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A mixed co-rotational curved quadrilateral shell element

A mixed co-rotational curved quadrilateral shell element This paper presents a 9-node isoparametric formulation of degenerated curved shell element, which is based on a co-rotational framework. Within this framework, the local reference axes are easily defined by the two diagonal vectors generated by the four corner nodes in the current deformed configuration. Furthermore, vectorial rotational variables are utilised, which consist of the two smaller components of each nodal orientation vector, enabling additive and commutative rotational operations. The element strain energy is evaluated in the local co-rotational system using the Green strain, where the Hellinger-Reissner functional is employed with assumed strain tensors for the membrane and shear strain fields to alleviate the membrane/shear locking phenomena. By defining the equilibrium conditions in terms of the out-of-balance between the work-conjugate internal and external forces, symmetric element tangent stiffness matrices are achieved in both the local and global systems, thus leading to considerable computational benefits. Finally, several examples of elastic shells subject to large displacements are considered, which demonstrate favourable performance of the proposed finite element formulation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Structural Engineering Inderscience Publishers

A mixed co-rotational curved quadrilateral shell element

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Publisher
Inderscience Publishers
Copyright
Copyright © Inderscience Enterprises Ltd. All rights reserved
ISSN
1758-7328
eISSN
1758-7336
DOI
10.1504/IJStructE.2011.039423
Publisher site
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Abstract

This paper presents a 9-node isoparametric formulation of degenerated curved shell element, which is based on a co-rotational framework. Within this framework, the local reference axes are easily defined by the two diagonal vectors generated by the four corner nodes in the current deformed configuration. Furthermore, vectorial rotational variables are utilised, which consist of the two smaller components of each nodal orientation vector, enabling additive and commutative rotational operations. The element strain energy is evaluated in the local co-rotational system using the Green strain, where the Hellinger-Reissner functional is employed with assumed strain tensors for the membrane and shear strain fields to alleviate the membrane/shear locking phenomena. By defining the equilibrium conditions in terms of the out-of-balance between the work-conjugate internal and external forces, symmetric element tangent stiffness matrices are achieved in both the local and global systems, thus leading to considerable computational benefits. Finally, several examples of elastic shells subject to large displacements are considered, which demonstrate favourable performance of the proposed finite element formulation.

Journal

International Journal of Structural EngineeringInderscience Publishers

Published: Jan 1, 2011

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