Dynamic shakedown and bounding theory for a class of nonlinear hardening discrete structural models

Shakedown analysis and bounding methods in elastic-plastic dynamics are dealt with here on the following basis: the model adopted for the constitutive (element) behavior is centered on a linear dependence of yield functions on (generalized) stresses and nonlinear dependence (hardening) of yield limits on sign-constraint internal variables which play here a central role in all developments; simple discrete structural models (basically trusses) are referred to; constrained optimization in finite dimensional spaces (nonlinear programming) is the mathematical and computational context employed. The contributions presented are as follows: a number of earlier results based on piecewiselinear plastic models are extended to nonlinear hardening; restrictions on the hardening rule are established for various conclusions to be valid; a systematic and unified theoretical framework is developed, so that shakedown theorems and various bounds are shown to be closely related. The theoretical results expounded are illustrated by simple numerical examples.