Shell Finite Element Formulated on Shell Middle Surface
Publication: Journal of Engineering Mechanics
Volume 119, Issue 10
Abstract
A four‐noded quadrilateral pure shell element based on the thin‐shell theory of Koiter (1966) has been developed. The element, having a variable number of nodal degrees of freedom with a maximum of 12, is formulated on the plane reference domain by a mapping of the curved shell middle surface from the three‐dimensional space. Any arbitrary global coordinate system can be used due to the implementation of tensorial coordinate transformation. Excellent behavior of the element is observed when tested against a set of severe benchmark tests. The benchmark tests demonstrate that the element is able to handle rigid‐body motion without straining, inextensional modes of deformation, complex membrane strain states, and skewed meshes. The two‐dimensional interpolation functions are formed from the tensor product of Lagrange and Hermitian one‐dimensional interpolation functions, and the order of interpolation can be varied.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Allmann, D. J. (1988). “A quadrilateral finite element including vertex rotations for plane elasticity analysis.” Int. J. Numerical Methods in Engrg., 26, 717–730.
2.
Argyris, J. H., Haase, M., and Malejannakis, G. A. (1973). “Natural geometry on surfaces with specific reference to the matrix displacement analysis of shells, I, II and III.” Proc. Kon. Ned. Akad. Wetensch., Series B, 76, 361–410.
3.
Belytschko, T., Stolarski, H., Liu, W. K., Carpenter, N., and Ong, J. S. J. (1985). “Stress projection for membrane and shear locking in shell finite elements.” Comp. Methods in Appl. Mech. and Engrg., 51, 221–258.
4.
Bernadou, M. (1984). “Numerical analysis of thin shell problems.” Finite elements: special problems in solid mechanics, J. T. Oden and G. F. Carey, eds., Prentice‐Hall, Englewood Cliffs, N.J.
5.
Bernadou, M., and Boiserrie, J. M. (1982). The finite element method in thin shell theory: application to arch dam simulations. Birkhauser, Boston, Mass.
6.
Carpenter, N., Stolarski, H., and Belytschko, T. (1985). “A flat triangular shell element with improved membrane interpolation.” Communications in Appl. Numerical Methods, 1, 161–168.
7.
Ciarlet, P. G. (1976). “Conforming finite element methods for shell problems.” The mathematics of finite elements and applications, vol. 2, J. R. Whiteman, ed., Academic Press, London, U.K., 105–123.
8.
Cook, R. D. (1987). “Plane hybrid element with rotational D.O.F. and adjustable stiffness.” Int. J. Numerical Methods in Engrg., 24, 1499–1508.
9.
Davies, G. A. O. (1986). Proposed NAFEMS linear benchmarks. NAFEMS Publications, Glasgow, U.K.
10.
Dupuis, G. (1971). “Application of Ritz method to thin elastic shell analysis.” J. Appl. Mech., 71‐APM‐32, 1–9.
11.
Dupuis, G., and Goel, J.‐J. (1970). “A curved finite element for thin elastic shells.” Int. J. for Solids and Struct., 6, 1413–1428.
12.
Dvorkin, E. N., and Bathe, K. J. (1984). “A continuum mechanics based four‐node shell element for general nonlinear analysis.” Engrg. Comput., 6, 77–88.
13.
Engelmann, B. E., Whirley, R. G., and Goudreau, G. L. (1989). “A simple shell element formulation for large‐scale elastoplastic analysis.” Analytical and computational models of shells, CED‐vol. 3, A. K. Noor, T. Belytschko, and J. C. Simo, eds., ASME, New York, N.Y.
14.
Flügge, W. (1972). Tensor analysis and continuum mechanics. Springer‐Verlag, Heidelberg, Germany.
15.
Frey, F. (1963). “Shell finite elements with six degrees of freedom per node.” Analytical and computational models of shells, CED‐vol. 3, A. K. Noor, T. Belytschko, and J. C. Simo, eds., ASME, New York, N.Y.
16.
Knowles, N. C., Razzaque, A., and Spooner, J. B. (1976). “Experience on finite element analysis of shell structures.” Finite elements for thin shells and curved members, D. G. Ashwell and R. H. Gallagher, eds., John Wiley and Sons, London, U.K., 245–265.
17.
Koiter, W. T. (1966). “On the nonlinear theory of thin elastic shells.” Proc. Kon. Ned. Akad., Wetensch., B69, 1–54.
18.
Lay, K. S. (1989). Finite element and boundary element methods for the seismic analysis of liquid storage tanks, PhD thesis, University of Auckland, Auckland, New Zealand.
19.
Lindberg, G. M., Olson, M. D., and Crowper, G. R. (1969). “New developments in the finite element analysis of shells.” Quart. Bull. Div. Mech. Engrg. and the Nat. Aeronautical Establishment, 4.
20.
Morley, L. S. D., and Morris, A. J. (1978). Conflict between finite elements and shell theory. Report, Royal Aircraft Establishment, London, U.K.
21.
Morley, L. S. D. (1963). Skew plates and structures. Int. Series of Monographs in Aeronautics and Astronautics, McMillan, New York, N.Y.
22.
Park, K. C., Stanley, G. M., and Flaggs, D. L. (1985). “A uniformly reduced four‐noded C∘ shell element with consistent rank corrections.” Comp. and Struct., 20, 129–139.
23.
Pinsky, P. M., and Jasti, R. V. (1963). “On the use of bubble functions for controlling accuracy and stability of mixed shell finite elements.” Analytical and computational models of shells, CED‐vol. 3, A. K. Noor, T. Belytschko, and J. C. Simo, ASME, New York, N.Y.
24.
Simo, J. C., Fox, D. D., and Rifai, M. S. (1989). “On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects.” Comp. Methods in Appl. Mech. and Engrg., 73, 53–92.
25.
Timoshenko, S. (1959). Theory of plates and shells, 2nd Ed., McGraw‐Hill, New York, N.Y., 206 and 544.
26.
Saigal, S., and Yang, T. Y. (1985). “Nonlinear dynamic analysis with a 48 D.O.F. curved thin shell element.” Int. J. Numerical Methods in Engrg., 21, 1115–1128.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jun 20, 1991
Published online: Oct 1, 1993
Published in print: Oct 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.