A minimum theorem for cyclic load in excess of shakedown, with application to the evaluation of a ratchet limit

Haofeng Chen, Alan R.S. Ponter

Research output: Contribution to journalArticle

94 Citations (Scopus)

Abstract

Although the shakedown theorems for perfect plasticity have been known since Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not appeared in the literature. In this paper a generalisation of the upper bound theorem is derived which reduces to the upper bound shakedown theorem in the limiting case when the load point approaches the shakedown boundary. The new theory is used to develop a method for identifying the ratchet limit for a class of loading histories through the sequential minimisation of two functionals. A programming method, based on the Elastic Compensation method for shakedown is then derived and convergence proven. Numerical examples of the application of the method to practical problems are discussed by us in an accompanying paper.
Original languageEnglish
Pages (from-to)539-553
Number of pages14
JournalEuropean Journal of Mechanics - A/Solids
Volume20
Issue number4
DOIs
Publication statusPublished - 2001

Keywords

  • cyclic loading
  • shakedown
  • ratchetting
  • reverse plasticity

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