A 9-node co-rotational quadrilateral shell element

Computational Mechanics

Volumn 42, Issue 6, 2008, Pages 873-884

  Li, Z X ^a   Izzuddin, B A ^b   Vu Quoc, L ^c  

^a ZHEJIANG UNIVERSITY   (China)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c J Crayton Pruitt Family Department of Biomedical Engineering   (United States)

Author keywords

Additive rotational variable; Co rotational approach; Quadrilateral shell element; Symmetric tangent stiffness matrix

Indexed keywords

COMPUTATIONAL EFFICIENCY; STIFFNESS; STRAIN ENERGY;

ELEMENT FORMULATION; GLOBAL COORDINATE SYSTEMS; INCREMENTAL SOLUTIONS; QUADRILATERAL SHELL ELEMENT; ROTATIONAL VARIABLE; SECOND DERIVATIVES; TANGENT STIFFNESS; TANGENT STIFFNESS MATRIX;

STIFFNESS MATRIX;

EID: 48349138231     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-008-0289-8     Document Type: Article

References (36)

1. Felippa CA and Haugen B (2005). A unified formulation of small-strain corotational finite elements: I. Theory. Comput Methods Appl Mech Eng 194: 2285-2335
2. Rankin CC and Brogan FA (1986). An element independent corotational procedure for the treatment of large rotation. ASME J Pressure Vessel Technol 108: 165-174
3. Crisfield MA and Moita GF (1996). A co-rotational formulation for 2-D continua including incompatible modes. Int J Numer Methods Eng 39: 2619-2633
4. Yang HTY, Saigal S, Masud A and Kapania RK (2000). Survey of recent shell finite elements. Int J Numer Methods Eng 47: 101-127
5. Tham CL, Zhang Z and Masud A (2005). An elasto-plastic damage model cast in a co-rotational kinematic framework for large deformation analysis of laminated composite shells. Comput Methods Appl Mech Eng 194: 2641-2660
6. Izzuddin BA (2005). An enhanced co-rotational approach for large displacement analysis of plates. Int J Numer Methods Eng 64: 1350-1374
7. Wempner G (1969). Finite elements, finite rotations and small strains of flexible shells. Int J Solids Struct 5: 117-153
8. Belytschko T and Hseih BJ (1973). Non-linear transient finite element analysis with convected co-ordinates. Int J Numer Methods Eng 7: 255-271
9. Belytschko T and Glaum LW (1979). Application of higher order corotational stretch theories to nonlinear finite element analysis. Comput Struct 10: 175-182
10. Argyris JH, Bahner H, Doltsnis J, et al. (1979) Finite element method-the natural approach. Comput Methods Appl Mech Eng 17/18:l-106
11. Oran C (1973). Tangent stiffness in plane frames. J Struct Div ASCE 99(ST6): 973-985
12. Oran C (1973). Tangent stiffness in space frames. J Struct Div ASCE 99(ST6): 987-1001
13. Stolarski H, Belytschko T and Lee SH (1995). Review of shell finite elements and corotational theories. Comput Mech Adv 2: 125-212
14. Cardoso RPR, Valente RAF, Yoon JW, Gracio JJ and Jorge RMN (2006). A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness - Part II: Nonlinear applications. Int J Numer Methods Eng 67: 160-188
15. Brunet M and Sabourin F (2006). Analysis of a rotation-free 4-node shell element. Int J Numer Methods Eng 66: 1483-1510
16. Kim KD and Lomboy GR (2006). A co-rotational quasi-conforming 4-node resultant shell element for large deformation elasto-plastic analysis. Comput Methods Appl Mech Eng 195: 6502-6522
17. Liu WK, Guo Y, Tang S and Belytschko T (1998). A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis. Comput Methods Appl Mech Eng 154: 69-132
18. Bathe KJ, Lee PS and Hiller JF (2003). Towards improving the MITC9 shell element. Comput Struct 81: 477-489
19. Simo JC, Rifai MS and Fox DD (1992). On a stress resultant geometrically exact shell-model. 6. Conserving algorithms for nonlinear dynamics. Int J Numer Methods Eng 34(1): 117-164
20. Simo JC and Tarnow N (1994). A new energy and momentum conserving algorithm for the non-linear dynamics of shells. Int J Numer Methods Eng 37: 2527-2549
21. Dickinson MH, Lehmann FO and Sane SP (1999). Wing rotation and the aerodynamic basis of insect flight. Science 284: 1954-1960
22. Li ZX (2007). A mixed co-rotational formulation of 2D beam element using vectorial rotational variables. Commun Numer Methods Eng 23: 45-69
23. Li ZX (2007). A co-rotational formulation for 3D beam element using vectorial rotational variables. Comput Mech 39: 309-322
24. Li ZX and Vu-Quoc L (2007). An efficient co-rotational formulation for curved triangular shell element. Int J Numer Methods Eng 72(9): 1029-1062
25. Crisfield MA (1991). Nonlinear finite element analysis of solid and structures, vol 1. Essentials Wiley, Chichester
26. Yang YB and Shieh MS (1990). Solution method for nonlinear problems with multiple critical points. AIAA J 28: 2110-2116
27. Belytschko T, Wong BL and Stolarski H (1989). Assumed strain stabilization procedure for the 9-node Lagrange shell element. Int J Numer Methods Eng 28: 385-414
28. MacNeal RH and Harder RL (1985). Proposed standard set of problems to test finite element accuracy. Finite Elements Anal Des 1: 3-20
29. Szilard R (1974). Theory and analysis of plates. Prentice-Hall, Englewood Cliffs
30. Bletzinger KU, Bischoff M and Ramm E (2000). Unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput Struct 75: 321-334
31. Campello EMB, Pimenta PM and Wriggers P (2003). A triangular finite shell element based on a fully nonlinear shell formulation. Comput Mech 31: 505-518
32. Simo JC, Fox DD and Rifai MS (1990). On a stress resultant geometrically exact shell model Part III: computational aspects of the nonlinear theory. Comput Methods Appl Mech Eng 79: 21-70
33. Jiang L and Chernuka MW (1994). A simple four-noded corotational shell element for arbitrarily large rotations. Comput Struct 53: 1123-1132
34. Celigoj CC (1996). Strain-and-displacement-based variational method applied to geometrically non-linear shells. Int J Numer Methods Eng 39: 2231-2248
35. Klinkel S, Gruttmann F and Wagner W (2006). A robust non-linear solid shell element based on a mixed variational formulation. Comput Methods Appl Mech Eng 195: 179-201
36. Klinkel S, Gruttmann F and Wagner W (1999). A continuum based three-dimensional shell element for laminated structures. Comput Struct 71: 43-62