A nine-node assumed strain finite element for large-deformation analysis of laminated shells

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 5, 1998, Pages 777-798

  Lee, S J ^a   Kanok Nukulchai, W ^b  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b ASIAN INSTITUTE OF TECHNOLOGY   (Thailand)

Author keywords

Arc length control method; Assumed strain method; Element based Lagrangian formulation; Equivalent natural constitutive equation; Laminated shell; Three successive finite rotations

Indexed keywords

COMPOSITE STRUCTURES; DEFORMATION; FINITE ELEMENT METHOD; LAMINATED COMPOSITES; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MULTILAYERS; ROTATION; STRAIN; STRESS ANALYSIS; STRUCTURAL ANALYSIS; STRUCTURAL LOADS;

ARC LENGTH CONTROL METHOD; ASSUMED STRAIN METHOD; EQUIVALENT NATURAL CONSTITUTIVE EQUATION; LAGRANGIAN FORMULATION;

SHELLS (STRUCTURES);

EID: 0032123836     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980715)42:5<777::AID-NME365>3.0.CO;2-P     Document Type: Article

References (59)

1. A. K. Noor, T. Belytschko and J. C. Simo, Analytical and Computational Models of Shells, CED-V01 3, ASME 1989.
2. P. C. Chou and J. Carleone, 'Elastic constants of layered media', J. Compos. Material., 6, 80-93 (1972).
3. R. A. Chaudhuri and P. Seide, 'Triangular finite element for analysis of thick laminated plates', 24, 1203-1224 (1987).
4. K. J. Bathe, E. Ramm and E. L. Wilson, 'Finite clement formulations for large deformation dynamic analysis', Int. J. Numer. Meth. Engng., 9, 353-386 (1975).
5. E. Ramm, 'A plate/shell element for large deflections and rotations', in K. J. Bathe, J. T. Oden and W. Wunderlick (eds.), Formulations and Computational Algorithms in Finite Element Analysis, MIT Press, Cambridge, MA, 1977.
6. L. E. Malvern, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood cliffs, N.J., 1969.
7. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th edn, Vols. 1 and 2, McGraw-Hill, New York, 1989.
8. K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood cliffs, N.J., 1982.
9. W. Kanok-Nukulchai and W. K. Wong, 'Element-based Lagrangian formulation for large-deformation analysis', Comput. Struct., 30, 967-974 (1988).
10. S. Ahmad, B. M. Irons and O. C. Zienkiewicz, 'Analysis of thick and thin shell structures by curved finite elements', Int. J. Numer. Meth. Engna., 2, 419-451 (1970)
11. O. C. Zienkiewicz, R. L. Taylor and J. M. Too, 'Reduced integration technique in general analysis of plates and shells', Int. J. Numer. Meth. Engng., 3, 275-290 (1971).
12. S. F. Pawsey and R. W. Clough, 'Improved numerical integration of thick shell finite elements', Int. J. Numer. Meth. Engng., 3, 575-586 (1971).
13. S. F. Pawsey, 'Discussion of papers by O. C. Zienkiewicz, R. L. Taylor and J. M. Too and S. F. Pawsey and R. W. Clough', Int. J. Numer. Meth. Engng., 4, 449-450 (1972).
14. T. J. R. Hughes, R. L. Taylor and W. Kanoknukulchai, 'A simple and efficient finite element for plate bending', Int. J. Numer. Meth. Engng., 11, 1529-1543 (1977).
15. T. Belytschko, J. S. Ong, W. K. Wong and J. M. Kennedy, 'Hourglass control in linear and nonlinear problems', Comput. Meth. Appl. Mech. Engng., 43, 251-276 (1984).
16. J. C. Schulz, 'Finite clement hourglassing control', Int. J. Numer. Meth. Engng., 21, 1039-1048 (1985).
17. B. C. Koh and N. Kikuchi, 'New improved hourglass control for bilinear and bilinear elements in anisotropic linear elasticity', Comput. Meth. Appl. Mech. Engng., 65, 1-46 (1987).
18. T. Belytschko, B. L. Wong and H. Stolarski, 'Assumed strain stabilization procedure for the 9-node Lagrangian shell element', Int. J. Numer. Meth. Engng., 28, 385-414 (1989).
19. E. N. Dvorkin and K. J. Bathe, 'A continuum mechanics based on four-node shell element for general nonlinear analysis', Engng. Comput., 1, 77-88 (1984).
20. H. C. Huang and E. Hinton, 'A new nine node degenerated shell element with enhanced membrane and shear interpolation', Int. J. Numer. Meth. Engng., 22, 73-92 (1986).
21. H. C. Huang, 'Implementation of assumed strain degenerated shell elements', Comput. Struct., 25, 147-155 (1987).
22. J. Jang and P. M. Pinsky, 'An assumed covariant strain based 9-node shell element', Int. J. Numer. Meth. Engng., 24, 2389-2411 (1987).
23. J. C. Simo and T. J. R. Hughes, 'On the variational formulations of assumed strain methods', J. Appl. Mech., 53, 51-54 (1986).
24. K.J. Bathe and E. N. Dvorkin, 'A formulation of general shell elements - The use of mixed interpolation of tensorial components', Int. J. Numer. Meth. Engng., 22, 697-722 (1986).
25. N. Stander, A. Matzenmiller and E. Ramm, 'An assessment of assumed strain methods in finite rotation shell analysis', Engng. Comput., 6, 58-66 (1989).
26. J. H. Kim and S. W. Lee, 'An efficient assumed strain element model with six DOF per node for geometrically nonlinear shell', Int. J. Numer. Meth. Engng., 38, 4101-4122 (1995).
27. K. C. Park and G. M. Stanley, 'A curved C○ shell element based on assumed natural-coordinate strains', J. Appl. Mech., 66, 173-198 (1988).
28. K. S. Surana and R. M. Sorem, 'Geometrically non-linear formulation for three dimensional curved beam elements with large rotations', Int. J. Numer. Meth. Engng., 28, 43-73 (1989).
29. J. H. Argyris, 'An excursion into large rotations', Comput. Meth. Appl. Mech. Engng., 32, 85-155 (1982)
30. K. M. Hsaio and Y. R. Chen, 'Nonlinear analysis of shell structures by degenerated isoparametric shell element', Comput. Struct., 31, 427-438 (1989).
31. J. C. Simo, D. D. Fox and M. S. Rifai, 'Geometrically Exact stress resultant shell problems: Formulation and computational aspect of the nonlinear theory', in A. K. Moor et al. (eds.), Analytical and Computational Models of Shells, CED-V01 3, ASME, 1989.
32. W. Kanok-Nukulchai, R. L. Taylor and T. J. R. Hughes, 'A large deformation formulation for shell analysis by finite element method', Comput. Struct., 13, 19-27 (1981).
33. W. Kanok-Nukulchai, 'A simple and efficient finite element for general shell analysis', Int. J. Numer. Meth. Engng., 14, 179-200 (1979).
34. H. Ma and W. Kanok-Nukulchai, 'On the application of assumed strained methods', in Kanok-Nukulchai et al. (eds.), Structural Engineering and Construction: Achievements, Trends and Challenges, 1989, pp. 1168-1175.
35. M. A. Crisfield, 'A fast incremental/iterative solution procedure that handles "snap-through", Comput. Struct., 13, 55-62 (1981).
36. T. Chaiomphob, W. Kanok-Nukulchai and F. Nishino, 'An automatic arc-length control algorithm for tracing equilibrium paths of nonlinear structures', Struct. Engng. Earthquake Engng., JSCE, 5, 205-208 (1988).
37. R. H. Macnel and R. L. Harder, 'A proposed standard set of problems to test finite element accuracy', Finite Elements Anal. design, 11, 3-20 (1985).
38. R. H. Macnel, 'Derivation of element stiffness matrices by assumed strain distributors', Nucl. Engng. Design, 70, 3-12 (1982).
39. D. W. White and J. F. Abel, 'Test of shell finite element accuracy and robustness', finite Elements Analysis Design, 6, 129-151 (1989).
40. K. J. Bathe and S. Bolourchi, 'A geometric and material non-linear plate and shell element', Comput. Struct., 11, 23-48 (1980).
41. K. S. Surana, 'A generalized geometrically nonlinear formulation with large rotations for finite elements with rotational degrees of freedoms', Comput. Struct., 24, 47-55 (1986).
42. K. S. Surana, 'Geometrically nonlinear formulation for the curved shell elements', Int. J. Numer. Meth. Engng., 19, 581-615 (1983).
43. A. F Saleeb, T. Y. Chang, W. Graf and S. Yingyeunyong, 'A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problems', Int. J. Numer. Meth. Engng., 29, 407-446 (1990).
44. A. S. Mawenya and J. D. Davies, 'Finite element bending analysis of multilayer plates', Int. J. Numer. Meth. Engng., 8, 215-225 (1974).
45. N. J. Pagano and S. J. Hatfield, 'Elastic behavior of multilayered bidirectional composites', AIAA, 10, 931-933 (1972).
46. S. C. Panda and R. Natarajan, 'Finite element analysis of laminated composite plates', Int. J. Numer. Meth. Engng., 14, 69-79 (1979).
47. J. N. Reddy, 'A penalty plate-bending element for the analysis of laminated anisotropic composite plates', Int. J. Numer. Meth. Engng., 15, 1187-1206 (1980).
48. S. Saigal, R. K. Kapania and Y. T. Yang, 'Geometrically nonlinear finite element analysis of imperfect laminated shells', J. Compos. Mater., 20, 197-214 (1986).
49. A. K. Noor and M. D. Mathers, 'Anisotropy and shear deformation in laminated composite plates', AIAA, 14, 282-285 (1976).
50. C. H. Yeom and S. W. Lee, 'An assumed strain finite element model for large deflection composite shells', Int. J. Numer. Meth. Engng., 28, 1749-1768 (1989).
51. P. G. Bergan, G. Horrigmoe, B. Krakeland and T. H. Søreide, 'Solution techniques for non-linear finite element problems', Int. J. Numer. Meth. Engna., 12, 1677-1696 (1978).
52. T. Y. Chang and K. Sawamiphakdi, 'Large deformation analysis of laminated shells by finite element method', Comput. Struct., 13, 331-340 (1981).
53. W. C. Chao and J. N. Reddy, 'Analysis of laminated composite shells using a degenerated 3-D element', Int. J. Numer. Meth. Engng., 20, 1991-2007 (1984).
54. S. W. Groesberg, Advanced Mechanics, Wiley, New York, 1968.
55. Y. H. Kim and S. W. Lee, 'A solid element formulation for large deflection analysis of composite shell structures', Comput. Struct., 30, 269-274 (1988).
56. S. G Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body, P. Fern (trans.), J. J. Brandstatter (ed.), Holden-Day, San Francisco, 1963.
57. C. L. Liao and J. N. Reddy, 'Analysis of anisotropic, stiffened composite laminates using a continuum-based shell elements', Comput. Struct., 34, 805-815 (1990).
58. A. S. Mawenya, 'Finite element analysis of sandwich plate structures', Ph.D. Thesis, University of Wales, Swansea.
59. 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. Methods Appl. Mech. Engng., 73, 53-92 (1989).