Shakedown of creeping structures

Abstract

The classical approach to shakedown in elastic-plastic structures is extended here to include unlimited time dependent creep in a new way: by way of illustration a simple time-hardening model is used. Shakedown analysis for creep is typically investigated in two steps: an elastic-plastic shakedown analysis based on the classical theorems followed by a correction for creep, for example based on isochronous stress-strain curves for large times with limited creep. This paper provides a different treatment of the problem of estimating creep strains where shakedown could occur by extending the classical shakedown approach to include unlimited creep. New static and kinematic shakedown theorems are established and it is demonstrated that a necessary and sufficient condition for shakedown with mechanical and thermal cyclic loading is the existence of a time-dependent safe residual stress field. Two kinematic theorems are introduced: the fast connected with a kinematically admissible cycle of inelastic strain rate and the second with kinematically inadmissiable plastic strain rate. In addition all of the results are expressed in terms of generalized variables for structural applications. A few simple examples are examined to verify these results.