A lagrangian curvilinear finite element
Keywords:
curvilinear, Fourier decomposition, lagrangian, large displacement, nonlinear, finite element, cylindrical, axisymmetric, non-axisymmetric, asymmetricAbstract
A total lagrangian formulation is developed in terms of a general orthogonal curvilinear coordinate system. The formulation is used to develop an axisymmetric finite element in cylindrical coordinates to mode/large displacement nonlinerarities arising out of large non-axisymmetric displacements. An axisymmetric shell under asymmetric loads and an axisymmetric beam-column are modelled to demonstrate this capability.
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References
[BAT 82] Bathe, K.J., Finite Element Procedures in Engineering Analysis, Prentice-llall
( 1982)
[ZlE 77] Zienkiewicz, O.C., The Finite Element Method, 3rd Ed., McGraw-Hill, New York
and London ( 1977).
[AD! 87] ADINA, A Finite Element Program for Automatic Dynamic Incremental Nonlinear
Analysis, Report ARD 87-1, AD rNA R & D Inc, Waterton, MA. 1987
[WIL 65] Wilson, E.L., "Structural Analysis of Axisymmetric Solids," AIAA Journal, 1965,
, 2269-2274.
[WrN 79] Winnicki, L.A., and Zienkiewicz, O,C., "Plastic (or Visco-Plastic) Behaviour of
Axisymmetric Bodies Subjected to Non-symmetric Loading - Semi-analytical Finite
Element Solution," Int. J. Num. Meth. Eng., 1979, 14, 1399-1412.
[SPI 81] Spilker, R.L., and Daugirda, D.M., "Analysis of Axisymmetric Structures under
Arbitrary Loading using the Hybrid-Stress Model", Int. J. Num. Meth. Eng., 1981, 17,
-828
[KLE 83] Kleiber, M., and Hien, T.D., "Nonlinear Dynamics of Complex Axisymmetric
Structures under Arbitrary Loads", Camp. Met h. in Applied Mech. and Eng., 1983, 37,
-107
[CHA 70] Chan, A.S.L. and Firmin, A., "The Analysis of Cooling Towers by Matrix Finite
Element Method - Large Displacements", Aeron. J. Roy. Aeron. Soc., 1970, 74, pp.
-982.
[CHA 76] Chan, A.S.L. and Trbojevic, V.M., "Thin Shell Finite Element by the Mixed
Method Formulation", Comp. Meth. in App. Mech. and Eng., 1976,9, pp. 337-367.
[CHA 77] Chan, A.S.L. and Trbojevic, V.M., "Thin Shell Finite Element by the Mixed
Method Formulation- Parts 2 and 3", Comp. Meth. in App. Mech. and Eng., 1977, 10,
pp. 75-103.
[WUN 89]Wunderlich, W., et. a!., "Semi-analytical Approach to the Nonlinear Analysis of
Shells of Revolution.", Anal. Comput. Model Shell, 1989, Winter Annual Meeting
ASME, pp. 509-536.
[MAL 69] Malvern, L.E., Introduction to the Mechanics of a Continuous Medium,
Prentice-Hall, 1969.
[FUN 65] Fung, Y.C., Foundations of Solid Mechanics, Prentice-Hall, 1965
[TRU 60] Truesdell, C., and Toupin, R.A., "The Classical Field Theories", Encyclopedia of
Physics, Principles of Classical Mechanics and Field Theory, Vol. III/I, Springer-Verlag
New York Inc., New York, 1960
[POP 78] Popov, E.P., Mechanics of Materials, Sf Version, Second Edition, Prentice-Hall
Inc., 1978
[KAI 91] Kaiser, T.M.V., Nonlinear Finite Element Analysis of Axisymmetric Solids with
Asymmetric Deformations, Ph.D. Doctoral Thesis, University of Alberta, Edmonton,
Alberta, Canada, 1991.
