Triangular finite elements with rotational degrees of freedom and enhanced strain modes

Computers and Structures

Volumn 75, Issue 4, 2000, Pages 361-368

  Piltner, R ^a   Taylor, R L ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b Univ of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; ROTATION; STRESS ANALYSIS; VARIATIONAL TECHNIQUES;

PLANE STRAIN-STRESS ANALYSIS; THREE-MODE TRIANGULAR FINITE ELEMENTS;

STRAIN;

EID: 0033908973     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(99)00095-4     Document Type: Article

References (29)

1. Allman D.J. A compatible triangular element including vertex rotations for plane elasticity analysis. Computers and Structures. 19:(2):1984;1-8.
2. Allman D.J. Evaluation of the constant strain triangle with drilling rotations. International Journal for Numerical Methods in Engineering. 26:(12):1988;2645-2655.
3. Allman D.J. A quadrilateral finite element including vertex rotations for plane elasticity analysis. International Journal for Numerical Methods in Engineering. 26:(3):1988;717-730.
4. Allman D.J. Variational validation of a membrane finite element with drilling rotations. Communications in Numerical Methods in Engineering. 9:(4):1993;345-351.
5. Bergan P.G., Felippa C.A. A triangular membrane element with rotational degrees of freedom. Comp. Meth. Appl. Mech. Eng. 50:1985;25-69.
6. Cook R.D. On the Allman triangle and a related quadrilateral element. Computers and Structures. 22:(6):1986;1065-1067.
7. Cook R.D. A plane hybrid element with rotational D.O.F. and adjustable stiffness. International Journal for Numerical Methods in Engineering. 24:1987;1499-1508.
8. Cook R.D. Modified formulations for nine-dof plane triangles that include vertex rotations. International Journal for Numerical Methods in Engineering. 31:(5):1991;825-835.
9. Hughes T.J.R., Masud A., Harari I. Numerical assessment of some membrane elements with drilling degrees of freedom. Computers and Structures. 55:(2):1995;297-314.
10. Hughes T.J.R., Masud A., Harari I. Dynamic analysis and drilling degrees of freedom. International Journal for Numerical Methods in Engineering. 38:(19):1995;3193-3210.
11. Ibrahimbegovic A., Taylor R.L., Wilson E.L. A robust quadrilateral membrane finite element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering. 30:(3):1990;445-457.
12. Pawlak T.P., Yunus S.M., Cook R.D. Solid elements with rotational degrees of freedom: Part II - tetrahedron elements. International Journal for Numerical Methods in Engineering. 31:(3):1991;593-610.
13. Yunus S.M., Pawlak T.P., Cook R.D. Solid elements with rotational degrees of freedom: Part 1 - hexahedron elements. International Journal for Numerical Methods in Engineering. 31:(3):1991;573-592.
14. Yunus S.M., Saigal S., Cook R.D. On improved hybrid finite elements with rotational degrees of freedom. International Journal for Numerical Methods in Engineering. 28:(4):1989;785-800.
15. Hausser C., Ramm E. Efficient three-node shear deformable plate/shell elements - an almost hopeless undertaking. Topping B.H.V. Advances in finite element technology. 1996;203-215 Civil-Comp Press, Edinburgh.
16. Simo J.C., Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 29:1990;1595-1638.
17. Simo J.C., Armero F. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 33:1992;1413-1449.
18. Simo J.C., Armero F., Taylor R.L. Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Comput. Methods Appl. Mech. Engrg. 110:1993;359-386.
19. Andelfinger U., Ramm E. EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. Int. J. Numer. Meth. Eng. 36:1993;1311-1337.
20. Freischläger C., Schweizerhof K. On a systematic development of trilinear three-dimensional solid elements based on Simo's enhanced strain formulation. International Journal of Solids and Structures. 33:1996;2993-3017.
21. Wriggers P., Korelc J. On enhanced strain methods for small and finite deformations of solids. Computational Mechanics. 18:1996;413-428.
22. Piltner R., Taylor R.L. A quadrilateral finite element with two enhanced strain modes. Int. J. Numer. Meth. Eng. 38:1995;1783-1808.
23. Piltner R., Taylor R.L. A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements. Int. J. Numer. Meth. Eng. 44:1999;615-639.
24. Taylor R.L., Beresford P.J., Wilson E.L. A non-conforming element for stress analysis. Int. J. Numer. Meth. Eng. 10:1976;1211-1219.
25. Ibrahimbegovic A., Wilson E.L. A modified method of incompatible modes. Communications in Applied Numerical Methods. 7:1991;187-194.
26. Zienkiewics O.C., Taylor R.L. The finite element method. vol. 1:1989;McGraw Hill, London, New York.
27. Cook R.D., Malkus D.S., Plesha M.E. Concepts and applications of finite element analysis. 1989;Wiley, New York.
28. Hughes T.J.R., Taylor R.L. The linear triangular bending element, pp. 127-142. Whiteman J.R. The mathematics of finite elements and applications IV (MAFELAP 1981). 1982;Academic Press, London, New York.
29. Brezzi F., Fortin M. Mixed and hybrid finite element methods. 1991;Springer, New York.