Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-12T22:07:10.234Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of general shells by flat facet finiteelement approximation

Published online by Cambridge University Press:  04 July 2016

D. J. Allman
D. J. Allman*
Affiliation:
Royal Aerospace Establishment, Farnborough
Get accessRights & Permissions [Opens in a new window]

Summary

A standard flat facet approximation for finite element analysis of general thin shells has been sought after for many years, but fundamental difficulties hindered the development of a definitive solution. Recent advances in the finite element method, however, have provided more rational resolutions of some of these difficulties than the kind of artifices which were employed formerly. This paper completes the theory of a basic triangular flat shell element which incorporates modern developments and meets practical criteria of mathematical simplicity and general applicability. The flat facet shell element is also, potentially, an appropriate basis for constructing a better curved approximation to a shell surface in order to achieve improved accuracy. Numerical results are given for a variety of shell test problems to provide comparisons with accepted benchmark solutions and to assess the available accuracy relative to other finite element formulations.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 95 , Issue 946 , July 1991, pp. 194 - 203
Copyright
Copyright © Royal Aeronautical Society 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Love, A. E. H. The small free vibrations and deformation of a thin elastic shell. Phil Trans R Soc, 1888, 179 A, pp 491–546.Google Scholar
2. Love, A. E. H. A treatise on the mathematical theory of elasticity. Cambridge University Press (fourth edition 1927).Google Scholar
3. Calladine, C. R. Love Centenary Lecture: The theory of thin shell structures (1888-1988). Proc Inst Mech Eng, 1988, 202, p42.Google Scholar
4. Koiter, W. T. A consistent first approximation in the general theory of thin elastic shells. Proc IUTAM Symposium on the Theory of Thin Elastic Shells, Ed. Koiter, W. T., pp 12–33, North-Holland, Amsterdam, 1960.Google Scholar
5. Turner, M. J., Clough, R. W., Martin, H. C., and Topp, L. J. Stiffness and deflection analysis of complex structures. J Aeronaut Sci, 1956, 23, (9), p 805.Google Scholar
6. Morley, L. S. D. On the constant moment plate bending element J Strain Anal, 1971, 6, (1), pp 20–24.Google Scholar
7. Dawe, D. J. Shell analysis using a simple facet element. J Strain Anal, 1972, 7, (4), pp 266–270.Google Scholar
8. Morley, L. S. D. and Mould, M. P. The role of bending in the finite element analysis of thin shells. Finite Elements Anal Des, 1987, 3, pp 213–240.Google Scholar
9. Kirchhoff, G. R. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. J Reine Angew Math (Crelle), 1850, Bd 40, pp 51–88.Google Scholar
10. Allman, D. J. A simple cubic displacement element for plate bending. Int J Numer Meth Eng, 1976, 10, pp 263–281.Google Scholar
11. Irons, B. M. and Ahmad, S. Techniques of finite elements. Ellis Horwood, Chichester, England, 1980.Google Scholar
12. Zienkiewicz, O C. The finite element method. Ch 13, McGraw- Hill Book Company, Maidenhead, England, 1977.Google Scholar
13. Argyris, J. H., Haase, M., Mlejnek, H.-P. and Schmolz, P. K. TRUNC for shells — an element possibly to the taste of Bruce Irons. Int J Numer Meth Eng, 1986, 22, pp 93–115.Google Scholar
14. Bathe, K.-J. and Ho, L.-W. A simple and effective element for analysis of general shells. Int J Comput Struct, 1981, 13, pp 673– 681.Google Scholar
15. Argyris, J. H., Dunne, P. C., Malejannakis, G. A. and Schelkl, E. A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems. Comput Meth Appl Mech Eng, 1977, 10, pp 371–403; 1977, 11, pp 97-131.Google Scholar
16. Felippa, C. A. Refined finite element analysis of linear and non linear two-dimensional structures. PhD Dissertation, SESM Report 66-26, Department of Civil Engineering, University of California, Berkeley, CA, 1966.Google Scholar
17. Carr, A. J. Refined finite element analysis of thin shell structures including dynamic loadings. PhD Dissertation, SESM Report 67-9, Department of Civil Engineering, University of California, Berkeley, CA, 1967.Google Scholar
18. Bergan, P. G. Plane stress analysis using the finite element method. Triangular element with six parameters at each node. Division of Structural Mechanics, The Norwegian Institute of Technology, Trondheim, 1967.Google Scholar
19. Holland, I. and Bergan, P. G. Higher order finite element for plane stress. Discussion. Proc ASCE, J Eng Mech Div, 1967, 93, (EM4), pp 149–174.Google Scholar
20. Tocher, J. L. and Hartz, B. J. Higher order finite element for plane stress. Proc ASCE, J Eng Mech Div, 1967, 93, (EM4), pp 149–174.Google Scholar
21. Olson, M. D. and Bearden, T. W. A simple flat shell element revisited. Int J Numer Meth Eng, 1979, 14, pp 51–68.Google Scholar
22. Mohr, G. A. Finite element formulation by nested interpolations: application to the drilling freedom problem. Int J Comput Struct, 1982, 15, (2), pp 185–190.Google Scholar
23. Allman, D. J. A compatible triangular finite element including vertex rotations for plane elasticity analysis. IntJ Comput Struct, 1984, 19, (1/2), pp 1–8.Google Scholar
24. Bergan, P. G. and Felippa, C. A. A triangular membrane element with rotational degrees of freedom. Comput Meth Appl Mech Eng, 1985, 50, pp 25–69.Google Scholar
25. Sabir, A. B. A rectangular and a triangular plane elasticity element with drilling degree of freedom. Proc 2nd Int Conf on Variational Methods in Engineering, Ch 9, pp 17–25, Springer-Verlag, Berlin, 1985.Google Scholar
26. Taylor, R. L. and Simo, J. C. Bending and membrane elements for analysis of thick and thin shells. NUMETA 85 Numerical Methods in Engineering: Theory and Applications, Eds: Pande, G. N. and Middleton, J., pp 587–591, Balkema, A. A., Rotterdam, 1985.Google Scholar
27. Carpenter, N., Stolarski, H. and Belytschko, T. A flat triangular shell element with improved membrane interpolation. Commun Appl Numer Meth, 1985, 1, pp 161–168.Google Scholar
28. Carpenter, N., Stolarski, H. and Belytschko, T. Improvements in 3-node triangular shell elements. Int J Numer Meth Eng, 1986, 23, pp 1643–1667.Google Scholar
29. Jetteur, P. and Frey, F. A four node MargUerre element for non-linear shell analysis. Eng Comp, 1986, 3, pp 276–282.Google Scholar
30. Cook, R. D. On the Allman triangle and a related quadrilateral element. Comput Struct, 1986, 22, pp 1065–1067.Google Scholar
31. Cook, R. D. A plane hybrid element with rotational D.O.F. and adjustable stiffness. Int J Numer Meth Eng, 1987, 24, (8), pp 1499–1508.Google Scholar
32. MacNeal, R. H. and Harder, R. L. A refined four-noded membrane element with rotational degrees of freedom. Comput Struct, 1988, 28, (1), pp 75–84.Google Scholar
33. Allman, D. J. A quadrilateral finite element including vertex rotations for plane elasticity analysis. Int J Numer Meth Eng, 1988, 26, pp 717–730.Google Scholar
34. Allman, D. J. The constant strain triangle with drilling rotations: a simple prospect for shell analysis. Proc 6th International Conference on the Mathematics of Finite Elements and Applications, MAFELAP VI, Ed. Whiteman, J. R., pp 233–240, 1988.Google Scholar
35. Allman, D. J. Evaluation of the constant strain triangle with drilling rotations. Int J Numer Meth Eng, 1988, 26, (12), pp 2645– 2655.Google Scholar
36. Hughes, T. R. J. and Brezzi, F. On drilling degrees of freedom. Comput Meth Appl Mech Eng, 1989, 72, pp 105–121.Google Scholar
37. Harris, J. ap C. and Bartholomew, P. Cubic triangular membrane element with drilling rotation freedoms. RAE Technical Report 89042, 1989.Google Scholar
38. Batoz, J. L., Bathe, K. J. and Ho, L. W. A study of three node triangular plate bending elements. Int J Numer Meth Eng, 1980, 15, pp 1771–1812.Google Scholar
39. Macneal, R. H. and Harder, R. L. A proposed standard set of problems to test finite element accuracy. Finite Elements Anal Des, 1985, 1, pp 3–20.Google Scholar
40. Allman, D. J. Triangular finite elements for plate bending with constant and linear bending moments. Proc IUTAM Symposium on High Speed Computing of Elastic Structures, 1971,1, pp 105–136, University of Liege.Google Scholar
41. Stolarski, H. and Belytschko, T. Membrane locking and reduced integration for curved elements. J Appl Mech, 1982, 49, pp 172–176.Google Scholar
42. Morley, L. S. D. Analysis of developable shells with special reference to the finite element method and circular cylinders. Phil Trans R Soc A, 1976, 281, (1300), pp 113–170.Google Scholar
43. Bergan, P. G. and Nygard, M. K. Non-linear shell analysis using free formulation finite elements. Europe — US Symposium on Finite Element Methods for Non-linear Problems, Eds. Bathe, K. J., Bergan, P. G. and Wunderlich, W. Vol II, Springer Verlag, 1986.Google Scholar
44. Dvorkin, E. N. and Bathe, K. J. A continuum mechanics based four-node shell element for general non-linear analysis. Eng Comput, 1984, 1, pp 77–88.Google Scholar
45. Scordelis, A. C. and Lo, K. S. Computer analysis of cylindrical shells. J Am Concr Inst, 1969, 61, pp 539–561.Google Scholar
46. Idelsohn, S. On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures. Comput Meths Appl Mech Eng, 1981, 26, pp 321–330.Google Scholar
47. Morley, L. S. D. A facet like shell theory. Int J Eng Sci, 1984, 22, (11/12), pp 1315–1327.Google Scholar
48. Morley, L. S. D. and Morris, A. J. Conflict between finite elements and shell theory. Proc 2nd World Conference on Finite Element Methods, Ch 25, Robinson and Associates, Bourne mouth, England, 1978.Google Scholar