✦ LIBER ✦

The inverse mapping and distortion measures for 8-node hexahedral isoparametric elements

✍ Scribed by K. -Y. Yuan; Y. -S. Huang; H. -T. Yang; T. H. H. Pian

Book ID: 104734673
Publisher: Springer
Year: 1994
Tongue: English
Weight: 809 KB
Volume: 14
Category: Article
ISSN: 0178-7675
DOI: 10.1007/bf00350284

No coin nor oath required. For personal study only.

✦ Synopsis

The inverse relations of the isoparametric mapping for the 8-node hexahedra are derived by using the theory of geodesics in differential geometry. Such inverse relations assume the form of infinite power series in the element geodesic coordinates, which are shown to be the skew Cartesian coordinates determined by the ]acobian of the mapping evaluated at the origin. By expressing the geodesic coordinates in turn in terms of the isoparametric coordinates, the coefficients in the resulted polynomials are suggested to be the distortion parameters of the element. These distortion parameters can be used to completely describe the inverse relations and the determinant of the ]acobian of the mapping. The meanings of them can also be explained geometrically and mathematically. These methods of defining the distortion measures and deriving the inverse relations of the mapping are completely general, and can be applied to any other two-or three-dimensional isoparametric elements. 1

📜 SIMILAR VOLUMES

Distortion measures and inverse mapping

Distortion measures and inverse mapping for isoparametric 8τnode plane finite elements with curved boundaries

✍ Lautersztajn-S, Nina ;Samuelsson, Alf 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB

Utilizing systematically dierential geometry the paper describes a method which substantially improves results obtained by Yuan et al. (1994), though the same technique is used in both articles. An 8-node isoparametric element with curved boundaries is analysed as an object of dierential geometry. I

Consistent diagonal mass matrices for th

Consistent diagonal mass matrices for the isoparametric 4-node quadrilateral and 8-node hexahedron elements

✍ Sauer, Gerhard 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 515 KB

Diagonal mass matrices offer computational advantages in many applications. Their general use is confronted, however, with the fact that usual finite-element formulations generate consistent mass matrices. Some methods have been suggested to diagonalize these consistent matrices. These methods are l