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Distortion measures and inverse mapping for isoparametric 8-node plane finite elements with curved boundaries. (English) Zbl 0947.74064

From the summary: An eight-node isoparametric element with curved boundaries is analysed as an object of differential geometry. Inverse transformations between normal (geodesic) coordinates and natural (isoparametric) coordinates are derived in terms of a Taylor series which is convergent and does not need many terms to give an approximation of the element shape with four curved sides. The concept of local normal coordinates results in the definition of distortion measures of a plane element. It is shown, by exploring the theory of geodesic curves, that the distortion parameters of a chord quadrilateral, spanned on the corner nodes of the eight-node element with curved boundaries, are the basic distortion measures for this eight-node element. The results are independent of coordinate systems. The meaning of element distortion measures is suggested. This analysis can be extended to curved surfaces in \(\mathbb{R}^3\).

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
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References:

[1] Yuan, The reference coordinates and distortion measures for quadrilateral hybrid stress membrane element, Comput. Mech. 14 pp 311– (1994) · Zbl 0807.73069
[2] Yuan, Inverse mapping and distortion measures for quadrilaterals with curved boundaries, Int. J. numer. methods eng. 37 pp 861– (1994) · Zbl 0796.73068 · doi:10.1002/nme.1620370510
[3] Eisenhart, Riemannian Geometry (1949)
[4] Veblen, Invariants of Quadratic Differential Forms (1962)
[5] Abraham, Foundations of Mechanics (1978)
[6] Choquet-Bruhat, Analysis, Manifolds and Physics (1978)
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