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Adaptive time‐step control in creep analysis
Author(s) -
Mahnken Rolf,
Stein Erwin
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280711
Subject(s) - estimator , finite element method , creep , midpoint , context (archaeology) , displacement (psychology) , numerical integration , mathematics , midpoint method , constitutive equation , adaptive control , numerical analysis , computer science , mathematical optimization , control (management) , structural engineering , mathematical analysis , engineering , geometry , statistics , artificial intelligence , psychology , paleontology , materials science , composite material , psychotherapist , biology
Concerning the integration in time of constitutive relations for Norton‐type creep problems two families of algorithms are examined, namely the generalized trapezoidal rule and the generalized midpoint rule. Based on a mathematical concept, the accuracy properties are derived for both stresses and strains. Since the choice of the step‐size is crucial for the accuracy of the numerical results, an adaptive step‐size procedure is carried out by means of error estimators. Specifically, attention is paid to features arising in the context of a finite element displacement method. Finally, two numerical examples are given to illustrate the effect of the step‐size control on the accuracy.