zbMATH — the first resource for mathematics

A triangular membrane element with rotational degrees of freedom. (English) Zbl 0593.73073
Summary: A new plane-stress triangular element is derived using the free formulation of the first author and M. K. Nygård [Int. J. Numer. Methods Eng. 20, 643-664 (1984; Zbl 0579.73077)]. The triangle possesses nine degrees of freedom: six corner translations and three corner normal rotations. The element is coordinate-invariant and passes the patch test for any geometry. Two free parameters in the formulation may be adjusted to optimize the behavior for in-plane bending patterns. With the recommended parameter choices the element performance is significantly better than that of the constant-strain triangle. Because of the presence of the rotational freedoms, this new element appears especially suitable as membrane component of a flat triangular element for modelling general shell structures.

74S05 Finite element methods applied to problems in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
PDF BibTeX Cite
Full Text: DOI
[1] Turner, M.J.; Clough, R.W.; Martin, H.C.; Topp, L.J., Stiffness and deflection analysis of complex structures, J. aero. sci., 23, (1956) · Zbl 0072.41003
[2] Taig, I.C.; Kerr, R.I., Some problems in the discrete element representation of aircraft structures, () · Zbl 0131.23101
[3] Zienkiewicz, O.C., The finite element method in engineering science, () · Zbl 0237.73071
[4] Abu-Gazaleh, B.N., Analysis of plate-type prismatic structures, ()
[5] Scordelis, A.C., Analysis of continuum box girder bridges, ()
[6] Willam, K.J., Finite element analysis of cellular structures, () · Zbl 0374.73038
[7] Almroth, B.O.; Brogan, F.A., Numerical procedures for analysis of structural shells, () · Zbl 0231.73021
[8] Irons, B.M.; Razzaque, A., Experiences with the patch test for convergence of finite elements, () · Zbl 0315.73091
[9] Irons, B.M.; Ahmad, S., Techniques of finite elements, (1980), Ellis Horwood Chichester
[10] Felippa, C.A., Refined finite element analysis of linear and nonlinear two-dimensional structures, () · Zbl 0313.73062
[11] Carr, A.J., Refined finite element analysis of thin shell structures including dynamic loadings, ()
[12] Bergan, P.G., Stress analysis using the finite element method. triangular element with 6 parameters at each node, (1967), Division of Structural Mechanics, The Norwegian Institute of Technology Trondheim, Norway
[13] Holand, I.; Bergan, P.G., Higher order finite element for plane stress, discussion, (), 698-702, (EM2)
[14] Tocher, J.L.; Hartz, B., Higher order finite element for plane stress, (), 149-174, (EM4)
[15] Bergan, P.G.; Nygård, M.K., Finite elements with increased freedom in choosing shape functions, Internat. J. numer. meth. engrg., 20, 643-664, (1984) · Zbl 0579.73077
[16] Bergan, P.G.; Hanssen, L., A new approach for deriving “good” finite elements, MAFELAP II conference, brunei university, 1975, (), 483-498
[17] Hanssen, L., Finite elements based on a new procedure for computing stiffness coefficients, ()
[18] Bergan, P.G., Finite elements based on energy orthogonal functions, Internat. J. numer. meths. engrg., Addendum, 17, 154-155, (1981) · Zbl 0445.73059
[19] Pian, T.H.H.; Tong, P., Basis of finite element methods for solid continua, Internat. J. numer. meths. engrg., 1, 3-29, (1969) · Zbl 0167.52805
[20] Wilson, E.L.; Taylor, R.L.; Doherty, W.P.; Ghaboussi, J., Incompatible displacement models, (), 43-57
[21] MacNeal, R.H., A simple quadrilateral shell element, Comput. & structures, 8, 175-183, (1978) · Zbl 0369.73085
[22] Strang, G.; Fix, G., An analysis of the finite element method, (1972), Prentice-Hall Englewood Cliffs, NJ · Zbl 0278.65116
[23] Cook, R.D., Improved two-dimensional finite element, J. structural div. ASCE, 100, ST6, 1851-1863, (1974)
[24] Taylor, R.L.; Beresford, P.J.; Wilson, E.L., A non-conforming element for stress analysis, Internat. J. numer. meths. engrg., 10, 1211-1219, (1976) · Zbl 0338.73041
[25] Cook, R.D., Ways to improve the bending response of finite elements, Internat. J. numer. meths. engrg., 11, 1029-1039, (1977) · Zbl 0368.73066
[26] Bergan, P.G.; Nygård, M.K., Nonlinear analysis of shells using free formulation finite elements, () · Zbl 0712.73090
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.