AN IMPROVEMENT OF THE STIFFNESS MODIFICATION METHOD TO FIND BIFURCATED PATHS AT A MULTIPLE BIFURCATION POINT

Abstract

Stiffness modification method is presented as a strong and pertinent means for the bifurcation analysis at a multiple bifurcation point with multiple critical eigenvectors. It hitherto has been problematic to find the directions of bifurcated paths with reference to the critical eigenvectors when the multiplicity is large. In order to resolve this problem, we revise the stiffness modification method, which is a systematic method to modify the entries in a few rows and columns of the tangent-stiffness matrix to reduce the symmetry of the system. The modification is conducted so as to reduce the apparent geometrical symmetry, and, in turn, to obtain the critical eigenvectors corresponding to the directions of bifurcated paths. The validity and usefulness of the present method improved herein are ensured by systematically obtaining a complete set of bifurcated paths of regular polygonal truss domes and honeycomb structures.