Premium
Algorithms for determining invertible two‐ and three‐dimensional quadratic isoparametric finite element transformations
Author(s) -
Field David A.
Publication year - 1983
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.1620190602
Subject(s) - jacobian matrix and determinant , mathematics , finite element method , tetrahedron , invertible matrix , transformation (genetics) , sign (mathematics) , node (physics) , quadratic equation , element (criminal law) , function (biology) , mixed finite element method , algorithm , mathematical analysis , pure mathematics , geometry , biochemistry , chemistry , physics , structural engineering , gene , law , political science , engineering , thermodynamics , evolutionary biology , biology
This paper presents an algorithm which determines the invertibility of any planar, triangular quadratic isoparametric finite element transformation. Extensions of the algorithm to three‐dimensional isoparametric finite element transformations yield conditions which guarantee invertibility of 10‐node tetrahedra and 8‐node bricks. The mathematical basis for the algorithm focuses on the Jacobian as a continuous function defined over a compact set where the Jacobian attains a maximum and a minimum value. The algorithm then determines whether these values are of opposite sign.