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Hybrid hexahedral element for solids, plates, shells and beams by selective scaling
Author(s) -
Sze K. Y.,
Ghali A.
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.1620360907
Subject(s) - hexahedron , scaling , computation , stiffness matrix , finite element method , matrix (chemical analysis) , element (criminal law) , structural engineering , shell (structure) , engineering , computer science , geometry , mathematics , algorithm , materials science , mechanical engineering , composite material , law , political science
A robust two‐field hexahedral element capable of handling plate/shell, beam and nearly incompressible material analyses without locking are presented. Starting with the assumed stress element of Pian and Tong, 7 parasitic strain components leading to locking in plate, shell and beam analyses are first identified. Locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix. Unfortunately, the element then fails the patch test. However, patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation . The resulting element is lock‐free and very efficient. All matrices involved in constructing the stiffness matrix can be derived explicitly. The accuracy of the element is tested by popular bench‐mark problems.