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Simple and accurate four‐node axisymmetric element
Author(s) -
Fredriksson Magnus,
Ottosen Niels Saabye
Publication year - 2006
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.1939
Subject(s) - rotational symmetry , simple (philosophy) , stiffness matrix , node (physics) , finite element method , matrix (chemical analysis) , compressibility , field (mathematics) , stress field , rank (graph theory) , element (criminal law) , stress (linguistics) , structural engineering , computer science , mathematics , mathematical analysis , geometry , engineering , mechanics , materials science , physics , composite material , combinatorics , philosophy , linguistics , epistemology , political science , law , pure mathematics
Based on the assumed strain method, a simple four‐node axisymmetric solid element is introduced. The assumed strain field is carefully selected to preserve the correct rank of the element stiffness matrix and to achieve high accuracy. The strain field is developed in conjunction with orthogonal projections and no matrix inversions are needed. The coarse mesh accuracy in bending and in typical axisymmetric load cases is excellent even for nearly incompressible materials. The strain‐driven format obtained is well suited for materials with non‐linear stress–strain relations. Several numerical examples are presented where the excellent performance of the proposed simple element is verified. Copyright © 2006 John Wiley & Sons, Ltd.