New enhanced strain elements for incompressible problems

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 2, 1999, Pages 229-248

  Cesar De Sa J M A ^a   Natal Jorge, R M ^b  

^a UNIVERSITY OF PORTO   (Portugal)

^b NONE

Author keywords

Enhanced strain; Incompressibility; Mixed methods

Indexed keywords

DEFORMATION; INCOMPRESSIBLE FLOW; STRAIN;

INCOMPRESSIBILITY;

FINITE ELEMENT METHOD;

EID: 0040142014     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990120)44:2<229::AID-NME503>3.0.CO;2-I     Document Type: Article

References (26)

1. D. J. Naylor, 'Stresses in nearly incompressible materials for the finite elements with the application to the calculation of excess pore pressures', Int. J. Numer. Meth. Engng., 8, 443-460 (1974).
2. J. C. Nagtegaal, D. M. Parks and J. R. Rice, 'On numerically accurate finite element solutions in the fully plastic range', Comput. Meth. Appl. Mech. Engng., 4, 153-178 (1974).
3. O. C. Zienkiewicz and P. N. Godbole, 'Viscous incompressible flow with special reference to non-Newtonian (plastic) flows', in R. H. Gallagher et al. (eds.), Finite Elements in Fluids, Vol. 1, Wiley Chichester, 1975.
4. T. J. R. Hughes, R. L. Taylor and J. F. Levy, 'High Reynolds number, steady, incompressible flows by a finite element method', in R. H. Gallagher et al. (eds.), Finite Elements in Fluids, Vol. 3, Wiley Chichester, 1978.
5. D. S. Malkus and T. J. R. Hughes, 'Mixed finite element methods-reduced and selective integration techniques: a unification of concepts', Comput. Meth. Appl. Mech. Engng., 15, 63-18 (1978).
6. T. J. R. Hughes, 'Generalisation of selective integration procedures to anisotropic and nonlinear media', Int. J. Numer. Meth. Engng., 15, 1413-1418 (1980).
7. T. J. R. Hughes, The Finite Element Method-Linear Static and Dynamic Finite Element Analysis, Prentice-Hall International Inc., Englewood Cliffs, N.J., 1987.
8. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Vol.1, McGraw-Hill, New York, 1989.
9. E. L. Wilson, R. L. Taylor, W. P. Doherty and J. Ghaboussi, 'Incompatible displacement models', in S. J. Fenves, N. Perrone, A. R. Robinson and W. C. Schnobrich (eds.), Numerical and Computer Models in Structural Mechanics, Academic Press, New York, 1973, pp. 43-57.
10. R. L. Taylor, P. J. Beresford and E. L. Wilson, 'A non-conforming element for stress analysis', Int. J. Numer. Meth. Engng., 10, 1211-1219 (1976).
11. D. Kosloff and G. A. Frazier, 'Treatment of hourglass pattern in low order finite element codes', Int. J. Num. Analyt. Meth. Geomech., 2, 57-72 (1972).
12. T. Belytschko and W. E. Bachrach, 'Efficient implementation of quadrilaterals with high coarse-mesh accuracy', Comput. Meth. Appl. Mech. Engng., 54, 279-301 (1986).
13. J. M. A. César de Sá, 'Numerical modelling of incompressible problems in glass forming and rubber technology', Ph.D. Thesis, University College of Swansea, C/Ph/91/86, U.K., 1986.
14. J. M. A. César de Sá. and D. R. J. Owen, 'The imposition of the incompressibility constraint in finite elements - A review of methods with a new insight to the locking phenomenon', in C. Taylor et al. (eds.), Proc. 3rd Int. Conf. on Numerical Methods for Non-Linear Problems, Dubrovnik, Pineridge Press Ltd., Swansea, U.K. 1986.
15. J. C. Simo and M. S. Rifai, 'A class of mixed assumed strain methods and the method of incompatible modes', Int. J. Numer. Meth. Engng., 29, 1595-1638 (1990).
16. J. C. Simo and F. Armero, 'Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes', Int. J. Numer. Meth. Engng., 33, 1413-1449 (1992).
17. J. C. Simo, F. Armero and R. L. Taylor, 'Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems', Comput. Meth. Appl. Mech. Engng., 110, 359-386 (1993).
18. M. A. Crisfield, G. F. Moita, G. Jelenic and L. P. R. Lyons, 'Enhanced lower-order element formulations for large strains', in D. R. J. Owen et al. (eds.), Proc. 4th Int. Conf. on Computational Plasticity: Fundamentals and Applications, Barcelona, Pineridge Press Ltd., Swansea, U.K., 1995, pp. 293-320.
19. K. Arunakirinathar and B. D. Reddy, 'Enhanced strain finite element methods', in D. R. J. Owen et al. (eds.), Proc. 4th Int. Conf. on Computational Plasticity: Fundamentals and Applications, Barcelona, Pineridge Press Ltd., Swansea, U.K., 1995, pp. 321-332.
20. M. Schonauer, E. A. de Souza Neto and D. R. J. Owen, 'Hencky tensor based enhanced large strain element for elasto-plastic analysis', in D. R. J. Owen et al. (eds.), Proc. 4th Int. Conf. on Computational Plasticity: Fundamentals and Applications, Barcelona, Pineridge Press Ltd., Swansea, U.K., 1995, pp. 333-348.
21. E. A. de Souza Neto, D. Peric, G. C. Huang and D. R. J. Owen, 'Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity', in D. R. J. Owen et al. (eds.), Proc. 4th Int. Conf. on Computational Plasticity: Fundamentals and Applications, Barcelona, Pineridge Press Ltd., Swansea, U.K., 1995, pp. 361-372.
22. E. A. de Souza Neto, D. Peric, M. Dutko and D. R. J. Owen, 'Design of simple low order finite elements for large strain analysis of nearly incompressible solids', Int. J. Solids Struct., 33, 3277-3296 (1996).
23. U. Hueck and P. Wriggers, 'A formulation for the 4-noded quadrilateral element', Int. J. Numer. Meth. Engng., 38, 3007-3037 (1995).
24. P. Wriggers and U. Hueck, 'A formulation for the QS6 element for large elastic deformations', Int. J. Numer. Meth. Engng., 39, 1437-1454 (1996).
25. E. N. Dvorkin and S. I. Vassolo, 'A quadrilateral 2-D finite element based on mixed interpolation of tensorial components', Engng. Comput., 6, 217-224 (1989).
26. R. D. Cook, D. S. Malkus and M. E. Plesha, Concepts and Applications of Finite Element Analysis, Wiley, New York, 1989.