Modification of the 8-node serendipity element

Computer Methods in Applied Mechanics and Engineering

Volumn 179, Issue 1-2, 1999, Pages 91-109

  Kikuchi, Fumio ^a   Okabe, Masayuki ^b   Fujio, Hidehiro ^c  

^a UNIVERSITY OF TOKYO   (Japan)

^b Optopian Incorporation   (Japan)

^c NEC CORPORATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; GEOMETRY; INTERPOLATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; POLYNOMIALS;

BILINEAR ISOPARAMETRIC SHAPE; CARTESIAN QUADRATIC POLYNOMIAL; NODE GENERATION TECHNIQUE; QUADRATIC TRIANGLE; SERENDIPITY QUADRILATERAL ELEMENT; SHAPE FUNCTIONS;

FINITE ELEMENT METHOD;

EID: 0033170333     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00031-6     Document Type: Article

References (16)

1. C. Taig, Structural analysis by the matrix displacement method, English Electric Aviation Report No. S017, 1961.
2. Irons B.M. Engineering application of numerical integration in stiffness method. J. AIAA. 14:1966;2035-2037.
3. G. Strang, G.J. Fix, An Analysis of the Finite Element Method, Ch. 3, Prentice-Hall, Englewood Cliffs, 1973.
4. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, Chs. 7 and 8, 4th ed., vol. 1, McGraw-Hill, London, 1988.
5. Lee N.-S., Bathe K.-J. Effects of element distortions on the performance of isoparametric elements. Int. J. Num. Meth. Eng. 36:1993;3553-3576.
6. MacNeal R.H., Harder R.L. Eight nodes or nine? Int. J. Num. Meth. Eng. 33:1992;1049-1058.
7. R.H. MacNeal, Finite Elements: Their Design and Performance, Ch. 8, Marcel Dekker, New York, 1994.
8. Kikuchi F. Explicit expressions of shape functions for the modified 8-node serendipity element. Com. Num. Meth. Eng. 10:1994;711-716.
9. K.-J. Bathe, Finite Element Procedures, Ch. 5, Prentice-Hall, Englewood Cliffs, 1996.
10. T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Part 1, Sec. 3, Prentice-Hall, Englewood Cliffs, 1987.
11. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, Chs. 1 and 2, North-Holland, Amsterdam, 1978.
12. S.C. Brenner, L.R. Scott, The Mathematical Theory of Finite Element Methods, Chs. 1 and 3, Springer, New York, 1994.
13. F. Kikuchi, K. Ishii, An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type, Preprint Series, Department of Mathematical Sciences, The University of Tokyo, No. 95-3 (1995).
14. Tessler A., Hughes T.J.R. An improved treatment of transverse shear in the Mindlin-type 4-node quadrilateral element. Comp. Meth. Appl. Mech. and Eng. 39:1995;311-335.
15. F. Kikuchi, Y. Ando, Triangular finite element for plate bending analysis with transverse shear deformation, J. Nucl. Sci. Tech. seems.
16. J. Zhang, F. Kikuchi, Interpolation error estimates of a modified 8-node serendipity finite element, Preprint Series, Graduate School of Mathematical Sciences, The University of Tokyo, No. 96-51 (1996).