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. 10011012.
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Abstract
Errors arising in finiteelement 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 sheardeformablebeam elements, extensional thinarch/curvedbeam elements, sheardeformable platebending elements, and planestress 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:  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, 175183 (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., 16,2913; 34(1978).13; R. L. Spilker and N. Munir, quot;The hybrid stress model for thin plates', Int.j. numer. methods eng., 15,12391260 (1980).13; G. Prathap and G. R. Bhashyam, 'Reduced integration and the shear flexible beam element', Int.j. numer. methods eng.,13; 18,195210 (1982).13; G. Prathap, The curved beam/deep arch/finite ring element revisited', Int.j. numer. methods eng., 21, 389407 (1985).13; H. Stolarski and T. Belytschko, 'Membrane locking and reduced integration for curved members', J. Appl. Mech., 49,13; 172178 (1982).13; J. E. Watz, R. E. Fulton, N. J. Cyrus and R. T. Eppink, 'Accuracy of finite element approximations to structural13; problems', NASA TND 5728 (1970).13; G. Prathap, 'The poor bending response of the fournode plane stress quadrilateral', Int.j. numer. methods eng., 21,82513; 835(1985).13; K. H. Murray, 'Comments on the convergence of finite element solutions', A.I.A.A. J., 4, 815816 (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., 11,265269 (1980).13; G. Prathap and S. Viswanath, 'An optimally integrated fournode quadrilateral plate bending element', Int. j. numer.13; methods eng., 19, 831840 (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, 17711812 (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, 305309 (1983).13; I. Fried, 'Residual energy balancing technique in the generation of plate bending finite elements', Comp. Struct., 4,77113; 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*, 31,303312 lt;1973).13; J. HyiaanGamet, CrouzetPascal and A. B. Pifko, 'Aspects of a simple triangular plate bending finite element', Comp.13; Struct^ 12, 783785 (1980).13; G. A. Mofcr,f Application of penalty reactions to a curved isoparametric axisymmetric thick shell element', Comp.13; Struct^ 15, 685690 (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. 4357.13; O. C. Senkiewicz, The Finite Element Method, 3rd edn, McGrawHill, London 1971, p. 400.13; R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd edn, Wiley, New York 1981, pp. 139140.13; J. H. Argyris, M. Haac and H. P. Mlejnek, 'Some considerations on the natural approach', Comp. Meth. Appl. Mech.13; Eng^ 30, 335346 (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. 116 (1976).13; J. H. Argyris, P. C. Dunne, T. Angejbpoulos and B. Bichat, 'Large natural strains and some special difficulties due to13; Homiaearity and incompressibffity in finite elements', Comp. Meth. Appl. Mech. Eng., 4, 219231 (1974). 
Subjects:  ENGINEERING > Structural Mechanics 
Depositing User:  M/S ICAST NAL 
Date Deposited:  27 Oct 2006 
Last Modified:  24 May 2010 04:21 
URI:  http://nalir.nal.res.in/id/eprint/2983 
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