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H ‐Adaptive finite element methods for dynamic problems, with emphasis on localization
Author(s) -
Belytschko T.,
Tabbara M.
Publication year - 1993
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.1620362409
Subject(s) - finite element method , emphasis (telecommunications) , instability , projection (relational algebra) , constant (computer programming) , mathematics , mixed finite element method , mathematical analysis , transient (computer programming) , shear (geology) , element (criminal law) , computer science , mathematical optimization , algorithm , structural engineering , mechanics , physics , engineering , materials science , telecommunications , composite material , programming language , operating system , law , political science
H‐adaptive procedures for the finite element solution of transient solid mechanics problems are studied, with particular emphasis on problems involving localization due to material instability. Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L 2 ‐projection of strains is the most effective for the constant strain elements considered here. Examples of one‐dimensional and two‐dimensional localization (shear band formation) problems are given.