Analysis of post-buckling branches at multiple symmetric bifurcations

A method to analyse and solve symmetric bifurcations by establishing the bifurcation equations using an asymptotic expansion method is presented. The bifurcation equations are obtained using a decomposition of the spaces by means of the theory of Lyapunov{Schmidt. To solve the bifurcation equations an asymptotic expansion method along the lines of Koiter is applied. The expansion is presented in a form suited for implementation in a nite element context. The present paper is focused on the treatment of symmetric multiple bifurcations where new forms of the bifurcation equations are established. The accuracy of the method is veri ed with three examples