On the love strain form of naturally curved and twisted rods

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Author(s)

  • A. Y T Leung
  • J. K W Chan

Detail(s)

Original languageEnglish
Pages (from-to)253-267
Journal / PublicationThin-Walled Structures
Volume28
Issue number3-4
Publication statusPublished - Jul 1997
Externally publishedYes

Abstract

Love proposed in 1944 [A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. Dover Publications, New York, 1944] that the non-vanishing (linear) strain components of a naturally curved and twist spatial rod, whose centroidal axis is along x and cross-section is in yz plane, can be represented nicely in the form εxx = e1 + zk2 - yk3 εxy = e2 - zk1 (*) εxz = e3 + yk1 where e1, e2, e3 are the strain components at y = z = 0 and k1, k2, k3 are the curvatures. Functions e1, e2, e3, k1, k2, k3 depend on x alone. Mottershead [J. E. Mottershead, "Finite elements for dynamical analysis for helical rods", International Journal of Mechanical Sciences, 22, (1980), pp 252-283], Pearson and Wittrick [D. Pearson and W. H. Witrick, "An exact solution for the vibration of helical springs using a Bernoulli-Euler Model", International Journal for Mechanical Sciences, 28, (1986), pp 83-96], Leung [A.Y.T. Leung "Exact shape functions for helix elements", Finite Elements in Analysis and Design, 9, (1991), pp 23-32], and Tabarrok and Xiong [B. Tabarrok and Y. Xiong, "On the buckling equations for spatial rods", International Journal for Mechanical Sciences, 31, (1980), pp 179-192] have made use of the Love form. We shall show that the Love form is not even valid for two-dimensionally curved beams when shear deformation is considered. The fact that the differential length ds at point P, on the cross-section with distance y, z away from the centroidal axis is different from the differential length dx at point S on the centroidal axis has been neglected. In fact ds = (1 -k3y + k2z)dx, where ki are initial curvatures, which contribute to the strain components of the first order of curvatures. © 1998 Elsevier Science Ltd. All rights reserved.

Citation Format(s)

On the love strain form of naturally curved and twisted rods. / Leung, A. Y T; Chan, J. K W.

In: Thin-Walled Structures, Vol. 28, No. 3-4, 07.1997, p. 253-267.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review