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Inverse mapping and distortion measures for quadrilaterals with curved boundaries
Author(s) -
Yuan KuanYa,
Huang YeongShyang,
Pian Theodore H. H.
Publication year - 1994
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.1620370510
Subject(s) - geodesic , mathematics , distortion (music) , quadrilateral , mathematical analysis , finite element method , inverse , geometry , transformation (genetics) , polygon mesh , element (criminal law) , physics , engineering , structural engineering , amplifier , biochemistry , chemistry , political science , law , gene , optoelectronics , cmos
By using the theory of geodesics in differential geometry, inverse relations of the mapping for 8‐node quadrilaterals with curved boundaries are derived and expressed in terms of the element geodesic co‐ordinates defined at the local origin. The parameters in the expressions of the geodesic co‐ordinates in terms of the isoparametric co‐ordinates are suggested to be the distortion measures of the element. The mathematical meanings of these parameters can be discussed and explained by using the coefficient vectors in the equations defining the isoparametric co‐ordinate transformation. This method of defining the element distortion measures is consistent and general, and can be applied to any other two‐ or three‐dimensional isoparametric finite elements.