Institute of Fundamental Technological Research

Multiple bifurcations due to symmetry are often encountered when analyzing nonlinear motifs of nano-mechanics or structures with axial multiple symmetry. The location of multiple bifurcation points and bifurcation path tracing become problems in numerical analysis. In this paper, as a solution to this problem, the a priori information of group-theoretic bifurcation theory is applied. By utilizing the irreducible representation of the dihedral group, we propose to represent the initial imperfection vectors according to the difference in symmetry of the structural system. A part of the tangent stiffness matrix is corrected by coordinate transformations, and
the modified stiffness method is proposed to separate the multiple bifurcation points to a single point in the direction of the bifurcation path. As a numerical analysis example, a bifurcation analysis of a fullerene structure is performed to demonstrate the feasibility of the presented method.

Graph-theory, Bifurcation, Imperfection, Fulerene, Dihedral group