Classification of stress modes in assumed stress fields of hybrid finite elements

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 23, 1997, Pages 4313-4339

  Feng, W ^a   Hoa, S V ^a   Huang, Q ^b  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Classification; Finite element; Stress modes

Indexed keywords

DEFORMATION; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; KINEMATICS; MATRIX ALGEBRA; STRESS ANALYSIS;

HYBRID FINITE ELEMENTS; ZERO ENERGY STRESS MODES;

FINITE ELEMENT METHOD;

EID: 0031375939     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N     Document Type: Article

References (23)

1. T. H. H. Pian, 'Derivation of element stiffness matrices by assumed stress distributions', AIAA J., 2, 1333-1336 (1964).
2. T. H. H. Pian, 'State-of-the-art development of hybrid/mixed finite element method', Finite Elements Anal. Des., 21, 5-20 (1995).
3. T. H. H. Pian and P. Tong, 'Mixed and hybrid finite element methods', in H. Kardestuncer and D. H. Norrie (ed.), Finite Element Handbook, McGraw-Hill, New York, 1987.
4. W. Feng and S. V. Hoa, 'A partial hybrid degenerated plate/shell element for the analysis of laminated composites', Int. J. Numer. Meth. Engng., 39, 3625-3639 (1996).
5. J. Han and S. V. Hoa, 'A three-dimensional multilayer composite finite element for stress analysis of composite laminates', Int. J. Numer. Meth. Engng., 36, 3903-3914 (1993).
6. S. V. Hoa and W. Feng, 'Finite elements for analysis of composite structures', in S. V. Hoa (ed.), Computer-aided Design of Polymer-Matrix Composite Structures, Marcel Dekker, New York, 1995.
7. R. D. Henshell, 'On hybrid finite elements', Proc. Brunel University Conf. of the Institute of Math and Its Applications, April, 1972.
8. E. F. Punch and S. N. Atluri, 'Development and testing of stable, invariant, isoparametric curvilinear 2-and 3-D hybrid-stress elements', Comput. Meth. Appl. Mech. Engng., 47, 331-356 (1984).
9. B. M. Fraeijs de Veubake, 'Bending and stretching of plates - special models for upper and lower bounds', Proc. Conf. on Matrix Methods in Structure Mechanics, AFFDL-TR-M66-80, 863-886 (1965).
10. T. H. H. Pian and P. Tong, 'Basis of finite element methods for solid continua', Int. J. Numer. Meth. Engng., 1, 3-28 (1969).
11. F. Brezzi, 'On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers', RAIRO 8(R2), 129-151 (1974).
12. I. Babuska, J. T. Oden and J. K. Lee, 'Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems', Comput. Meth. Appl. Mech. Engng., 11, 175-206 (1977).
13. S. Ahmad and B. M. Irons, 'An assumed stress approach to refined isoparametric finite elements in three dimensions', Finite Element Method in Engineering, University of New South Wales, 1974, pp. 85-100.
14. Q. Huang, Three dimensional composite finite element for stress analysis of anisotropic laminate structures', Ph.D. Thesis, Concordia University, Montreal, Canada, 1989.
15. R. Rubinstein, E. F. Punch and S. N. Atluri, 'An analysis of, and remedies for, kinematic models in hybrid-stress finite elements: Selection of stable, invariant stress fields', Comput. Meth. Appl. Mech. Engng., 38, 63-92 (1983).
16. T. H. H. Pian and D. P. Chen, 'On the suppression of zero energy deformation modes', Int. J. Numer. Meth. Engng., 19, 1741-1752 (1983).
17. T. H. H. Pian and P. Tong, 'Relations between incompatible displacement model and hybrid stress model', Int. J. Numer, Meth. Engng., 22, 173-181 (1986).
18. T. H. H. Pian and C. C. Wu, 'A rational approach for choosing stress terms for hybrid finite element formulations', Int. J. Numer. Meth. Engng., 26, 2331-2343 (1988).
19. K. Y. Sze, C. L. Chow and W. J. Chen, 'A rational formulation of iso-parametric hybrid stress element for three dimensional stress analysis', Finite Elements Anal. Des., 7, 61-72 (1990).
20. W. J. Chen and Y. K. Cheung, Three-dimensional 8-node and 20-node refined hybrid isoparametric elements', Int. J. Numer. Meth. Engng., 35, 1871-1889 (1992).
21. K. Y. Sze, 'Control of spurious mechanisms for 20-node and transition sub-integrated hexahedral elements', Int. J. Numer. Meth. Engng., 37, 2235-2250 (1994).
22. C. C. Wu and Y. K. Cheung, 'On optimization approaches of hybrid stress elements', Finite Elements Anal. Des., 21, 111-128 (1995).
23. J. Han and S. V. Hoa, Three dimensional composite elements for finite element analysis of anisotropic laminated structures', Proc. 2nd Int. Conf. on Computer Aided Design in Composite Material Technology, Computational Mechanics Publications, 1990, pp. 189-200.