An additional stiffness parameter measure of error of the second kind in the finite element method

Prathap, Gangan (1985) An additional stiffness parameter measure of error of the second kind in the finite element method. International Journal for Numerical Methods in Engineering., 21 . pp. 1001-1012.

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    Abstract

    Errors arising in finite-element formulations of continuum problems with multiple field variables due to spurious constraints (the errors of the second kind defined by Prathap and Bhashyam, 1982, and Prathap, 1985) are investigated analytically. A technique based on the addition of an extra stiffness parameter is developed to detect and evaluate the effects of these errors and applied to sample problems involving shear-deformable-beam elements, extensional thin-arch/curved-beam elements, shear-deformable plate-bending elements, and plane-stress modeling of cantilever beams. The results are presented in graphs, and applications to problems with overstraining (such as incompressible fluid flow and incompressible elasticity) are suggested. 13; 13;

    Item Type: Journal Article
    Uncontrolled Keywords: Continuum modeling;error analysis;finite element method;shear strain;structural analysis;beams (supports); cantilevar beams;computational grids;incompressibal flow;metal plates;plane stress;stiffness.21.13; 2113; 23.13; 24,13; 25.13; 26.13; 27.13; 28.13; 29.13; R. H. MacNcal, *A simple quadrilateral shell element', Comp. Struct., 8, 175-183 (1978).13; S. W. Lee and T. H. H. Pian, 'Improvement of plate and shell finite elements by mixed formulations', A.I. A. A. J., 16,29-13; 34(1978).13; R. L. Spilker and N. Munir, quot;The hybrid stress model for thin plates', Int.j. numer. methods eng., 15,1239-1260 (1980).13; G. Prathap and G. R. Bhashyam, 'Reduced integration and the shear flexible beam element', Int.j. numer. methods eng.,13; 18,195-210 (1982).13; G. Prathap, The curved beam/deep arch/finite ring element revisited', Int.j. numer. methods eng., 21, 389-407 (1985).13; H. Stolarski and T. Belytschko, 'Membrane locking and reduced integration for curved members', J. Appl. Mech., 49,13; 172-178 (1982).13; J. E. Watz, R. E. Fulton, N. J. Cyrus and R. T. Eppink, 'Accuracy of finite element approximations to structural13; problems', NASA TN-D 5728 (1970).13; G. Prathap, 'The poor bending response of the four-node plane stress quadrilateral', Int.j. numer. methods eng., 21,825-13; 835(1985).13; K. H. Murray, 'Comments on the convergence of finite element solutions', A.I.A.A. J., 4, 815-816 (1966).13; D. G, Ashwefl and R. H. Gallagher, Eds,, Finite Elements for Thin Shells and Curved Members, Wiley, London, 1076.13; H. R. Meek, 'An accurate polynomial displacement function for finite ring elements', Comp. Struct., 11,265-269 (1980).13; G. Prathap and S. Viswanath, 'An optimally integrated four-node quadrilateral plate bending element', Int. j. numer.13; methods eng., 19, 831-840 (1983).13; J. L. Batoz, K. J. Bathe and L. W. Ho, 'Study of three node triangular plate bending elements', Int.j. numer. methods eng.,13; 15, 1771-1812 (1983).13; S. Viswanath and G. Prathap, 'A note on locking in a shear flexible triangular plate bending element', Int. j. numer.13; methods eng^ 19, 305-309 (1983).13; I. Fried, 'Residual energy balancing technique in the generation of plate bending finite elements', Comp. Struct., 4,771-13; 778(1974).13; L Fried aad S. K, Yang, Triangular, nine degree of freedom C plate bending element of quadratic accuracy', Q. Appl.13; Ate*, 31,303-312 lt;1973).13; J. Hyiaan-Gamet, Crouzet-Pascal and A. B. Pifko, 'Aspects of a simple triangular plate bending finite element', Comp.13; Struct^ 12, 783-785 (1980).13; G. A. Mofcr,f Application of penalty reactions to a curved isoparametric axisymmetric thick shell element', Comp.13; Struct^ 15, 685-690 (1982).13; E L Wilson, R. L. Taylor, W. P. Doherty and T. Ghabussi, 'Incompatible displacement models', in Numerical and13; Computer methods in Structural mechanics, (Ed. S. P. Fenves et al), Academic Press, 1973, pp. 43-57.13; O. C. Senkiewicz, The Finite Element Method, 3rd edn, McGraw-Hill, London 1971, p. 400.13; R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd edn, Wiley, New York 1981, pp. 139-140.13; J. H. Argyris, M. Haac and H. P. Mlejnek, 'Some considerations on the natural approach', Comp. Meth. Appl. Mech.13; Eng^ 30, 335-346 (1982).13; T. J. R. Hughes, R. L Taylor and J. F. Levy, 'A finite element method for incompressible flows', Conf. Finite Element13; Methods k Flow Problems, St. Margaritha, Italy, pp. 1-16 (1976).13; J. H. Argyris, P. C. Dunne, T. Angejbpoulos and B. Bichat, 'Large natural strains and some special difficulties due to13; Hom-iaearity and incompressibffity in finite elements', Comp. Meth. Appl. Mech. Eng., 4, 219-231 (1974).
    Subjects: ENGINEERING > Structural Mechanics
    Division/Department: Structures Division
    Depositing User: M/S ICAST NAL
    Date Deposited: 27 Oct 2006
    Last Modified: 24 May 2010 09:51
    URI: http://nal-ir.nal.res.in/id/eprint/2983

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