Treatment of bifurcation points with asymptotic expansion

A method to analyse bifurcation points by establishing bifurcation equations and solving them with an asymptotic expansion method is presented. Bifurcation equations are obtained using a decomposition of the spaces by means of the theory of Lyapunov–Schmidt. To solve these bifurcation equations, an asymptotic expansion along the lines of Koiter is applied. The expansion is presented in a form suited for implementation in a finite element context. It is easy to extend the expansion to higher order terms in order to increase the accuracy. The accuracy of the method is verified with two examples.