AN ASSUMED STRAIN BASED ON TRIANGULAR ELEMENT WITH DRILLING ROTATION
Résumé
The lack of compatibility betweendegrees of freedom of various elements isa problem frequently encountered in practice
during modeling complex structures. Coupling of membrane and beam elements is an illustrating classical example. The
problem is generally treated through an additional rotational degree of freedom [1]. In this respect a new element based on the
strain field has been developed with a drilling rotation in the Bergan sense [2]. The triangular element, with three nodes and
three degrees of freedom constructed in this way, presentsvery good performance and may be used in various practical
problems.
Références
1] D.J. Allman, A compatible triangular element
including vertex rotations for plane elasticity, C.S,
Vol. 19, pp. 1-8, 1984.
[2] Bergan P.G. & Felippa C.A., A triangular membrane
element with rotational degrees of freedom, CMAME,
Vol. 50, pp. 25-69, 1985.
[3] Ashwell D.G. and Sabir A.B., A new cylindrical shell
finite element based on simple independent strain
functions, IJMS, Vol.14, pp.171-183, 1972.
[4] Sabir A.B., A new class of Finite Elements for plane
elasticity problems, CAFEM 7
th
, Int. Conf. Struct.
Mech. in Reactor Technology, Chicago, 1983.
[5] Sabir A.B. and Sfendji A., Triangular and Rectangular
plane elasticity finite elements. Thin-walled Structures
21.pp 225-232 .1995
[6] Sabir A.B., A rectangular and triangular plane
elasticity element with drilling degrees of freedom,
Chapter 9 in proceeding of the 2nd international
conference on variational methods in engineering,
Southampton University, Springer-Verlag, Berlin, pp.
17-25, 1985.
[7] Belarbi M.T. et Charif A., Nouvel élément secteur
basé sur le modèle de déformation avec rotation dans
le plan, Revue Européenne des Eléments Finis, Vol. 7,
N° 4, pp. 439-458, Juin 1998.
[8] Belarbi M.T. Développementde nouvel élément fini
basé sur le modèle en déformation. Application
linéaire et non linéaire. Thèse de Doctorat d’état,
Université de Constantine 2000 (ALGERIE)
[9] Sze K.Y., Chen W. and Cheung Y.K., An efficient
quadrilateral plane element with drilling degrees of
freedom using orthogonal stress modes, C.S., Vol. 42,
N° 5, pp. 695-705, 1992.
[10] Taylor R.L., Simo J.C., Zienkiewicz O.C. and Chan
A.C., The patch test: A Condition for Assessing
Finite Element Convergence, IJNME, Vol. 22, pp. 39-62, 1986.
[11] Batoz J.L. et Dhatt G., Modélisation des structures par
éléments finis, Vol. 1 : Solides élastiques, Eds Hermès,
Paris, 1990.
[12] Ibrahimbegovic A., Frey F. et Rebora B., Une
approche unifiée de la modélisation des structures
complexes : les éléments finis avec degré de liberté de
rotation, LSC Rapport interne 93/10, Ecole
polytechnique fédérale de Lausanne (Suisse), juin
1993
[13] D.J. Allman, Evaluation of the constant strain triangle
with drilling rotations, Int. Jou. Num. Meth. Eng. 26,
pp. 2645-2655, 1988.
[14] Timoshenko S. and Goodier J. N., Theory of
Elasticity, Mc Graw-Hill, New York, 1951.
[15] MacNeal R. H. and Harder R. L., A proposed standard
set of problems to test finite element accuracy, Finite
Element Anal. Des. 1, pp. 3-20, 1985.
[16] MacNeal R. H., A theorem regarding the locking of
An assumed strain based on triangular element with drilling rotation
123
tapered four-noded membraneelements, IJNME., Vol.
24, pp. 1793-1799, 1987.
[17] Wilson E.L., Taylor R., Doherty W.P. & Ghaboussi J.,
Incompatible displacement models, In Fenves et al.
(eds), NCMSM, Acadelic Press, New York, pp. 43-57,
1973.
[18] Taylor R., Beresford P.J. & Wilson E.L., Non
conforming element for stress analysis, IJNME, Vol.
10, pp. 1211-1219, 1976.
[19] Pian T.H. and Sumihara K., Rational approach for
assumed stress finite elements, IJNME, Vol. 20, pp.
1685-1695, 1984.
[20] Ayad R., Eléments finis de plaque et coque en
formulation mixte avec projection en cisaillement,
Thèse de Doctorat, U.T.C, 1993. 217 pages.
including vertex rotations for plane elasticity, C.S,
Vol. 19, pp. 1-8, 1984.
[2] Bergan P.G. & Felippa C.A., A triangular membrane
element with rotational degrees of freedom, CMAME,
Vol. 50, pp. 25-69, 1985.
[3] Ashwell D.G. and Sabir A.B., A new cylindrical shell
finite element based on simple independent strain
functions, IJMS, Vol.14, pp.171-183, 1972.
[4] Sabir A.B., A new class of Finite Elements for plane
elasticity problems, CAFEM 7
th
, Int. Conf. Struct.
Mech. in Reactor Technology, Chicago, 1983.
[5] Sabir A.B. and Sfendji A., Triangular and Rectangular
plane elasticity finite elements. Thin-walled Structures
21.pp 225-232 .1995
[6] Sabir A.B., A rectangular and triangular plane
elasticity element with drilling degrees of freedom,
Chapter 9 in proceeding of the 2nd international
conference on variational methods in engineering,
Southampton University, Springer-Verlag, Berlin, pp.
17-25, 1985.
[7] Belarbi M.T. et Charif A., Nouvel élément secteur
basé sur le modèle de déformation avec rotation dans
le plan, Revue Européenne des Eléments Finis, Vol. 7,
N° 4, pp. 439-458, Juin 1998.
[8] Belarbi M.T. Développementde nouvel élément fini
basé sur le modèle en déformation. Application
linéaire et non linéaire. Thèse de Doctorat d’état,
Université de Constantine 2000 (ALGERIE)
[9] Sze K.Y., Chen W. and Cheung Y.K., An efficient
quadrilateral plane element with drilling degrees of
freedom using orthogonal stress modes, C.S., Vol. 42,
N° 5, pp. 695-705, 1992.
[10] Taylor R.L., Simo J.C., Zienkiewicz O.C. and Chan
A.C., The patch test: A Condition for Assessing
Finite Element Convergence, IJNME, Vol. 22, pp. 39-62, 1986.
[11] Batoz J.L. et Dhatt G., Modélisation des structures par
éléments finis, Vol. 1 : Solides élastiques, Eds Hermès,
Paris, 1990.
[12] Ibrahimbegovic A., Frey F. et Rebora B., Une
approche unifiée de la modélisation des structures
complexes : les éléments finis avec degré de liberté de
rotation, LSC Rapport interne 93/10, Ecole
polytechnique fédérale de Lausanne (Suisse), juin
1993
[13] D.J. Allman, Evaluation of the constant strain triangle
with drilling rotations, Int. Jou. Num. Meth. Eng. 26,
pp. 2645-2655, 1988.
[14] Timoshenko S. and Goodier J. N., Theory of
Elasticity, Mc Graw-Hill, New York, 1951.
[15] MacNeal R. H. and Harder R. L., A proposed standard
set of problems to test finite element accuracy, Finite
Element Anal. Des. 1, pp. 3-20, 1985.
[16] MacNeal R. H., A theorem regarding the locking of
An assumed strain based on triangular element with drilling rotation
123
tapered four-noded membraneelements, IJNME., Vol.
24, pp. 1793-1799, 1987.
[17] Wilson E.L., Taylor R., Doherty W.P. & Ghaboussi J.,
Incompatible displacement models, In Fenves et al.
(eds), NCMSM, Acadelic Press, New York, pp. 43-57,
1973.
[18] Taylor R., Beresford P.J. & Wilson E.L., Non
conforming element for stress analysis, IJNME, Vol.
10, pp. 1211-1219, 1976.
[19] Pian T.H. and Sumihara K., Rational approach for
assumed stress finite elements, IJNME, Vol. 20, pp.
1685-1695, 1984.
[20] Ayad R., Eléments finis de plaque et coque en
formulation mixte avec projection en cisaillement,
Thèse de Doctorat, U.T.C, 1993. 217 pages.
Comment citer
BELARBI, M.T.; BOUREZANE, M..
AN ASSUMED STRAIN BASED ON TRIANGULAR ELEMENT WITH DRILLING ROTATION.
Courrier du Savoir, [S.l.], v. 6, avr. 2014.
ISSN 1112-3338.
Disponible à l'adresse : >https://revues.univ-biskra.dz/index.php/cds/article/view/330>. Date de consultation : 26 avr. 2024
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