Vol. 6, No. 1-4, 2011

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ISSN: 1559-3959
On small azimuthal shear deformation of fibre-reinforced cylindrical tubes

Mohamed A. Dagher and Kostas P. Soldatos

Vol. 6 (2011), No. 1-4, 141–168
Abstract

The problem of azimuthal shear deformation of a transversely isotropic elastic circular cylindrical tube is considered and studied in the small deformation regime. The preferred direction of the transverse isotropy is assumed to lie on the plane of the tube cross-section and is due to the existence of a single family of plane spiral fibres. Consideration of the manner that either the tube material or the fibres may be constrained gives rise to four different versions of the problem which are all susceptible to an exact closed form solution when fibres are perfectly flexible. Particular attention is paid to the special case of straight fibres aligned along the radial direction of the tube cross-section, where comparisons are made between the aforementioned solution obtained when fibres are perfectly flexible and a corresponding solution obtained when fibres posses bending stiffness. It is found that the conventional linear elasticity considerations associated with the perfectly flexible fibre assumption cannot adequately account for the effects of material anisotropy. In contrast, effects of material anisotropy can be accounted for when fibres posses bending stiffness, by taking into consideration the action of couple-stress and therefore asymmetric stress. Moreover, an intrinsic material length parameter which appears naturally in the associated governing equations may be chosen as a representative of the fibre thickness in this case. It is also seen that deformation patterns of fibres possessing bending stiffness as well as corresponding stress distributions developed within the tube cross-section fit physical expectation much closer than their perfectly flexible fibre counterparts.

Keywords
anisotropic elasticity, azimuthal shear strain, fibre bending stiffness, fibre-reinforced materials, linear elasticity, transverse isotropy
Milestones
Received: 12 May 2010
Accepted: 17 July 2010
Published: 28 June 2011
Authors
Mohamed A. Dagher
Theoretical Mechanics
School of Mathematical Sciences
University of Nottingham
University Park
Nottingham
MG7 2RD
United Kingdom
Department of Science and Engineering Mathematics
Faculty of Petroleum and Mining Engineering
Suez Canal University
Suez
Egypt
Kostas P. Soldatos
Theoretical Mechanics
School of Mathematical Sciences
University of Nottingham
University Park
Nottingham
MG7 2RD
United Kingdom