Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization

In the nonlinear bifurcation analysis for large-scaled structures, the standard eigenanalysis of the tangent stiffness matrix yields important information, but, at the same time, demands a large amount of computational cost. The scaled corrector method was developed as a numerically efficient, eigenanalysis-free, bifurcation-analysis strategy, which exploits byproducts of the numerical iteration for path tracing. This method, however, has a problem in its accuracy, especially when eigenvalues are nearly or exactly coincidental. As a remedy for this, we propose a new bifurcation analysis method through the implementation of bifurcation mechanism of a symmetric structure into the scaled corrector method. The bifurcation mode is accurately approximated by decomposing a scaled corrector vector into a number of vectors by means of block-diagonalization method in group-theoretic bifurcation theory and, in turn, by choosing the predominant one among these vectors. In order to demonstrate the usefulness of this method, it is applied to the bifurcation analysis of reticulated regular-hexagonal truss domes to compute accurately the locations of double bifurcation points and nearly coincidental bifurcation points, and associated bifurcation modes.