Kinematic nonuniqueness of elastoplastic structures

Abstract

Lack of uniqueness of the kinematic solution of structures, analyzed as an assemblage of discretized elements assuming nonholonomic linearly-elastic/perfectly-plastic behaviour and a linearized yield surface, is studied. The occurrence of an elastoplastic mechanism leads to nonuniqueness; an elastoplastic mechanism is defined as a kinematically-admissible strain rate field made up of an admissible elastoplastic solution of the governing conditions and an add-on variable component consisting of a linear combination of plastic (collapse) mechanisms. The scalar multipliers of this linear combination are bounded, except at plastic collapse in which case the elastoplastic mechanism degenerates to a plastic mechanism. In the space of loads, the load paths that could coexist with nonuniqueness are restricted to a hyperplane or a crease of intersection of hyperplanes, defined by the equilibrium equations arising from the associated plastic mechanisms of the elastoplastic mechanism. The difference between any two competing displacement vectors would be normal to that hyperplane or crease, in the same manner plastic strain rates are to the yield surface according to the flow rule. © 1991.