re-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 simpl
e 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 f
ollow the required postbuckling branches at bifurcation points, the as
ymptotic postbuckling solution at the approximate bifurcation points,
and the initial postbuckling behavior based on Koiter's theory are giv
en and used for the branch-switching. Some numerical examples of postb
uckling behavior of metallic as well as laminated composite structures
are computed using a ''quasi-conforming'' triangular shell element to
demonstrate the proposed method.