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Title: An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations

Abstract

Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface 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, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite elementmore » and handbuilt meshes.« less

Authors:
; ;  [1]
  1. Sandia National Labs., Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (United States)
OSTI Identifier:
332738
Report Number(s):
SAND-98-1591; CONF-9709141-PROC.
ON: DE99000778; TRN: IM9916%%40
Resource Type:
Conference
Resource Relation:
Conference: 5. joint Russian-American computational mathematics conference, Albuquerque, NM (United States), 2-5 Sep 1997; Other Information: PBD: [1997]; Related Information: Is Part Of Proceedings of the 5. joint Russian-American computational mathematics conference; PB: 312 p.
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 66 PHYSICS; USES; FINITE ELEMENT METHOD; MESH GENERATION; WAVE PROPAGATION; IMPACT TESTS; DYNAMICS; PERFORMANCE; ALGORITHMS

Citation Formats

Key, S.W., Heinstein, M.W., and Stone, C.M. An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations. United States: N. p., 1997. Web.
Key, S.W., Heinstein, M.W., & Stone, C.M. An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations. United States.
Key, S.W., Heinstein, M.W., and Stone, C.M. Wed . "An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations". United States. https://www.osti.gov/servlets/purl/332738.
@article{osti_332738,
title = {An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations},
author = {Key, S.W. and Heinstein, M.W. and Stone, C.M.},
abstractNote = {Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface 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, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 1997},
month = {Wed Dec 31 00:00:00 EST 1997}
}

Conference:
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