Algorithms for determining invertible two- and three-dimensional quadratic isoparametric finite element transformations

✍ Scribed by David A. Field

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 595 KB
• Volume: 19
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620190602

✦ Synopsis

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.