Minimum theorems and iterative solutions methods for creep cyclic loading problems

Authors
Citation
Ars. Ponter, Minimum theorems and iterative solutions methods for creep cyclic loading problems, MECCANICA, 36(1), 2001, pp. 37-47
Citations number
30
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
MECCANICA
ISSN journal
0025-6455 → ACNP
Volume
36
Issue
1
Year of publication
2001
Pages
37 - 47
Database
ISI
SICI code
0025-6455(2001)36:1<37:MTAISM>2.0.ZU;2-X
Abstract
In recent years a particular programming method, the linear matching method , has been particularly successful in the evaluation of optimal upper bound s to shakedown limits for an elastic perfectly plastic body. The method app lies to any convex yield condition with an associated flow rule and suffici ent conditions for convergence exist. For creep constitutive equations and for a body under cyclic loading, there exist a class of cyclic solutions, t he so called 'rapid cycle' solutions for which the residual stress field re mains constant throughout the cycle. In this paper an upper bound theorem f or the rapid cycle solution is derived and related to the upper bound shake down theorem. This allows the linear matching method to be extended to this class of creep problems. A sufficient condition for convergence is derived . For a flow potential expressed in terms of a Von Mises effective stress, the sufficient condition is shown to be a simple and common property of cre ep equations.