A suitable low-order, tetrahedral finite element for solids

✍ Scribed by S. W. Key; M. W. Heinstein; C. M. Stone; F. J. Mello; M. L. Blanford; K. G. Budge

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 201 KB
• Volume: 44
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990430)44:12<1785::aid-nme561>3.0.co;2-5

✦ Synopsis

To use the all-tetrahedral mesh generation capabilities existing today, we have explored the creation of a computationally e cient eight-node tetrahedral ÿnite element (a four-node tetrahedral ÿnite element enriched with four mid-face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping and the element's performance in applications are presented. In particular, we examine the eight-node tetrahedral ÿnite element's behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the eight-node, mean-quadrature hexahedral ÿnite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral ÿnite element and the four-node tetrahedral ÿnite element are included. Given automatic all-tetrahedral meshing, the eight-node, mean-quadrature tetrahedral ÿnite element is a suitable replacement for the eight-node, mean-quadrature hexahedral ÿnite element and meshes requiring an inordinate amount of user intervention and direction to generate.