The inverse mapping and distortion measures for 8-node hexahedral isoparametric elements
| Autor: | Yeong-Shyang Huang, Kuan-Ya Yuan, Theodore H. H. Pian, H. T. Yang |
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| Rok vydání: | 1994 |
| Předmět: |
Power series
Geodesic Applied Mathematics Mechanical Engineering Mathematical analysis Computational Mechanics Inverse Ocean Engineering law.invention Distortion (mathematics) Computational Mathematics symbols.namesake Computational Theory and Mathematics Differential geometry law Jacobian matrix and determinant symbols Inverse relation Cartesian coordinate system Mathematics::Differential Geometry Mathematics |
| Zdroj: | Computational Mechanics. 14:189-199 |
| ISSN: | 1432-0924 0178-7675 |
| DOI: | 10.1007/bf00350284 |
| Popis: | 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 Jacobian 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 sompletely describe the inverse relations and the determinant of the Jacobian 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. |
| Databáze: | OpenAIRE |
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