Mixed finite element methods - reduced and selective integration techniques: a unification of concepts. (English) Zbl 0381.73075


74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI


[1] de Veubeke, B.Fraeijs, Displacement and equilibrium models in the finite element method, () · Zbl 0245.73031
[2] Herrmann, L.R., Elasticity equations for incompressible and nearly incompressible materials by a variational theorem, Aiaa j., 3, 1896-1900, (1965)
[3] Hughes, T.J.R.; Allik, H., Finite elements for compressible and incompressible continua, (), 27-62
[4] Babuska, I.; Oden, J.T.; Lee, J.K., Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, () · Zbl 0382.65056
[5] Zienkiewicz, O.C.; Taylor, R.L.; Too, J.M., Reduced integration technique in general analysis of plates and shells, Int. J. numer. meths. eng., 3, 275-290, (1971) · Zbl 0253.73048
[6] Naylor, D.J., Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressures, Int. J. numer. meths. eng., 8, 443-460, (1974) · Zbl 0282.73048
[7] Zienkiewicz, O.C.; Godbole, P.N., Viscous incompressible flow with special reference to non-Newtonian (plastic) fluids, () · Zbl 0271.73038
[8] Doherty, W.P.; Wilson, E.L.; Taylor, R.L., Stress analysis of axisymmetric solids utilizing higher order quadrilateral finite elements, ()
[9] Fried, I., Finite element analysis of incompressible material by residual energy balancing, Int. J. solids structs., 10, 993-1002, (1974) · Zbl 0281.73045
[10] Nagtegaal, J.C.; Parks, D.M.; Rice, J.R., On numerically accurate finite element solutions in the fully plastic range, Comp. meths. appl. mech. eng., 4, 153-178, (1974) · Zbl 0284.73048
[11] Argyris, J.H.; Dunne, P.C.; Angelopoulos, T.; Bichat, B., Large natural strains and some special difficulties due to nonlinearity and incompressibility in finite elements, Computer meths. appl. mech. eng., 4, 219-278, (1974) · Zbl 0284.73049
[12] Malkus, D.S., Finite element analysis of incompressible solids, () · Zbl 0472.73088
[13] Malkus, D.S., A finite element displacement model valid for any value of the compressibility, Int. J. solids struct., 12, 731-738, (1976) · Zbl 0342.73054
[14] Malkus, D.S., Calculation of hole error by finite element methods, (), 618-619
[15] Malkus, D.S.; Kearsley, E.A., Application of the finite element method to problems in rheology, (1976), (preprint)
[16] Hughes, T.J.R.; Taylor, R.L.; Sackman, J.L., Finite element formulation and solution of contact-impact problems in continuum mechanics-III, ()
[17] Hughes, T.J.R.; Taylor, R.L.; Sackman, J.L.; Kanoknukulchai, W., Finite element formulation and solution of contact-impact problems in continuum mechanics-IV, ()
[18] Hughes, T.J.R.; Taylor, R.L.; Levy, J.F., A finite element method for incompressible viscous flows, () · Zbl 0442.76027
[19] T.J.R. Hughes, R.L. Taylor and J.F. Levy, High Reynolds number steady, incompressible flows by a finite element method, Finite Elems. In Fluids 3 (Wiley, London, 197x) 000-000.
[20] Hughes, T.J.R.; Taylor, R.L.; Kanoknukulchai, W., A simple and efficient finite element for plate bending, Int. J. numer. meths. eng., 11, 1529-1543, (1977) · Zbl 0363.73067
[21] Hughes, T.J.R., Equivalence of finite elements for nearly-incompressible elasticity, J. appl. mech., 44, 181-183, (1977)
[22] Argyris, J.H.; Dunne, P.C.; Johnsen, T.L.; Müller, M., Linear systems with a large number of sparse constraints with applications to incompressible materials, Comp. meths. appl. mech. eng., 10, 105-132, (1977) · Zbl 0364.73069
[23] R.S. Sandhu and K.J. Singh, Reduced integration for improved accuracy of finite element approximations, Comp. Meths. Appl. Mech. Eng. 00 (197x) 000-000.
[24] Oden, J.T.; Reddy, J.N., An introduction to the mathematical theory of finite elements, (1976), Wiley New York · Zbl 0336.35001
[25] Luenberger, D.G., Introduction ot linear and nonlinear programming, (1973), Addison-Wesley Reading, MA · Zbl 0241.90052
[26] Fichera, G., Existence theorems in elasticity, () · Zbl 0317.73008
[27] Cook, R.D., Concepts and applications of finite element analysis, (1974), Wiley New York
[28] Oden, J.T., Finite elements of nonlinear continua, (1972), McGraw-Hill New York · Zbl 0235.73038
[29] Batchelor, G.K., An introduction of fluid mechanics, (1970), Cambridge Univ. Press Cambridge · Zbl 0193.25702
[30] Taylor, R.L.; Beresford, P.J.; Wilson, E.L., A. non-conforming element for stress analysis, Int. J. numer. meth. eng., 10, 1211-1219, (1976) · Zbl 0338.73041
[31] Pian, T.H.H., Hybrid models, () · Zbl 0403.73047
[32] Gallagher, R.H., Finite element analysis fundamentals, (1975), Prentice-Hall Englewood Cliffs, NJ
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.