A numerical study of the effect of penalty parameters for membrane elements with independent rotation fields and penalized equilibrium

Finite Elements in Analysis and Design

Volumn 42, Issue 8-9, 2006, Pages 757-765

  Long, Craig S ^a   Geyer, Sannelie ^a   Groenwold, Albert A ^a,b  

^a UNIVERSITY OF PRETORIA   (South Africa)

^b STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

Drilling degrees of freedom; Penalty parameter; Stress equilibrium

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DRILLING; STRESS ANALYSIS; TENSORS;

DRILLING DEGREES OF FREEDOM; PENALTY PARAMETER; STRESS EQUILIBRIUM;

NUMERICAL ANALYSIS;

EID: 33645403646     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2005.12.001     Document Type: Article

References (38)

1. F. Frey Shell finite elements with six degrees of freedom per node ASME Winter Annual Meeting 1989 San Francisco
2. P.G. Bergan, and C.A. Felippa A triangular membrane element with rotational degrees of freedom Comput. Meth. Appl. Mech. Eng. 50 1985 25 69
3. D.J. Allman A compatible triangular element including vertex rotations for plane elasticity analysis Comput. Struct. 19 1984 1 8
4. R.D. Cook On the Allman triangle and a related quadrilateral element Comput. Struct. 22 1986 1065 1067
5. D.J. Allman A quadrilateral finite element including vertex rotations for plane elasticity analysis Int. J. Numer. Meth. Eng. 26 1988 717 730
6. P. Jetteur, A shallow shell element with in-plane rotational degrees of freedom, IREM Internal Report 86/3, Ecole Polytechnique Federale de Lausanne, 1986.
7. S. Jaamei, "Jet" thin shell finite element with drilling rotations, IREM Internal Report 88/7, Ecole Polytechnique Federale de Lausanne, 1988.
8. P. Jetteur, Improvement of the quadrilateral "JET" shell element for a particular class of shell problems, IREM Internal Report 87/1, Ecole Polytechnique Federale de Lausanne, 1987.
9. R.L. Taylor Finite element analysis of linear shell problems J.R. Whiteman Proceedings of the Mathematics in Finite Elements and Applications 1987 Academic Press New York 191 203
10. R.L. Taylor, J.C. Simo, Bending and membrane elements for analysis of thick and thin shells, in: Proceedings of NUMETA Conference, Swansea, 1985.
11. J.C. Simo, D.D. Fox, and M.S. Rifai On a stress resultant geometrically exact shell model, Part II: The linear theory; computational aspects Comput. Meth. Appl. Mech. Eng. 73 1989 53 92
12. T.J.R. Hughes, and F. Brezzi On drilling degrees of freedom Comput. Meth. Appl. Mech. Eng. 72 1989 105 121
13. E. Reissner A note on variational principles in elasticity Int. J. Solids Struct. 1 1965 93 95
14. T.J.R. Hughes, F. Brezzi, A. Masud, and I. Harari Finite element with drilling degree of freedom: theory and numerical evaluation R. Gruber J. Periaux R.P. Shaw Proceedings of the Fifth International Symposium on Numerical Methods in Engineering vol. 1 1989 Springer Berlin 3 17
15. A. Ibrahimbegovic, R.L. Taylor, and E.L. Wilson A robust quadrilateral membrane finite element with drilling degrees of freedom Int. J. Numer. Meth. Eng. 30 1990 445 457
16. A. Ibrahimbegovic, and E.L. Wilson A unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom Commun. Appl. Numer. Meth. 7 1991 1 9
17. S. Geyer, and A.A. Groenwold Two hybrid stress membrane finite element families with drilling rotations Int. J. Numer. Meth. Eng. 53 2002 583 601
18. T.J.R. Hughes, A. Masud, and I. Harari Numerical assessment of some membrane elements with drilling degrees of freedom Comput. Struct. 55 1995 297 314
19. T.J.R. Hughes, A. Masud, and I. Harari Dynamic analysis and drilling degrees of freedom Int. J. Numer. Meth. Eng. 38 1995 3193 3210
20. S. Geyer, and A.A. Groenwold On reduced integration and locking of flat shell finite elements with drilling rotations Commun. Numer. Meth. Eng. 19 2003 85 97
21. T.H.H. Pian Derivation of element stiffness matrices by assumed stress distributions AIAA J. 2 1964 1333 1336
22. T.H.H. Pian State-of-the-art development of the hybrid/mixed finite element method Finite Elem. Anal. Des. 21 1995 5 20
23. M.A. Aminpour An assumed-stress hybrid 4-node shell element with drilling degrees of freedom Int. J. Numer. Meth. Eng. 33 1992 19 38
24. G. Rengarajan, M.A. Aminpour, and N.F. Knight Improved assumed-stress hybrid shell element with drilling degrees of freedom for linear stress buckling and free vibration analyses Int. J. Numer. Meth. Eng. 38 1995 1917 1943
25. K.Y. Sze, and A. Ghali Hybrid plane quadrilateral element with corner rotations ASCE J. Struct. Eng. 119 1993 2552 2572
26. C.-C. Wu, and Y.K. Cheung On optimization approaches of hybrid stress elements Finite Elem. Anal. Des. 21 1995 111 128
27. T.H.H. Pian, and K. Sumihara Rational approach for assumed stress finite elements Int. J. Numer. Meth. Eng. 20 1984 1685 1695
28. A.A. Groenwold, Q.Z. Xiao, N.J. Theron, Representing traction free boundaries using drilling degrees of freedom, in: B.H.V. Topping, Z. Bittnar (Eds.), The Sixth International Conference on Computational Structures Technology, Prague, Czech Republic, September 2002, Paper no. 22.
29. A.A. Groenwold, Q.Z. Xiao, and N.J. Theron Accurate solution of traction free boundaries using hybrid stress membrane elements with drilling degrees of freedom Comput. Struct. 82 2004 2071 2081
30. S. Di, and E. Ramm On alternative hybrid stress 2D and 3D elements Eng. Comput. 11 1994 49 68
31. R.D. Cook, D.S. Malkus, M.E. Plesha, and R.J. Witt Concepts and Applications of Finite Element Analaysis 2002 Wiley New York
32. Q.Z. Xiao, B.L. Karihaloo, and F.W. Williams Application of penalty-equilibrium hybrid stress element method to crack problems Eng. Fract. Mech. 63 1999 1 22
33. B.L. Karihaloo, and Q.Z. Xiao Hybrid stress elements for accurate solution of elasticity problems with traction-free segments B.H.V. Topping The Fifth International Conference on Computational Structures Technology, Computational Mechanics for the Twenty-First Century September 2000 Leuven Belgium 109 125
34. A.A. Groenwold, and N. Stander An efficient 4-node 24 d.o.f. thick shell finite element with 5-point quadrature Eng. Comput. 12 1995 723 748
35. C.S Long, A. de Klerk, A.A. Groenwold, Convergence of assumed stress elements with penalized equilibrium fields, Technical Report 2005/F/02, University of Pretoria, Structural Optimization Research Group, Department of Mechanical Engineering, February 2005 (Draft).
36. C.C. Wu, Q.Z. Xiao, and G. Yagawa Dual analysis for path integrals and bounds for crack parameter Int. J. Solids Struct. 35 1998 1635 1652
37. A. de Klerk, A.A. Groenwold, Finite element analysis of plane isotropic and orthotropic fracture problems, Technical Report 2005/F/03, University of Pretoria, Structural Optimization Research Group, Department of Mechanical Engineering, February 2005 (Draft).
38. G. Pimpinelli An assumed strain quadrilateral element with drilling degrees of freedom Finite Elem. Anal. Des. 41 2004 267 283