Une approche unifiee de Ia modelisation des structures complexes : les elements finis avec degre de Iiberte de rotation
Keywords:
Finite elements for beams, plates, membranes and solids, rotational degree of freedom, junctionsAbstract
In FE models of complex structural ~ystem.s, different element& need to be used such as: beams, membranes, solids, plates and shells. Elements of different kind, based on classical formulations, generally do not share the same nodal degrees of freedom, which complicate& construction of a compatible model. To resolve this modeling problem, we propose a family of finite elements ba.sed on a non-classical variational formulation of classical continuum, in which an independent rotation field is present. Along with a modified method of incompatible modes, this provides a unified basis for construction of variou.s finite elements with the same nodal degree11 of freedom, which can be freely combined. More specifically, new membrane, solid and triangular plate elements are given in the paper. The performance of presented elements is evaluated on a set of numerical examples, which include the numerical studies of the element junctions.
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(ALL 84] ALLMAN D.J., A Compatible Triangular Element Including Vertex Rotations
for Plane Elasticity Problems, Comput. Struct., 19, 1984, p. 1-8.
[BAT 90] BATOZ J.-L. et DHATT G., Modelisation des structures par elements
finis, Hermes, Paris, 1990.
[BAT 81] BATHE K.J. and L.W. HO, Some Results in the Analysis of Thin Shell
Structures, in Nonlinear Finite Element Analysis in Structural Mechanics, ( eds.
W. Wunderlich et a!.), Springer, Berlin, 1981, p. 122-150.
[BAT 82] BATHE K.J., Finite Element Procedures in Engineering Analysis, Prentice
Hall, Englewood Cliffs, NJ, 1982.
[BBH 80] BATOZ J.L., BATHE K.J. and L.W. HO, A Study of Three Node Trinagular
Plate Bending Elements, Int. J. Numer. Methods Eng., 15, 1980, p.
-1812.
[BEL 85] BELYTSCHKO T., H. STOLARSKI, W.K. LIU, N. CARPENTER and
J.S. ONG, Stress Projection for Membrane and Shear Locking in Shell Finite
Elements, Comput. Methods Appl. Mech. Eng., 51, 1985, p. 221-258.
[BER 89] BERNADOU M., S. FOYOLLE and F. LENE, Numerical Analysis of
Junctions Between the Plates, Comput. Methods Appl. Mech. Eng., 74, 1989,
p. 307-326.
[BRE 86] BREZZI F. and K.J. BATHE, Studies of Finite Element ProceduresThe
Inf-Sup Conditions, Equivalent Forms and Applications, in Reliability
of Methods for Engineering Analysis (eds. K.J. Bathe and D.R.J. Owen),
Pineridge Press, 1986, p. 7-219.
[CIA 87] CIARLET P.G., H. LED RET et R. NZENGWA, Modelisation de Ia jonction
entre un corps elastique tridimensionel et une plaque, C.R. Acad. Sci.
Paris, 305 (I), 1987, p. 55-58.
[COO 91] COOK R. D., Beam Cantilevered From Elastic Support: Finite -Element
Modeling, Commun. Appl. Numer. Methods, 7, 1991, p. 621-623.
[DON 60] O'DONNELL W.J., The Additional Deflection of a Cantilever due to the
Elasticity of the Support, J. Appl. Mech., 27, 1960, p. 461-464.
[FRE 89] FREY F., Shell Finite Elements with Six Degrees of Freedom per Node,
in Analytical and Computational Models for Shells (eds. A.K. Ncar, T. Belytschko,
J.C. Sima), ASME, 1989, p. 291-317.
[FRE 91] FREY F. et al., FELINA Finite Element Linear and Incremental Nonlinear
Analysis, LSC Report 91/14, Swiss Federal Institute of Technology, Lausanne,
[HUG 81] HUGHES T.J.R. and T.E. TEZDUYAR, Finite Elements Based Upon
Mindlin Plate Theory with Particular Reference to the Four-Node Bilinear
Isoparametric Element, J. Appl. Mech., 46, 1981, p. 587-596.
[HUG 87] HUGHES T.J.R., The Finite Element Method: Linear Static and Dynamic
Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.
[HUG 89] HUGHES T.J.R. and F. BREZZI, On Drilling Degrees of Freedom, Comput.
Methods Appl. Mech. Eng., 72, 1989, p. 105-121.
[IBR 90] IBRAHIMBEGOVIC A., R.L. TAYLOR and E.L. WILSON, A Robust
Membrane Quadrilateral Element With Drilling Degrees of Freedom, Int. J.
Numer. Methods Eng., 30, 1990, p. 445-457.
[IBR 91a] IBRAHIMBEGOVIC A. and E.L. WILSON, A Modified Method of Incompatible
Modes, Commun. Appl. Numer. Methods, 7, 1991, p. 187-194.
[IBR 91b] IBRAHIMBEGOVIC A. and E.L. WILSON, Thick Shell and Solid Finite
Elements with Independent Rotation Fields, Int. J. Numer. Methods Eng., 31,
, p. 1393-1414.
[IBR 91c] IBRAHIMBEGOVIC A. and E.L. WILSON, A Unified Formulation for
Triangular and Quadrilateral Thin Shell Finite Elements with Six Degrees of
Freedom, Commun. Appl. Numer. Methods, 7, 1991, p. 1-9.
[IBR 92a] IBRAHIMBEGOVIC A., Plate Quadrilateral Finite Element With Incompatible
Modes, Commun. Appl. Numer. Methods, 8, 1992, p. 497- 504.
[IBR 93a] IBRAHIMBEGOVIC A., Mixed Finite Element for Plane Problems in
Finite Elasticity, Comput. Methods Appl. Mech. Eng., 106, 1993, in press.
[IBR 93b] IBRAHIMBEGOVIC A., Quadrilateral Finite Elements for Analysis of
Thick and Thin Plates, Comput. Methods Appl. Mech. Eng., 93, 1993, in
press.
[IBR 93c] IBRAHIMBEGOVIC A., Stress Resultant Geometrically Nonlinear Shell
Theory With Drilling Rotations. Part I: A Consistent Formulation, Comput.
Methods Appl. Mech. Eng., 1993, submitted.
[IBF 93a] IBRAHIMBEGOVIC A. and F. FREY, Finite Element Analysis of Linear
and Nonlinear Planar Deformations of Elastic Initially Curved Beams, Int. J.
Numer. Methods Eng., 36, 1993, in press.
[IBF 93b] IBRAHIMBEGOVIC A. and F. FREY, An Efficient Implementation of
Stress Resultant Plasticity in Finite Element Analysis of Reissner-Mindlin Plates,
Int. J. Numer. Methods Eng., 36, 1993, p. 301-322.
[IBF 93c] IBRAHIMBEGOVIC A. and F. FREY, Geometrically Nonlinear Method
of Incompatible Modes in Application to Finite Elasticity With Independent
Rotations, Int. J. Numer. Methods Eng., 37, 1993, in press.
(KWA 92] KWAN A. K. H., Rotational dofin the Frame Method Analysis of Coupled
Shear/Core Wall Structure, Computer. Struct., 14, 1992, p. 989-1005.
(MUS53] MUSKHELISHVILI N .I., Some Basic Problems of the Mathematical Theory
of Elasticity, P. Noordhoff, Groningen, Holland, 1953.
(REI 65] REISSNER E., A Note on Variational Principles in Elasticity, Int. J. Solids
Struct., 1, 1965, p. 93-95.
(SCO 61] SCORDELIS A.C., E.L. CROY and I.R. STUBBS, Experimental and
Analytical Study of a Folded Plate, ASCE J. Struct. Div., 87, 1961, p. 139-
(TAY 86] TAYLOR R.L., J.C. SIMO, O.C. ZIENKIEWICZ and A.C. CHAN, The
Patch Test: A Condition for Assessing Finite Element Convergence, Int. J.
Numer. Methods Eng., 22, 1986, p. 39-62.
(TES 81] TESSLER A. and S.B. DONG, On a Hierarchy of Conforming Timoshenko
Beam Elements, J. Comput. Struct., 14, 1981, p. 335-344.
[TSO 73] TSO W.K. and J.K. BISWAS, General Analysis of Nonplanar Coupled
Shear Walls, ASCE J. Struct. Div., 99, 1973, p. 365-380.
[WIL 73] WILSON E.L., R.L. TAYLOR, W.P. DOHERTY and J. GHABOUSSI,
Incompatible Displacement Models, in Numerical and Computer Methods in
Structural Mechanics, (eds. S.J. Fenves, N. Perrone, A.R. Robinson and W.C.
Schnobrich), Academic Press, 1973, p. 43-57.
[WIL 74] WILSON E.L., The Static Condensation Algorithm, Int. J. Numer. Methods
Eng., 8, 1974, p. 9-203.
[ZIE 91] ZIENKIEWICZ O.C. and R.L. TAYLOR, The Finite Element Method:
Solid and Fluid Mechanics, Dynamics and Non-linearity, McGraw-Hill, London,
