An internal variable approach applied to the dynamic analysis of elastic–plastic structural systems

Abstract

AbstractDiscrete elastic–plastic systems subjected to dynamic load conditions are considered and properties related to an implicit time‐integration scheme are discussed on the basis of an internal variable formulation. The material models accounted for are quite general: elastic–perfectly plastic and elastic–plastic (subjected to linear or non‐linear, kinematic or isotropic hardening). The internal variable approach adopted in the paper leads easily to extremum theorems from which convergence properties of convenient time‐integration schemes immediately follow. Next, taking account of the stabilising effect due to inertial and damping forces, it is shown how the above results can be extended to the case of softening (again linear or non‐linear, kinematic or isotropic). Finally, some numerical examples are given and an extension to damage models is envisaged.