A co eight node finite element based on a shell theory
Comparison with the degenerated approach
Keywords:
shell theory, degenerated approach, finite element, shear locking, membrane locking, linear static testsAbstract
The development of ()l eight node shell finite elements based upon the ReissnerMindlin kinematics for geometrically and materially linear applications in structural mechanics is presented. Special attention is given ta the two ways of obtaining a shell finite element : shell theory and degenerated solid approach. We compare, with the same mechanical assumptions and the same finite element approximations, a new eight node semithick shell finite element based on a doubly curved shell theory ( M2D) and an eight node finite element based on the degenerated approach ( MDG ). These two finite elements have the same five degrees of freedom (three translations and two rotations), use an explicit integration throughout the thickness and the same methodology to avoid shear and membrane locking.
Downloads
References
[Ahm70] S. Ahmad, B.M. Irons, and O.C. Zienkiewicz. Analysis of thick and
thin shell structures by curved elements. Int. Jour. Num. Meth.
Eng., 2:419-451, 1970.
[ And93] U. Andel finger and E. Ramm. Bas-elements for two dimensional,
three dimensional, plate and shell structure and their equivalence to
hr-element. Int. Jour. Num. Meth. Eng., 36:1311-1337, 1993.
[Buc93] M.L. Bucalem and K.-J. Bathe. Higher-order mite general shell elements.
Int. Jour. Num. Meth. Eng., 36:3729-3754, 1993.
[Bat86] K.-J. Bathe and E.N. Dvorkin. A formulation of general shell elements-
the use of mixed interpolation of tensorial components. Int.
Jour. Num. Meth. Eng., 22:697-722, 1986.
[Bat92] J.L. Batoz and G. Dhatt. Modelling of structures by finite elements.
Hermes, Paris, 1992. (in french).
[Bue92] N. Buechter and E. Ramm. Shell theory versus degeneration - a
comparison in large rotation finite element analysis. Int. Jour. Num.
Meth. Eng., 34:39-59, 1992.
[Bab92] I. Babuska and M. Suri. On locking and robustness in the finite
element method. SIAM Jour. Numer. Anal., 51:221-258, 1992.
[Bel85] T. Belytschko, H. Stolarski, W.K. Liu, N. Carpenter, and J.S.-J.
Ong. Stress projection for membrane and shear locking in shell finite
elements. Camp. Meth. Applied Mech. and Eng., 51:221-258, 1985.
[Cha98] D. Chapelle and K.J. Bathe. Fundamental considerations for the finite
element analysis of shell structures. Camp. and Struc., 66(1):19-
, 1998.
[Coo74] R.D. Cook. Concepts and Applications of Finite Element Analysis.
J. Wileys and Sons, New-York, 1974.
[Gil91] W. Gilewski and M. Radwanska. A survey of finite element models
for the analysis of moderately thick shells. Finite Elements in
Analysis and Design, 9:1-21, 1991.
[Hin86] E. Hinton and H.C. Huang. A family of quadrilateral mindlin plate
elements with substitute shear strain fields. Camp. and Struc.,
(3):409-431, 1986.
[Hua86] H.C. Huang and E. Hinton. A new nine node degenerated shell
element with enhanced membrane strain interpolation. Int. Jour.
Num. Meth. Eng., 22:73-92, 1986.
[Ide81] S. ldelsohn. On the use of deep, shallow or flat shell finite elements
for the analysis of thin shell structures. Camp. Meth. Applied Mech.
and Eng., 26:321-330, 1981.
[Mac85] R.H. MacNeal and R.L. Harder. A proposed set of problems to test
finite element accuracy. Finite Elements in Analysis and Design,
:3-20, 1985.
[Mac92] R.H. MacNeal and R.L. Harder. Eight nodes or nine? Int. Jour.
Num. Meth. Eng., 33:1049-1992, 1992.
[Noo89] A.K. Noor. List of books, monographs, conference proceeding and
survey papers on shells. In Noor et al., editor, Analytical and Computational
Models of Shells, volume 3, pages 7-33, 1989.
[Pin89] P.M. Pinsky and R.V. Jasti. On the use of bubble functions for
controlling accuracy and stability of mixed shell finite elements. In
Noor et al., editor, Analytical and Computational Models of Shells,
volume 3, pages 359-382, 1989.
[Pol92] 0. Polit. Developpement d'elements finis de plaques semi-epaisses et
de coques semi-epaisses d double courbure. PhD thesis, University
P. and M. Curie, Paris VI, 1992.
[Par89] K.C. Park, E. Pramono, G.M. Stanley, and H.A. Cabiness. The ans
shell elements : earlier and recent improvements. In Noor et al.,
editor, Analytical and Computational Models of Shells, volume 3,
pages 359-382, 1989.
[Pol94] 0. Polit, M. Touratier, and P. Lory. A new eight-node quadrilateral
shear-bending plate finite element. Int. Jour. Num. Meth. Eng.,
:387-411, 1994.
[Sim89] J.C. Simo, D.D. Fox, and M.S. Rifai. On a stress resultant geometrically
exact shell model. part ii : the linear theory ; computational
aspects. Comp. Meth. Applied Mech. and Eng., 73:53-92, 1989.
[San89] E. Sanchez-Palencia. Statique et dynamique des coques minces. i. cas
de flexion pure non inhibee. C.R. Acad. Sci. Paris, t.309:411-417,
[Wem89] G. Wempner. Mechanics and finite elements of shells. App. Mech.
Rev., 42(5):129-142, 1989.
[Yan90] H.T.Y. Yang, S. Saigal, and D.G. Liaw. Advances of thin shell
finite elements and some applications- version i. Camp. and Struc.,
(4):481-504, 1990.
