Analysis of post‐buckling branches at multiple symmetric bifurcations

Abstract

SUMMARYA 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 ÿnite 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 veriÿed with three examples.

Analytical and Numerical Investigation of Second-Order Infinitesimal Mechanism in Rigid Origami

“…It is well known that at most (3 𝑛 − 1)∕2 bifurcation (secondary) paths exist for a structure with 𝑛-fold symmetric bifurcation points [31,32]. Magnusson [33] pointed out there may be more than (3 𝑛 − 1)∕2 bifurcation paths for a special case. Ohsaki and Ikeda investigated imperfection sensitivity of a limit point with many bifurcation points [34].…”

Improvement of the Postbucklng Behavior of Imperfection-Sensitive Elastic Structures

“…Recently, Magnusson has used such expansions for the treatment of bifurcation points (Magnusson, 2000) and the analysis of post-buckling branches of multiple symmetric bifurcations (Magnusson, 2001).…”