Explicit eight-noded quadrilateral elements

Finite Elements in Analysis and Design

Volumn 31, Issue 3, 1999, Pages 209-222

  Barrett, K E ^a  

^a Institute for Clean Growth and Future Mobility   (United Kingdom)

Author keywords

Element; Explicit; Isoparametric; Quadrilateral; Stiffness

Indexed keywords

COMPUTER PROGRAMMING LANGUAGES; CONTINUUM MECHANICS; GEOMETRY; INTEGRATION; MATRIX ALGEBRA; STIFFNESS;

EXPLICIT; ISOPARAMETRIC; MAPLE; QUADRILATERAL;

FINITE ELEMENT METHOD;

EID: 0032631606     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(98)00067-5     Document Type: Article

References (16)

1. D.K. Babu, G.F. Pinder, Analytical integration formulae for linear isoparametric finite elements, Int. J. Num. Methods Eng. 20 (1984) 1153-1166.
2. D.V. Griffiths, Stiffness matrix of the four-node quadrilateral element in closed form, Int. J. Num. Methods Eng. 37 (1994) 1027-1038.
3. D.V. Griffiths, G.G.W. Mustoe, Selective reduced integration of four-node plane element in closed form, J. Eng. Mech. (1995) 725-729.
4. W.L. Hacker, H.L. Schreyer, Eigenvalue analysis of compatible and incompatible finite elements, Int. J. Num. Methods Eng. 28 (1989) 687-703.
5. M. Okabe, Analytical integration formulae related to convex quadrilateral finite element, Comput. Methods Appl. Mech. Eng. 29 (1978) 201-208.
6. H.D. Rathod, Some analytical integration formulae for a four node isoparametric element, Comput. Struct. 30 (1988) 1101-1109.
7. L. Videla, M. Cerrolaza, N. Aparicio, Explicit integration of the stiffness matrix of a four-noded plane elasticity finite element, Comm. Numer. Methods Eng. 12 (11) (1996).
8. S.W. Ye, G. Yagawa, S. Yoshimura, A numerical integration scheme for finite element method based on symbolic manipulation, Int. J. Num. Methods Eng. 29 (1990) 1539-1549.
9. M. Ledvinka, A program for the explicit integration of a four-noded planar isoparametric hybrid stress element, Comm. Appl. Numer. Methods 4 (1988) 573-576.
10. T. Y. Chang, H.Q. Tan, D. Zheng, M. W. Yuan, Application of symbolic method to hybrid/mixed finite elements and computer implementation, Comput. Struct. 35 (1990) 293-299.
11. R.L. Spilker, Invariant eight-node hybrid stress elements for thin and moderately thick plates, Int. J. Num. Methods Eng. 18 (1982) 1153-1178.
12. P. Tong, A family of hybrid plate elements, Int. J. Num. Methods Eng. 18 (1982) 1455-1468.
13. K.E. Barrett, Jacobians for isoparametric finite elements, Comm. Num. Methods Eng. 12 (11) (1996) 755-766.
14. C.V. Durrell, Algebraic Geometry, Bell, London, 1955.
15. E.A. Maxwell, The Methods of Plane Projective Geometry Based on the Use of General Homogeneous Coordinates, Cambridge University Press, Cambridge, 1952.
16. K.-Y. Yuan, Y.-S. Huang, T.H. Pian, Inverse mapping and distortion measures for quadrilaterals with curved boundaries, Int. J. Num. Methods Eng. 37 (1994) 861-875.