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Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications. (English) Zbl 1082.74547
Summary: This papers summarizes two linear tetrahedral FE formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications. In particular, the average nodal pressure (ANP) technique described by J. Bonet and A. J. Burton [Commun. Numer. Methods Eng. 14, No. 5, 437–449 (1998; Zbl 0906.73060)] is briefly reviewed. In addition, the split-based formulation proposed by O. C. Zienkiewicz et al. [Int. J. Numer. Methods Eng. 43, No. 3, 565–583 (1998; Zbl 0939.74073)] is described here in terms of a time integration of the nodal Jacobian. This will make it simple to compare both techniques and will enable a new combined method to be presented. The paper will then discuss the stability constraints that each technique places on the timestep size. A von-Neumann stability analysis on simple 1-D uniform meshes will show that the ANP element permits the use of much larger timesteps than the split based formulations. Finally, numerical examples corroborating in 3-D this analytical conclusions will be presented.
Reviewer: Reviewer (Berlin)

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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[2] Zienkiewicz, International Journal for Numerical Methods in Engineering 43 pp 565– (1998) · Zbl 0939.74073 · doi:10.1002/(SICI)1097-0207(19981015)43:3<565::AID-NME454>3.0.CO;2-9
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