A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 5, 1999, Pages 615-639

  Piltner, R ^a   Taylor, R L ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Mixed finite element; Quadrilateral enhanced strain element

Indexed keywords

ELASTICITY; FUNCTIONS; MATRIX ALGEBRA; PROBLEM SOLVING; STRAIN; STRESS ANALYSIS; VARIATIONAL TECHNIQUES;

B-BAR FUNCTIONS; MIXED FINITE ELEMENTS; QUADRILATERAL ENHANCED STRAIN ELEMENT;

FINITE ELEMENT METHOD;

EID: 0033079918     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990220)44:5<615::AID-NME518>3.0.CO;2-U     Document Type: Article

References (34)

1. R. Piltner and R. L. Taylor, 'A quadrilateral finite element with two enhanced strain modes', Int. J. Numer. Meth. Engng., 38, 1783-1808 (1995).
2. T. J. R. Hughes, 'Equivalence of finite elements for nearly incompressible elasticity', J. Appl. Mech., 44, 181-193 (1977).
3. T. J. R. Hughes, 'Generalizing of selective integration procedures to anisotropic and nonlinear media', Int. J. Numer. Meth. Engng., 15, 1413-1418 (1980).
4. 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).
5. 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).
6. T. H. H. Pian and K. Sumihara, 'Rational approach for assumed stress elements', Int. J. Numer. Meth. Engng., 20, 1685-1695 (1984).
7. K.-Y. Yuan, Y.-S. Huang and T. H. H. Pian, 'New strategy for assumed stresses for 4-node hybrid stress membrane element', Int. J. Numer. Meth. Engng., 36, 1747-1763 (1993).
8. 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).
9. J. C. Simo, F. Armero and R. L. Taylor, 'Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems', Comput. Methods Appl. Mech. Engng., 110, 359-386 (1993).
10. U. Andelfinger and E. Ramm, 'EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements', Int. J. Numer. Meth. Engng., 36, 1311-1337 (1993).
11. 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 and E. Onate (eds.), Computational Plasticity - Fundamentals and Applications, Pineridge Press, Swansea, 1995, pp. 293-320.
12. C. Freischläger and K. Schweizerhof, 'On a systematic development of trilinear three-dimensional solid elements based on Simo's enhanced strain formulation', Int. J. Solids Struct., 33, 2993-3017 (1996).
13. S. Glaser and F. Armero, 'Recent developments in the formulation of assumed enhanced strain finite elements for finite deformation problems', Report No. UCB/SEMM-95/13, University of California, Berkeley, 1995.
14. S. Glaser and F. Armero, 'On the formulation of enhanced strain finite elements in finite deformations', Engng. Comput., 1996, submitted.
15. J. Korelc and P. Wriggers, 'Consistent gradient formulation for a stable enhanced strain method for large deformations', Engng. Comput., 13, 103-123 (1996).
16. P. Wriggers and J. Korelc, 'On enhanced strain methods for small and finite deformations of solids', Comput. Mech., 18, 413-428 (1996).
17. J. C. Nagtegaal and D. D. Fox, 'Using assumed enhanced strain elements for large compressive deformation', Int. J. Solids Struct., 33, 3151-3159 (1996).
18. D. Roehl and E. Ramm, 'Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept', Int. J. Solids Struct., 33, 3215-3237 (1996).
19. 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 and E. Onate (eds.), Computational Plasticity - Fundamentals and Applications, Pineridge Press, Swansea, 1995,
20. P. Wriggers and S. Reese, 'A note on enhanced strain methods for large deformations', Comput. Methods Appl. Mech. Engng., 135, 201-209 (1996).
21. J. Jirousek and L. Guex, 'The hybrid-Trefftz finite element model and its application to plate bending', Int. J. Numer. Meth. Engng., 23, 651-693 (1986).
22. J. Jirousek, 'Hybrid-Trefftz plate bending elements with p-method capabilities', Int. J. Numer. Meth. Engng., 24, 1367-1393 (1987).
23. J. Jirousek, A. Venkatesh, A. P. Zielinski and H. Rabemanantosa, 'Comparative study of p-extensions based on conventional assumed displacement and hybrid-Trefftz FE models', Comput. Struct., 46, 261-278 (1993).
24. J. Jirousek, 'Improvement of computational efficiency of the 9 DOF triangular hybrid-Trefftz plate bending element', Int. J. Numer. Meth. Engng., 23, 2167-2168 (1986).
25. A. Venkatesh and J. Jirousek, 'An improved 9 DOF Hybrid-Trefftz triangular element of plate bending', Engng. Comput., 4, 207-222 (1987).
26. R. Piltner, 'Recent developments in the Trefftz method for finite element and boundary element applications', Adv. Engng. Software, 24, 107-115 (1995).
27. R. Piltner, 'A quadrilateral hybrid-Trefftz plate bending element for the inclusion of warping based on a three-dimensional plate formulation', Int. J. Numer. Meth. Engng., 33, 387-408 (1992).
28. A. P. Zielinski and O. C. Zienkiewicz, 'Generalized finite element analysis with T-complete solution functions', Int. J. Numer. Meth. Engng., 21, 509-528 (1985).
29. M. F. Beatty, 'Introduction to Nonlinear Elasticity', in M. M. Carroll and M. A. Hayes (eds.), Nonlinear Effects in Fluids and Solids, Plenum Press, New York/London, 1996, pp. 13-112.
30. M. F. Beatty, 'Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues - with examples', Appl. Mech. Rev., 40, 1699-1734 (1987).
31. J. K. Knowles and Eli Sternberg, 'On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics', J. Elasticity, 8(4), 329-379 (1978).
32. I. C. Taig, 'Structural analysis by the matrix displacement method', English Electric Aviation Report No. S017, 1961.
33. T. J. R. Hughes, The Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1987.
34. K.-J. Bathe and E. L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1976.