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THE p ‐VERSION OF THE FINITE ELEMENT METHOD IN INCREMENTAL ELASTO‐PLASTIC ANALYSIS
Author(s) -
HOLZER S. M.,
YOSIBASH Z.
Publication year - 1996
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/(sici)1097-0207(19960615)39:11<1859::aid-nme932>3.0.co;2-7
Subject(s) - finite element method , discretization , mathematics , order (exchange) , computer science , exploit , algorithm , mathematical optimization , calculus (dental) , structural engineering , engineering , mathematical analysis , finance , economics , medicine , computer security , dentistry
Whereas the higher‐order versions of the finite element method ( p ‐ and hp ‐versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto‐plastic structural analysis. In this paper, we discuss which aspects of incremental elasto‐plastic finite element analysis are particularly amenable to improvements by the p ‐version. These theoretical considerations are supported by several numerical experiments. First, we study an example for which an analytical solution is available. It is demonstrated that the p ‐version performs very well even in cycles of elasto‐plastic loading and unloading, not only as compared with the traditional h ‐version but also with respect to the exact solution. Finally, an example of considerable practical importance—the analysis of a cold‐working lug—is presented which demonstrates how the modelling tools offered by higher‐order finite element techniques can contribute to an improved approximation of practical problems.