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An improved isoparametric transformation for finite element analysis
Author(s) -
Celia Michael A.,
Gray William G.
Publication year - 1984
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.1620200808
Subject(s) - quadrilateral , jacobian matrix and determinant , transformation (genetics) , finite element method , mathematics , context (archaeology) , quadratic equation , flexibility (engineering) , reduction (mathematics) , element (criminal law) , geometry , mathematical analysis , topology (electrical circuits) , structural engineering , engineering , combinatorics , paleontology , biochemistry , chemistry , statistics , biology , gene , political science , law
The standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes. Side nodes positioned at the same relative distance from corner nodes in both local and global space, and interior nodes positioned such that they do not affect the Jacobian of the co‐ordinate transformation, provide improved accuracy over nodes positioned locally without regard for the global configuration. This concept is demonstrated in the context of two‐dimensional quadratic quadrilateral isoparametrics, but is also applicable to higher orders and dimensions. In the test cases examined, the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations.