×

Tetrahedral composite finite elements. (English) Zbl 1112.74544

Summary: We develop and analyse a composite CT3D tetrahedral element consisting of an ensemble of 12 four-node linear tetrahedral elements, coupled to a linear assumed deformation defined over the entire domain of the composite element. The element is designed to have well-defined lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of volume constraints per element. The relation between displacements and deformations is enforced weakly by recourse to the Hu-Washizu principle. The element arrays are formulated in accordance with the assumed-strain prescription. The formulation of the element accounts for fully nonlinear kinematics. Integrals over the domain of the element are computed by a five-point quadrature rule. The element passes the patch test in arbitrarily distorted configurations. Our numerical tests demonstrate that CT element has been found to possess a convergence rate comparable to those of linear simplicial elements, and that these convergence rates are maintained as the near-incompressible limit is approached. We have also verified that the element satisfies the Babuka-Brezzi condition for a regular mesh configuration. These tests suggest that the CT3D element can indeed be used reliably in calculations involving near-incompressible behaviour which arises, e.g., in the presence of unconfined plastic flow.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Camacho, International Journal of Solids and Structures 33 pp 2899– (1996)
[2] Computational modelling of impact damage and penetration of brittle and ductile materials. Ph.D. Dissertation, Brown University, Providence, RI, 1995.
[3] Guo, International Journal for Numerical Methods in Engineering 47 pp 287– (2000)
[4] Zienkiewicz, International Journal for Numerical Methods in Engineering 28 pp 2191– (1989)
[5] Simo, Journal of Applied Mechanics 53 pp 51– (1986)
[6] Hughes, International Journal for Numerical Methods in Engineering 15 pp 1413– (1980)
[7] Babu?ka, Numerische Mathematik 16 pp 322– (1971)
[8] Brezzi, RAIRO 8 pp 129– (1974)
[9] Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970.
[10] Chappelle, Computers and Structures 47 pp 537– (1993)
[11] Finite Element Procedures. Prentice-Hall of India Pvt. Ltd: New Delhi, 1997.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.