Improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type

Computational Mechanics

Volumn 23, Issue 3, 1999, Pages 240-249

  Kikuchi, Fumio ^a   Ishii, Keizo ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b Quint Corporation   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING (DEFORMATION); DEFLECTION (STRUCTURES); DEGREES OF FREEDOM (MECHANICS); FUNCTIONS; STIFFNESS MATRIX; STRUCTURAL ANALYSIS; VECTORS;

NODE DEGENERATION TECHNIQUE; REISSNER-MINDLIN PLATE BENDING ELEMENTS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0032650296     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050405     Document Type: Article

References (25)

1. Hughes TJR (1987) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, Chs. 3 & 5
2. MacNeal RH (1994) Finite Elements: Their Design and Performance, Marcel Dekker, Inc., New York, Ch. 9
3. Tessler A, Hughes TJR (1983) An improved treatment of transverse shear in the Mindlin-type four-node quadrilateral element. Comp. Meth. Appl. Mech. Eng. 39:311-335
4. Kikuchi F, Ando Y (1971) Triangular finite element for plate bending analysis with transverse shear deformation. J. Nucl. Sci. Tech. 8:715-717
5. Greimann LF, Lynn PP (1970) Finite element analysis of plate bending with transverse shear deformation. Nucl. Eng. Design 14:223-230
6. Reissner E (1945) The effect of transverse-shear deformation on the bending of elastic plates. J. Appl. Mech. 12:69-77
7. Mindlin RD (1951) Thickness-shear and flexural vibrations of crystal plates. J. Appl. Mech. 23:316-323
8. Washizu K (1975) Variational Methods in Elasticity and Plasticity, 2nd ed., Pergamon, Ch. 8
9. Lions JL (1973) Perturbations Singulieres dans les Problemes aux Limites et en Controle Optimal, Lecture Notes in Mathematics, No. 323, Springer-Verlag
10. Arnold DN (1981) Discretization by finite elements of a model parameter dependent problem. Numer. Math. 37:405-421
11. Brezzi F, Fortin M (1991) Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, Ch. 7
12. Zienkiewicz OC, Taylor RL (1988) The Finite Element Method, 4th ed., Vol. 1, McGraw-Hill, London, Ch. 8
13. Strang G, Fix GJ (1973) An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, Ch. 3
14. Lee N-S, Bathe K-J (1993) Effects of element distortions on the performance of isoparametric elements. Int. J. Num. Meth. Eng. 36:3553-3576
15. Kikuchi F (1994) Explicit expressions of shape functions for the modified 8-node serendipity element. Commun. Num. Meth. Eng. 10:711-716
16. Park HC, Lee SW (1995) A local coordinate system for assumed strain shell element formulation'. Comput. Mech. 15:473-484
17. Cheung YK, Jiao Z-P, Wu C-C (1995) General formulation of C° bending models based on the rational w-〈theta〉 constraint. Comput. Mech. 16:53-61
18. Flores FG, Onate E, Zarate F (1995) New assumed strain triangles for non linear shell analysis. Comput. Mech. 17:107-114
19. Huang BZ, Shenoy VB, Atluri SN (1993) A quasi-conforming triangular laminated composite shell element based on a refined first-order theory. Comput. Mech. 13:295-314
20. Bathe K-J (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, Part II, Ch. 5
21. Hughes TJR, Tezduyar TE (1981) Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J. Appl. Mech. 48:587-596
22. Fried I (1974) Residual energy balancing technique in the generation of plate bending element. Comput. Structures 4:771-778
23. Kant T, Kulkarni PB (1986) A C° continuous linear beam/bilinear plate flexure element. Comput. Structures 22:413-425
24. Timoshenko S, Woinowsky-Krieger S (1959) Theory of Plates and Shells, McGraw-Hill, New York, 2nd ed., Chs. 5 & 6
25. Reference Manual (1994) MSC/NASTRAN for Windows, Ver 1.0, The MacNeal-Schwendler Corporation, Los Angeles