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A unified numerical integration formula for the perfectly plastic von Mises model
Author(s) -
Wu W.
Publication year - 1990
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.1620300308
Subject(s) - von mises yield criterion , numerical integration , mathematics , constitutive equation , numerical analysis , constant (computer programming) , computer science , calculus (dental) , mathematical analysis , finite element method , structural engineering , engineering , medicine , dentistry , programming language
The accuracy of numerical integration of the perfectly plastic constitutive equation of von Mises is examined. Based on the analysis of the three existing numerical integration schemes a unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately. According to the UNIF there are, in fact, many integration schemes depending on the direction of the trial stress. The validity of the UNIF is verified by presenting ten contours of constant angular error calculated with the UNIF. We then come to the conclusion that the three widely used schemes are by no means the most accurate ones. Some other schemes with better accuracy are thereby suggested. The determination of the number of substeps is also discussed in conjunction with the UNIF, when a multi‐step method is used.