A simplified method of solution for the short cycle creep-plasticity problem
type: Item
instance of: scholarly article
title: A simplified method of solution for the short cycle creep-plasticity problem
zbMATH Open document ID: 0608.73041
DOI: 10.1016/0045-7825(87)90134-4
author: A. S. L. Chan
author: Konstantinos Spiliopoulos
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: This paper describes a method for estimating the long-term effects on structures under cyclic changes of loading. For loads less than a certain critical amplitude (shakedown limit), the stress in the struture will asymptote to a cyclic stationary state consisting of an elastic part in response to the cyclic loading, plus a system of self-equilibrating residuals constant in time. It is shown that corresponding to this cyclic stationary state, the creep energy dissipation per cycle of loading is a maximum. Instead of following the exact time history to reach this state, in this paper it is found by a procedure of successive approximations. It corrects the admissible residual stress distribution at the beginning of a cycle by the creep and plastic strains accumulated over an entire cycle, which are in general not compatible, and requires additional self- equilibrating stresses to give an elastic strain distribution such that the total strain satisfies compatibility. The steady state is reached when no further correction is necessary. Convergence may be accelerated by a suitable choice of initial starting value, and by an artificial choice of the cycle time for the best computational convenience, upon which the steady-state solution can be proved to be independent. The procedure is a powerful device to obtain the cyclic steady-state solution, which will give an upper bound to the creep deformation per cycle and may also be used to find the shakedown limit. The formulation of the procedure in conjunction with the finite element method is given in detail and results of a few examples of the analysis are shown.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74R20
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 3984694
zbMATH Keywords: bounding theorem
zbMATH Keywords: estimating the long-term effects
zbMATH Keywords: structures under cyclic changes of loading
zbMATH Keywords: shakedown limit
zbMATH Keywords: asymptote to a cyclic stationary state
zbMATH Keywords: elastic part
zbMATH Keywords: response to the cyclic loading
zbMATH Keywords: system of self-equilibrating residuals constant in time
zbMATH Keywords: creep energy dissipation
zbMATH Keywords: maximum
zbMATH Keywords: finite element method
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90134-4
OpenAlex ID: W2039810847
cites work: Q5672287
cites work: The analysis of cyclically loaded creeping structures for short cycle times
cites work: On the Stress Analysis of Creeping Structures Subject to Variable Loading
cites work: Q3270462
cites work: Q5523520
description: scientific article; zbMATH DE number 3984694