Nonuniqueness in elastoplastic frames

Abstract

Lack of uniqueness of the kinematic solution of elastoplastic flexural frames is studied by deriving a general solution for nonholonomic behavior. A singular hinge set is defined as a collection of plastic hinges that would form a mechanism if they were replaced by mechanical hinges. It is shown that whenever singular subsets can be found among active plastic hinges, the kinematic solution may become nonunique. The rate of work done by the load rates on the contributing mechanisms must be zero if a prevailing nonuniqueness is to sustain.