2015 Volume 81 Issue 830 Pages 15-00419
For error-free computation of high-derivatives of mathematical functions used in engineering applications, hyper-dual numbers (HDN) are receiving much attention in computational mechanics. Differently from classical finite differences, HDN provides a practically exact evaluation of higher-derivatives, such as the first and second derivatives of stiffness matrix with respect to nodal degrees-of-freedom (dof). As a preliminary step for introducing HDN in stability problems, the present paper formulates the theoretical basis of a 2-mode asymptotic bifurcation theory and examines its versatility on simple bench models. All obtained results in numerical examples well predict the stability behavior and agree with existing analytical solutions.
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A