ON THE DETERMINATION OF BIFURCATION AND LIMIT POINTS

Necessary and sufficient conditions for the occurrence of a bifurcatio n in the equilibrium path of a discrete structural system are establis hed as a consequence of the degeneracy of the solution of the rate pro blem at a critical point. Such result is based on the properties of th e elastic-plastic rate problem formulated as a linear complementarity problem (LCP) in terms of plastic multipliers (the moduli of the plast ic strain rate vectors) as basic unknowns. The conditions here given a llow to distinguish, both theoretically and practically, among bounded bifurcations, unbounded bifurcations, limit points, and unloading poi nts. All of the needed quantities depend either on the starting situat ion or on the actual known term increment; there is no need to compute eigenvalues or eigenvectors of stiffness matrices. The results obtain ed can be seen as a refinement, for the discrete elastic-plastic probl em, of the uniqueness theory given by Hill. The refinement allows cove ring the case of vector-valued yield functions and clearly distinguish ing, in operative terms, between different types of critical/limit poi nts.