Bounds to shakedown loads

The shakedown analysis of structures under variable loads is considered, an d the corresponding variational principles are presented. Separate formulat ions for elastic (or classical) shakedown, plastic shakedown and incrementa l collapse are compared. Two upper bounds for classical safety factors are presented and interpreted as the result of separate analysis concerning alt ernating plasticity and prevention of simple mechanisms of incremental coll apse. As a first application, exact solutions are obtained for a closed tub e under variable pressure and temperature. This example is the Bree problem with logarithmic temperature variation across the wall. A finite element p rocedure for shakedown analysis of tubes is then presented. This numerical procedure is validated by comparison with the exact solutions for the close d tube. Finally, the numerical method is applied to a restrained tube under variable pressure and logarithmic temperature. (C) 2001 Elsevier Science L td. All rights reserved.