14-Node brick element, PN5X1, exactly representing linear stress fields

Computers and Structures

Volumn 74, Issue 2, 2000, Pages 147-165

  Bassayya, K ^a   Shrinivasa, U ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; MATHEMATICAL MODELS; POLYNOMIALS; STRESS ANALYSIS;

NAVIER EQUATION; PAPCOVITCH-NEUBER SOLUTION;

STRUCTURAL ANALYSIS;

EID: 0033897290     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(98)00323-X     Document Type: Article

References (28)

1. MacNeal R.H., Harder R.L. A proposed set of problems to test finite element accuracy. Finite Elements Anal Des. 1:1985;3-20.
2. Bassayya K, Bhattacharya K, Shrinivasa U. An eight node brick element, PN340, to represent every constant stress field exactly. Comput Struct (accepted)
3. Venkatesh D.N., Shrinivasa U. Generation of an eight node brick element using Papcovitch-Neuber functions. Comput Struct. 54:1995;1077-1084.
4. Venkatesh D.N., Shrinivasa U. Hexahedral elements using PN functions - application to beams. Comput Struct. 60:1996;305-313.
5. Kidger D.J. The fourteen node brick element. Finite Element Anal Des. 6:1990.
6. Smith I.M., Kidger D.J. Elastoplastic analysis using the 14-node brick element family. Int J Numer Meth Engng. 35:1992;1263-1275.
7. Bassayya K. Ph.D. thesis, Department of Mechanical Engineering, Indian Institute of Science, Bangalore 1997
8. Stroud A.H. Approximate calculation of multiple integrals. 1972;306-315 Prentice-Hall, Englewood Cliffs, NJ.
9. Papcovitch P.F. Solution général des équations différentielles fundamentals d'élasticité, exprimée par trois fonctions harmoniques. CR Acad Sci Paris. 195:1932;513.
10. Neuber H. Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätheorie. Z angew Math Meth. 14:1934;203.
11. Wilson E.L., Ibrahimbegovic A. Use of incompatible displacement modes for the calculation of element stiffnesses or stress. Finite Elements Anal Des. 7:1990;229-241.
12. Chandra S., Prathap G. A field-consistent formulation for the eight-noded solid finite element. Comput Struct. 33:1989;345-355.
13. Robinson J. New FEM user project - single element test for aspect ratio sensitivity of solids (Part I). Finite Element News. 1:1986;26-32.
14. Cheung Y.K., Chen W. Isoparametric hybrid hexahedral elements for three dimensional stress analysis. Int J Numer Meth Engng. 26:1988;677-693.
15. Chen W., Cheung Y.K. Three-dimensional 8-node and 20-node refined hybrid isoparametric elements. Int J Numer Meth Engng. 35:1992;1871-1889.
16. Bretl J.L., Cook R.D. A new eight-node solid element. Int J Numer Meth Engng. 14:1979;593-615.
17. Bachrach W.E. An efficient formulation of hexahedral element with high accuracy in bending and incompressibility. Comput Struct. 26:1987;453-467.
18. Venkatesh DN. A rational approach to solid finite elements, Ph.D. thesis, Indian Institute of Science, Bangalore 1994
19. Sze K.Y., Ghali A. Hybrid hexahedral element for solids, plates, shells and beams by selective scaling. Int J Numer Meth Engng. 36:1993;1519-1540.
20. Allman D.J. A compatible triangular element including vertex rotation for plane elasticity problems. Comput Struct. 19:1984;1-8.
21. Yunus S.M., Saigal S., Cook R.D. On improved hybrid finite elements with rotational degrees of freedom. Int J Numer Meth Engng. 28:1989;785-800.
22. Pian T.H.H., Sumihara K. Rational approach for assumed stress finite elements. Int J Numer Meth Engng. 20:1984;1685-1695.
23. Taylor R.L., Beresford P.J., Wilson E.L. A non-conforming element for stress analysis. Int J Numer Meth Engng. 10:1976;1211-1219.
24. Bergan P.G., Felippa C.A. A triangular membrane element with rotational degrees of freedom. Comput Meth Appl Mech Engng. 50:1985;25-69.
25. Sze K.Y., Chen W., Cheung Y.K. An efficient quadrilateral plane element with drilling degrees of freedom using orthogonal stress modes. Comput Struct. 42:1992;695-705.
26. MacNeal R.H. A theorem regarding the locking of tapered four-noded membrane elements. Int J Numer Meth Engng. 24:1987;1793-1799.
27. Punch E.F., Atluri S.N. Application of isoparametric three-dimensional hybrid-stress finite elements with least order fields. Comput Struct. 19:1984;409-430.
28. Cheung Y.K., Chen W. Refined hybrid method for plane isoparametric element using an orthogonal approach. Comput Struct. 5:1992;683-694.