On a mixed-hybrid finite element method for anisotropic plate bending problems

International Journal for Numerical Methods in Engineering

Volumn 39, Issue 23, 1996, Pages 4063-4089

  Nataraj, Neela ^a   Bhattacharyya, P K ^a   Balasundaram, S ^b   Gopalsamy, S ^c  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^b JAWAHARLAL NEHRU UNIVERSITY   (India)

^c Centre for Development of Advanced Computing Mumbai   (India)

Author keywords

Anisotropic plates; Mixed hybrid finite element method

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; BENDING (DEFORMATION); COMPUTER SIMULATION; FINITE ELEMENT METHOD;

TWISTING;

PLATES (STRUCTURAL COMPONENTS);

EID: 0030412178     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19961215)39:23<4063::AID-NME40>3.0.CO;2-T     Document Type: Article

References (25)

1. S. Balasundaram and P. K. Bhattacharyya, 'A mixed finite element method for dirichlet problem of fourth order elliptic operators with variable coefficients', in T. Kawai (ed.), Finite Element Flow Analysis, Proc. 4th Int. Symp. on F.E.M. in Flow Probs., Tokyo University Press, Tokyo, 1982, pp. 995-1001.
2. S. Balasundaram and P. K. Bhattacharyya, 'A mixed finite element method for fourth order elliptic partial differential equations with variable coefficients', Comput. Maths. Appls., 10, 245-256 (1984).
3. S. Balasundaram and P. K. Bhattacharyya, 'A mixed finite element method for fourth order elliptic problems with variable coefficients', Z. Angw. Math. Mech. (ZAMM), 66, 489-499 (1986).
4. S. Balasundaram and P. K. Bhattacharyya, 'A mixed finite element method for fourth order elliptic problems with variable coefficients', J. Comput. Appl. Maths., 22, 1-24 (1988).
5. P. K. Bhattacharyya, 'Mixed finite element methods for fourth order elliptic equations with variable coefficients', in C.A. Brebbia (ed.), Variational Methods in Engineering, Springer, Berlin, 1985, pp. 2/3-2/12.
6. J. E. Roberts and J. M. Thomas, 'Mixed and hybrid methods', in Handbook on Numerical Analysis, Vol. II, P. G. Ciarlet, J. L. Lions (eds.), North-Holland, Amsterdam, 1994, pp. 523-633.
7. T. H. H. Pian and P. Tong, 'Basis of finite element methods for solid continua', Int. j. numer. methods eng., 1, 3-28 (1969).
8. T. H. H. Pian and P. Tong, 'A variational principle and convergence of finite element method based on assumed stress distribution', Int. j. numer. methods eng., 5, 463-472 (1969).
9. F. Brezzi and L. D. Marini, 'On the numerical solution of plate bending problems by hybrid methods', R.A.I.R.O., No. R-3, 1975, pp. 5-50.
10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
11. L. D. Marini, 'Implementation of hybrid finite element methods and associated numerical problems', Part I & Part II, Publicazioni No. 136 & 182, Laboratorio di Analisi Numerica, CNR, Pavia, 1976 & 1978.
12. P. K. Bhattacharyya and S. Gopalsamy, 'On a mixed-hybrid finite element method for fourth order elliptic partial differential equations with variable coefficients', paper to be published.
13. N. Neela, S. Balasundaram, S. Gopalsamy and P. K. Bhattacharyya, 'On a dual hybrid finite element method for fourth order elliptic boundary value problems with variable coefficients', submitted for publication.
14. S. G. Lekhnitskii, Anisotropic Plates, Gordon and Breach, New York, 1968.
15. P. K. Bhattacharyya and S. Gopalsamy, 'On existence and uniqueness of solutions of boundary value problems of fourth order elliptic partial differential equations with variable coefficients', J. Math. Anal. Appl., 136, 589-608 (1988).
16. S. Balasundaram and P. K. Bhattacharyya, 'On existence of solution of dirichlet problem of fourth order partial differential equations with variable coefficients', Quart. Appl. Maths., 39, 311-317 (1983).
17. P. K. Bhattacharyya and S. Gopalsamy, 'An equilibrium finite element method for fourth order elliptic equations with variable coefficients', Comput. Maths. Appls., 15, 405-424 (1988).
18. S. Gopalsamy, 'Mixed/equilibrium/hybrid finite element methods for fourth order elliptic equations with variable coefficients', Ph.D. dissertation, Dept. of Maths., Indian Institute of Technology, Delhi, 1988.
19. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1977.
20. L. S. D. Morley, Skew Plates and Structures, Pergamon Press, Oxford, 1963.
21. G. Sander, 'Applications de la méthode des éléments finis à la flexion des plaques', D.Sc. Thesis, Univ. of Liège, Belgium, 1969.
22. J. E. Ashton, 'Clamped skew plates of orthotropic material under transverse load', Dev. Mech., 5, Proc. 11th Midwestern Mechanics Conf., 1969, pp. 297-306.
23. D. R. J. Owen and J. A. Figueiras, 'Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells', Int. j. numer. methods eng., 19, 541-566 (1983).
24. A. K. Noor and M. D. Mathers, 'Finite element analysis of anisotropic plates', Int. j. numer. methods eng., 11, 289-307 (1977).
25. S. Gopalsamy, S. Balasundaram and P. K. Bhattacharyya, 'On a mixed finite element method for clamped anisotropic plate bending problems', Int. j. numer. methods eng., 28, 1351-1370 (1989).