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On the limits of finite element perfectability
Author(s) -
Macneal Richard H.
Publication year - 1992
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.1620350804
Subject(s) - finite element method , element (criminal law) , displacement (psychology) , modal , coupling (piping) , basis (linear algebra) , structural engineering , mode (computer interface) , mathematics , modal analysis using fem , finite element limit analysis , mixed finite element method , mathematical analysis , lock (firearm) , modal analysis , engineering , geometry , modal testing , computer science , mechanical engineering , materials science , psychology , political science , law , polymer chemistry , psychotherapist , operating system
It has been shown 2 that a four‐noded membrane element of trapezoidal shape must either lock or fail constant strain patch tests. That result is generalized here to establish similar limitations for all finite elements. A modal analysis is used to show that essential coupling exists between low modes whose displacement states can be exactly represented by an element's basis functions and higher modes whose displacement states cannot be so represented. Such coupling can be avoided only when an element has particular shapes. In all other cases the element designer is faced with the choice of patch test failure in a low mode or locking in a higher mode. Several examples are described.