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A STRAIN‐AND‐DISPLACEMENT‐BASED VARIATIONAL METHOD APPLIED TO GEOMETRICALLY NON‐LINEAR SHELLS
Author(s) -
CELIGOJ C. C.
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(19960715)39:13<2231::aid-nme952>3.0.co;2-8
Subject(s) - cartesian coordinate system , mathematics , shell (structure) , displacement (psychology) , finite element method , geometry , centroid , mathematical analysis , rotation (mathematics) , rank (graph theory) , element (criminal law) , structural engineering , engineering , combinatorics , psychology , civil engineering , political science , law , psychotherapist
A geometrically non‐linear hybrid nine‐node finite 2D‐shell element is presented. The theoretical formulation is based on a Reissner functional in strains and displacements. The increments of which are interpolated with respect to different spatially fixed triads: both the displacement and rotation increments in the material frame (global rectangular Cartesian) and the Green–Lagrange‐strain increments in a suitably chosen local rectangular Cartesian in the centroid of the considered element in the reference configuration. Corresponding transformations then deliver the components on the shell mid‐surface. Although a single element possesses one spurious zero‐energy mode, an assemblage performs excellently (also in comparison with a full‐rank element).