Abstract
On the premise that tetrahedra (particularly ten noded ones) make good finite elements and that they should be as near regular as possible a procedure for generating structured meshes of such elements is outlined. This involves two stages: First the definition, by means of macro elements, of a regular array of optimally shaped and suitably sized tetrahedra which fill the region. Then the distortion of the mesh thus obtained to better fit the boundaries. Examples are given which demonstrate the suitability of the procedure for, in particular, static analyses in geomechanics.
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References
Cavendish, J.C., Field, D.A. and Frey, W.H. (1985). An approach to automatic three-dimensional finite element mesh generation. Int. J. Numer. Methods in Engng, 21: 329–347.
Nagtegaal, J.C., Parks, D.M. and Rice, J.R. (1974). On numerically accurate finite element solutions in the fully plastic range. Comp. Meth, Appl. Mech. Engng, 4: 153–177.
Naylor, D.J. (1998). Filling space with tetrahedra. Accepted for publication in Int. J. Numer. Methods in Engng.
Senechal, M. (1981). Which tetrahedra fill space?. Mathematics Magazine, 54: 227–243.
Sloane, S.W. and Randolph, M.F. (1982). Numerical prediction of collapse loads using finite element methods. Int. J. Numer. Anal. Methods in Geomech, 6: 47–76.
Smith, I.M. (1991). Are there any new elements? The finite element method in the 1990’s. (Ed: Onate, Periaux, Samuelsson) Springer-Verlag. 109–118.
Sommerville, D.M.Y. (1923). Space-filling Tetrahedra in Euclidean Space. Proc. Edinburgh Mathematical Soc. 41: 49–57.
Weatherill, N.P., Hassan, O. and Marcum, D.L. (1995). Compressible Flowfield Solutions with Unstructured Grids Generated by Delaunay Triangulation. AIAA Journal, 33, No. 7: 1196–1204.
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© 1998 Springer-Verlag Wien
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Naylor, D.J. (1998). A Procedure for Generating Well Conditioned Tetrahedral Meshes. In: Cividini, A. (eds) Application of Numerical Methods to Geotechnical Problems. International Centre for Mechanical Sciences, vol 397. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2512-0_51
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DOI: https://doi.org/10.1007/978-3-7091-2512-0_51
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83141-0
Online ISBN: 978-3-7091-2512-0
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