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The development of hybrid axisymmetric elements based on the Hellinger-Reissner variational principle

Jog, CS and Annabattula, R (2005) The development of hybrid axisymmetric elements based on the Hellinger-Reissner variational principle. In: International Journal for Numerical Methods in Engineering .

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Abstract

We present a general procedure for the development of hybrid axisymmetric elements based on the Hellinger-Reissner principle within the context of linear elasticity. Similar to planar elements, the stress interpolation is obtained by an identification of the zero-energy modes. We illustrate our procedure by designing a lower-order (four-node) and a higher-order (nine-node) element. Both elements are of correct rank, and moreover use the minimum number of stress parameters, namely seven and 17. Several examples are presented to show the excellent performance of both elements under various demanding situations such as when the material is almost incompressible, when the thickness to radius ratio is very small, etc. When the variation of the field variables is along the radial direction alone, when the mesh is uniform, and the loading is of pressure type, the developed elements are superconvergent, i.e. they yield the exact nodal displacement values.

Item Type: Journal Article
Additional Information: The copyright belongs to John Wiley & Sons, Ltd. Online publication, print awaited.
Keywords: hybrid axisymmetric elements;zero energy modes;hellinger reissner principle
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 07 Dec 2005
Last Modified: 19 Sep 2010 04:21
URI: http://eprints.iisc.ernet.in/id/eprint/4233

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