On reduced integration and locking of flat shell finite elements with drilling rotations

Communications in Numerical Methods in Engineering

Volumn 19, Issue 2, 2003, Pages 85-97

  Geyer, Sannelie ^a   Groenwold, Albert A ^a  

^a UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Drilling rotations; Flat shell finite element; Locking; Reduced integration

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DRILLING; FINITE ELEMENT METHOD;

STRESS MEMBRANE FINITE ELEMENTS;

ROTATION;

DRILLING; FINITE ELEMENT ANALYSIS;

EID: 0037294231     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.567     Document Type: Article

References (22)

1. Geyer S, Groenwold AA. Two hybrid stress membrane finite element families with drilling rotations. International Journal for Numerical Methods in Engineering 2002; 53:583-601.
2. Hughes TJR, Brezzi F. On drilling degrees of freedom. Computer Methods in Applied Mechanics and Engineering 1989; 72:105-121.
3. Di S, Ramm E. On alternative hybrid stress 2D and 3D elements. Engineering Computations 1994; 11:49-68.
4. Feng W, Hoa SV, Huang Q. Classification of stress modes in assumed stress fields of hybrid finite elements. International Journal for Numerical Methods in Engineering 1997; 40:4313-4339.
5. Taylor RL. Finite element analysis of linear shell problems. In Proceedings of the Mathematics in Finite Elements and Applications, Whiteman JR (ed.). Academic Press: New York, 1987; 191-203.
6. Chapelle D, Bathe KJ. Fundamental considerations for the finite element analysis of shell structures. Computers and Structures 1998; 66:19-36.
7. Ibrahimbegovic A, Taylor RL, Wilson EL. A robust quadrilateral membrane finite element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering 1990; 30:445-457.
8. Ibrahimbegovic A, Wilson EL. A unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom. Communications in Applied Numerical Methods 1991; 7:1-9.
9. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Analysis. Prentice-Hall; London, 1987.
10. Reissner E. A note on variational principles in elasticity. International Journal of Solids and Structures 1965; 1:93-95.
11. Fraeijs du Veubeke B. Displacement and equilibrium models in the finite element method. In Stress Analysis, Zienkiewicz OC, Holister GC (eds). Wiley: Chichester, 1965; 145-197.
12. Groenwold AA, Stander N. An efficient 4-node 24 d.o.f. thick shell finite element with 5-point quadrature. Engineering Computations 1995: 12:723-748.
13. Sze K-Y, Ghali A. Hybrid plane quadrilateral element with corner rotations. Journal of Structural Engineering 1993; 119:2552-2572.
14. Dvorkin EN, Bathe K-J. A continuum mechanics based four-node shell element for general non-linear analysis. Engineering Computations 1984; 1:77-88.
15. Bathe K-J, Dvorkin EN. A four node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation. International Journal for Numerical Methods in Engineering 1985; 21:367-383.
16. Bathe KJ, Brezzi F. A simplified analysis of two plate bending elements-the MITC4 and MITC9 elements. In Proceedings of the Mathematics in Finite Elements and Applications, NUMETA 87, Pande GN, Middleton J (eds), vol. 17. Martinus Nijhoff: Dordrecht, 1987.
17. Hughes TJR, Tezduyar TE. Finite elements based upon mindlin plate theory, with particular reference to the 4-node bilinear isoparametric element. Journal of Applied Mechanics 1981; 48:587-595.
18. Macneal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Journal of Finite Elements in Analytical Design 1985; 1:3-20.
19. Parisch H. An investigation of a finite rotation four node assumed strain shell element. International Journal for Numerical Methods in Engineering 1991; 31:127-150.
20. Simo JC, Fox DD, Rifai MS. On a stress resultant geometrically exact shell model, Part II: The linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering 1989; 73:53-92.
21. Dovey HH. Extension of three dimensional analysis to shell structures using the finite element idealization. Ph.D. Dissertation, University of California, Berkeley, 1974 (Report No. UC SESM 74-2).
22. Stander N, Wilson EL. A 4-node quadrilateral membrane element with in-plane vertex rotations and modified reduced quadrature. Engineering Computations 1989; 6:266-271.