Abstract
The design of accurate and robust elements for modelling thin shell and moderately thick shell structures has been a problem challenging researchers for more than 30 years and extensive studies can be found in the literature [10.1–10.3]. Over the years, we can identify four distinct approaches to finite element modelling of shell structures. These are the facet representation using flat plate elements, the use of elements based on shell theories in a curvilinear co-ordinate system, the use of 3D solid elements, and the degenerate shell elements. In recent years, the degenerate shell element has been receiving considerable attention. It is arguably, the most difficult of all the finite elements taken up for study in this book and it is still not clear that all the problems faced in formulating it have been resolved. In this chapter, we shall take up this element formulation for study. We shall first briefly review the other approaches before proceeding to the study of the degenerate shell element.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Zienkiewicz, The Finite Element Method, 3rd edn., McGraw-Hill, London, 1977.
D. G. Ashwell and R. H. Gallagher, Finite Elements for Thin Shells and Curved Members, Wiley, London, 1976.
W. Gilewski and M. Radwanska,“A survey of finite element models for the analysis of moderately thick shells,” Finite Elements in Anal. & Des., Vol. 9, 1991, pp. 1–21.
S. Ahmad, B. M. Irons and 0. C. Zienkiewicz, C., “Analysis of thick and thin shell structures by curved finite elements,” Int. J. Numer. Meths. Engrg., Vol. 2, 1970, pp. 419–451.
C. Zienkiewicz, R. L. Taylor and J. M. Too, “Reduced integration techniques in general analysis of plates and shells,” Int. J. Numer. Meths. Engrg., Vol. 3, 1971, pp. 275–290.
S. E. Pawsey and R. W. Clough, “Improved numerical integration of thick shell finite elements,” Int. J. Numer. Meths. Engrg., Vol. 3, 1971, pp. 545–586.
G. Prathap and B. R. Somashekar, “Field-and edge-consistency synthesis of a four-node quadrilateral plate bending element,” Int. J. Numer. Meths. Engrg., Vol. 26, 1988, pp. 1693–1708.
G. Prathap, B. P. Naganarayana and B. R. Somashekar, “Field-consistency analysis of the isoparametric eight-noded plate bending element,” Comp. Struct., Vol. 29, 1988, pp. 857–873.
B. P. Naganarayana and G. Prathap, “Displacement and stress predictions from field-and line-consistent versions of the eight-node Mindlin plate element,” Comp. Struct., Vol. 33, 1987, pp. 1095–1106.
S. W. Lee and T. H. H. Pian, “Improvement of plate and shell elements by mixed formulations,” AIAA J, Vol. 16, 1978, pp. 29–34.
J. Donea and L. G. Lamain, “A modified representation of transverse shear in C° quadrilateral plate elements,” Comp. Methods Appl. Mech. Eng., Vol. 63, 1987, pp. 183–207.
E. Hinton and H. C. Huang, “A family of quadrilateral Mindlin plate elements with substitute shear strain fields,” Comp. Struct., Vol. 23, 1986, pp. 409–431.
K. J. Bathe and E. N. Dvorkin, “A formulation of general shell elements–the use of mixed interpolation of tensorial components,” Int. J. Numer. Meths. Engrg., Vol. 22, 1986, pp. 697–722.
G. Prathap and B. P. Naganarayana, “Stress oscillations and spurious load mechanisms in variationally inconsistent formulations,” Int. J. Mumer. Meths. Engrg., Vol. 33, 1992, pp. 2181–2197.
B. P. Naganarayana, G. Prathap, B. Dattaguru and T. S. Ramamurthy, “A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element,” Comp. Methods Appl. Mech. Eng., Vol. 97, 1992, pp. 355–374.
C. K. Choi and S. W. Yoo, “Combined use of multiple improvement techniques in degenerated shell element,” Comp. Struct., Vol. 39, 1991, pp. 557–569.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Prathap, G. (1993). General Shell Elements. In: The Finite Element Method in Structural Mechanics. Solid Mechanics and Its Applications, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3319-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-017-3319-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4326-9
Online ISBN: 978-94-017-3319-9
eBook Packages: Springer Book Archive