General trifurcation analysis in elastic stability

A general theory of trifurcation analysis is presented, in the context of t he elastic stability of discrete systems. Under certain conditions, an elas tic structure can display critical states for which there is coincidence of the critical load and the critical direction. Such states are called trifu rcation, because three equilibrium paths intersect at the critical state. A s in the general theory of bifurcation, a regular perturbation analysis is employed for each one of the emerging path. It is shown that methods of sol ution of perturbation equations in trifurcation analysis are different from those employed in bifurcation. The present development is based in the V-f ormulation; i.e., the total potential energy is written in terms of the ori ginal generalized coordinates of the system.