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

Citation
Ars. Ponter et Hf. Chen, A minimum theorem for cyclic load in excess of shakedown, with applicationto the evaluation of a ratchet limit, EUR J MEC A, 20(4), 2001, pp. 539-553
Citations number
23
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
ISSN journal
0997-7538 → ACNP
Volume
20
Issue
4
Year of publication
2001
Pages
539 - 553
Database
ISI
SICI code
0997-7538(200107/08)20:4<539:AMTFCL>2.0.ZU;2-D
Abstract
Although the shakedown theorems for perfect plasticity have been known sinc e Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not ap peared in the literature. In this paper a generalisation of the upper bound theorem is derived which reduces to the upper bound shakedown theorem in t he Limiting case when the load point approaches the shakedown boundary. The new theory is used to develop a method for identifying the ratchet Limit f or 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 o f the application of the method to practical problems are discussed by us i n an accompanying paper. (C) 2001 Editions scientifiques et medicales Elsev ier SAS.