Mixed finite element formulations and related limitation principles: A general treatment

Computer Methods in Applied Mechanics and Engineering

Volumn 138, Issue 1-4, 1996, Pages 105-130

  Alfano, G ^a   Marotti De Sciarra, F ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELASTICITY; MATHEMATICAL MODELS; MATRIX ALGEBRA; MECHANICS; STRAIN;

GENERAL TREATMENT; LIMITATION PRINCIPLES;

FINITE ELEMENT METHOD;

EID: 0030406641     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(96)01129-2     Document Type: Article

References (26)

1. D.S. Malkus and T.J. Hughes, Mixed finite element methods - reduced and selective integration techniques: a unification of concept, Comput. Methods Appl. Mech. Engrg. 15 (1978) 63-81.
2. J.C. Simo, J.G. Kennedy and R.L. Taylor, Complementary mixed finite element formulations for elastoplasticity, Comput. Methods Appl. Mech. Engrg. 74 (1989) 177-206.
3. O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method (McGraw-Hill, London, 1989).
4. B.D. Reddy and J.B. Martin, Algorithms for the solution of internal variable problems in plasticity, Comput. Methods Appl. Mech. Engrg. 93 (1991) 253-273.
5. M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, Vol. 1 (John Wiley, New York, 1991).
6. C. Comi, G. Maier and U. Perego, Generalized variable finite element modelling and extremum theorems in stepwise holonomic elastoplasticy with internal variables, Comput. Methods Appl. Mech. Engrg. 96 (1992) 213-237.
7. C. Comi and U. Perego, A unified approach for variationally consistent finite elements in elastoplasticity, Comput. Methods Appl. Mech. Engrg. 121 (1995) 321-344.
8. B. Fraeijs de Veubeke, Displacement and equilibrium models in the finite element method, in: O.C. Zienkiewicz and G.S. Holister eds., Stress Analysis (John Wiley, London, 1965) 145-196.
9. H. Stolarski and T. Belytschko, Limitation principles for mixed finite elements based on the Hu-Washizu variational formulation, Comput. Methods Appl. Mech. Engrg. 60 (1987) 195-216.
10. G. Romano, L. Rosati, F. Marotti de Sciarra and P. Bisegna, A potential theory for monotone multi-valued operators, Quart. Appl. Math. LI, 4 (1993) 613-631.
11. R.T. Rockafellar, Convex Analysis (Princeton University Press, 1970).
12. P.D. Panagiotopoulos, Inequality Problems in Mechanics and Applications (Birkhauser, 1985).
13. M.M. Vainberg, Variational Methods for the Study of Non-Linear Operators (Holden-Day Inc., San Francisco, 1964).
14. G. Romano, Elasticità generalizzata, Proc. XXIII Congresso Naz. AIAS, Rende, 1994.
15. K. Washizu, Variational Methods in Elasticity and Plasticity, 3rd edition (Pergamon, New York, 1982).
16. G. Romano, New results in subdifferential calculus with applications to convex optimization, Appl. Math. Optim. 32 (1995) 213-234.
17. G. Romano, Elementi di teoria delle strutture, Seminario, Napoli, 1989.
18. M. Froier, C. Nilsson and A. Samuelsson, The rectangular plane stress element by Turner, Pian and Wilson, Int. J. Numer. Methods Engrg. 8 (1974) 433-437.
19. T.H.H. Pian and H. Sumihara, Rational approach for assumed stress finite elements. Int. J. Numer. Methods Engrg. 20 (1984) 1685-1695.
20. H. Shimodaira, Equivalence between mixed models and displacement models using reduced integration, Int. J. Numer. Methods Engrg. 21 (1985) 89-104.
21. T. Belytschko and W.E. Bachrach. Efficient implementation of quadrilaterals with high coarse-mesh accuracy, Comput. Methods Appl. Mech. Engrg. 54 (1986) 279-301.
22. T. Belytschko, W.K. Liu and J.S.-J. Ong, Mixed variational principles and stabilization of spurious modes in the 9-node element finite elements, Comput. Methods Appl. Mech. Engrg. 62 (1987) 275-292.
23. P.M. Pinsky, A finite element formulation for elastoplasticity based on a three-field variational equation, Comput. Methods Appl. Mech. Engrg. 61 (1987) 41-60.
24. W.H. Greub, Linear Algebra (Springer-Verlag, Berlin, 1967).
25. P.R. Halmos, Finite-Dimensional Vector Spaces (Van Nostrand Reinhold Company, New York, 1958).
26. D.G. Luenberger, Optimization by Vector Space Methods (John Wiley, New York, 1969).