Numerical Bifurcation and Secondary Bifurcation: A Case History.

摘要

Secondary transitions or secondary bifurcations occur frequently in many nonlinear stability problems. In hydrodynamic stability, secondary bifurcations are called secondary transitions and in elastic stability they are called secondary bucklings. Secondary bifurcation phenomena were known at least since the time of poincare. In fact, it was poincare who invented the term secondary bifurcation in his classical studies of the equilibrium states of rotating and self-gravitating liquid masses. In this paper we describe some recent progress that has been made in the theory and numerical computation of secondary bifurcation by considering two problems for the nonlinear buckling of elastic plates. (Author)