On the use of an enhanced transverse shear strain shell element for problems involving large rotations

Computational Mechanics

Volumn 30, Issue 4, 2003, Pages 286-296

  Fontes Valente, R A ^a   Natal Jorge, R M ^b   Cardoso, R P R ^a   Cesar de Sa J M A ^b   Gracio J J A ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

^b UNIVERSITY OF PORTO   (Portugal)

Author keywords

Enhanced shear strains; Large rotations; Shear locking; Shell elements

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; MATHEMATICAL MODELS; SHEAR STRESS; SHELLS (STRUCTURES);

ENHANCED SHEAR STRAIN; SHEAR LOCKING; TRANSVERSE SHEAR STRAIN;

STRAIN;

EID: 0037623347     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0388-x     Document Type: Article

References (51)

1. Ahmad S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved finite elements. Int. J. Numer. Meth. Eng. 2: 419-451
2. Andelfinger U, Ramm E (1993) EAS-Elements for two-dimensional, three-dimensional, plate and shells and their equivalence to HR-elements. Int. J. Numer. Meth. Eng. 36: 1413-1449
3. Basar Y, Ding Y, Krätzig WB (1992) Finite-rotation shell elements via mixed formulation. Comput. Mech. 10: 289-306
4. Basar Y, Weicher D (2000) Nonlinear Continuum Mechanics of Solids. Springer-Verlag, Berlin Heidelberg New York
5. Bathe KJ, Bolourchi S (1980) A geometric and material nonlinear plate and shell element. Comput. Struct. 11: 23-48
6. Bathe KJ, Dvorkin E (1986) A formulation of general shell elements - the use of mixed interpolation of tensorial components. Int. J. Numer. Meth. Eng. 22: 697-722
7. Bathe KJ (1996) Finite Element Procedures. 2nd edn. Prentice-Hall, New Jersey
8. Belytschko T, Liu WK, Moran B (2000) Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, West Sussex
9. Betsch P, Gruttmann F, Stein E (1996) A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains. Comput. Meth. Appl. Mech. Eng. 130: 57-79
10. Bischoff M, Ramm E (1997) Shear deformable shell elements for large strains and rotations. Int. J. Numer. Meth. Eng. 40: 4427-4449
11. Brank B, Peric D, Damjanic FB (1995) On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells. Comput. Mech. 16: 341-359
12. Brank B, Peric D, Damjanic FB (1997) On large deformations of thin elasto-plastic shells: implementation of a finite rotation model for a quadrilateral shell element. Int. J. Numer. Meth. Eng. 40: 689-726
13. Büchter N, Ramm E, Roehl D (1994) Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept. Int. J. Numer. Meth. Eng. 37: 2551-2568
14. Cardoso RPR, Yoon JW, Grácio JJA, Barlat F, César de Sá JMA (2002) Development of a one point quadrature shell element for nonlinear applications with contact and anisotropy. Comput. Meth. Appl. Mech. Eng. 191: 5177-5206
15. César de Sá JMA, Owen DRJ (1986) The imposition of the incompressibility constraint in finite elements - A review of methods with a new insight to the locking phenomenon. In: Taylor C et al. (eds) Proceedings of the 3rd International Conference on Numerical Methods for Non-Linear Problems. Pineridge Press Ltd, Swansea
16. Cé de Sá JMA, Natal Jorge RM (1999) New enhanced strain elements for incompressible problems. Int. J. Numer. Meth. Eng. 44: 229-248
17. César de Sá JMA, Areias PMA, Natal Jorge RM (2001) Quadrilateral elements for the solution of elasto-plastic finite strain problems. Int. J. Numer. Meth. Eng. 51: 883-917
18. César de Sá JMA, Natal Jorge RM, Fontes Valente RA, Areias PMA (2002) Development of shear locking-free shell elements using an enhanced assumed strain formulation. Int. J. Numer. Meth. Eng. 53: 1721-1750
19. Crisfield MA (1981) A fast incremental/iterative solution procedure that handles "snap-through". Comput. Struct. 13: 55-62
20. Crisfield MA (1983) An arc-length method including line searches and accelerations. Int. J. Numer. Meth. Eng. 19: 1269-1289
21. Crisfield MA, Peng X (1996) Short communication: Instabilities induced by coarse meshes for a nonlinear shell problem. Eng. Comput. 13: 110-114
22. Crisfield MA (1997) Non-Linear Finite Element Analysis of Solids and Structures, Vol. 1: Essentials, Vol. 2: Advanced Topics. John Wiley & Sons, West Sussex
23. Doghri I (2000) Mechanics of Deformable Solids - Linear, Nonlinear, Analytical and Computational Aspects. Springer-Verlag, Berlin Heidelberg New York
24. Dvorkin E, Bathe KJ (1984) A continuum mechanics based four-node shell element for general nonlinear analysis. Eng. Comput. 1: 77-88
25. Flanagan DP, Taylor LM (1987) An accurate numerical algorithm for stress integration with finite rotations. Comput. Meth. Appl. Mech. Eng. 62: 305-320
26. Horrigmoe G, Bergan PG (1978) Nonlinear analysis of free-form shells by flat finite elements. Comput. Meth. Appl. Mech. Eng. 16: 11-35
27. Hughes TJR, Cohen M, Haroun M (1978) Reduced and selective integration techniques in finite element analysis of plates. Nucl. Eng. Des. 46: 203-222
28. Hughes TJR, Liu WK (1981) Nonlinear finite element analysis of shells: Part I. Three-dimensional shells. Comput. Meth. Appl. Mech. Eng. 26: 331-362
29. Hughes TJR, Tezduyar TE (1981) Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J. Appl. Mech. 48: 587-596
30. Hughes TJR (2000) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. 2nd edn. Dover Editions, Toronto
31. Ibrahimbegovic A, Brank B, Courtois P (2001) Stress resultant geometrically exact form of classical shell model and vector-like parameterization of constrained finite rotations. Int. J. Numer. Meth. Eng. 52: 1235-1252
32. Jiang L, Chernuka MW (1994) A simple four-noded corotational shell element for arbitrarily large rotations. Comput. Struct. 53: 1123-1132
33. Krakeland B (1977) Large displacement analysis of shells considering elastic-plastic and elasto-viscoplastic materials. Report No. 776, Norwegian Institute of Technology, University of Trondheim, Norway
34. Liu WK, Lam D, Law SE, Belytschko T (1986) Resultant stress degenerated shell element. Comput. Meth. Appl. Mech. Eng. 55: 259-300
35. MacNeal RH (1978) A simple quadrilateral shell element. Comput. Struct. 8: 175-183
36. MacNeal RH (1982) Derivation of element stiffness matrices by assumed strain distribution. Nucl. Eng. Des. 70: 3-12
37. Masud A, Tham CL, Liu WK (2000) A stabilized 3D co-rotational formulation for geometrically nonlinear analysis of multi-layered composite shells. Comput. Mech. 26(1): 1-12
38. Moita GF, Crisfield MA (1996) A finite element formulation for 3D continua using the corotational technique. Int. J. Numer. Meth. Eng. 39: 3775-3792
39. 0 elements. Int. J. Numer. Meth. Eng. 22: 281-288
40. 0 shell element based on assumed natural coordinate strains. J. Appl. Mech. 53: 278-290
41. Peng X, Crisfield MA (1992) A consistent corotational formulation for shells using the constant stress/constant moment triangle. Int. J. Numer. Meth. Eng. 35: 1829-1847
42. Ramm E (1977) A plate/shell element for large deflections and rotations. In: Bathe KJ, Oden JT, Wunderlich W (eds) Formulations and Computational Algorithms in Finite Element Analysis, M.I.T. Press
43. Saleeb AF, Chang TY, Graf W, Yingyeunyong S (1990) A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problems. Int. J. Numer. Meth. Eng. 29: 407-446
44. Sansour C, Bufler H (1992) An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation. Int. J. Numer. Meth. Eng. 34: 73-115
45. Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 29: 1595-1638
46. Simo JC, Fox DD, Rifai MS (1990) On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory. Comput. Meth. Appl. Mech. Eng. 79: 21-70
47. Simo JC, Armero F (1992) Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 33: 1413-1449
48. Simo JC, Armero F, Taylor RL (1993) Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Comput. Meth. Appl. Mech. Eng. 110: 359-386
49. Stanley GM, Park KC, Hughes TJR (1986) Continuum-based resultant shell elements. In: Hughes TJR, Hinton E (eds) Finite Element Methods for Plate and Shell Structures, Pineridge Press, Swansea, pp. 1-45
50. Yoon JW, Yang DY, Chung K (1999) Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials. Comput. Meth. Appl. Mech. Eng. 174: 23-56
51. Zienkiewicz OC, Taylor RL, Too JM (1979) Reduced integration techniques in general analysis of plates and shells. Int. J. Numer. Meth. Eng. 3: 275-290