A revisit of a cylindrically anisotropic tube subjected to pressuring, shearing, torsion, extension and a uniform temperature change

Tungyang Chen, Chi Tai Chung, Wei Long Lin

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)

Abstract

The problem of a cylindrically anisotropic tube or bar was seemed to be first examined by Lekhnitskii (1981) [Lekhnitskii, S.G., 1981. Theory of Elasticity of an Anisotropic Body. (Trans, from the revised 1977 Russian edition.) Mir, Moscow]. Recently, a thorough investigation of the subject was performed by Ting (1996) [Ting, T.C.T., 1996. Pressuring, shearing, torsion and extension of a circular tube or bar of cylindrically anisotropic material. Proc. Roy. Soc. Lond. A452, 2397-2421] in which a formulation akin to that of Stroh's formalism is employed to resolve the boundary value problem subjected to a uniform pressure, shearing, torsion and uniform extension. In a continuing paper, Ting (1999) [Ting, T.C.T., 1999. New solutions to pressuring, shearing, torsion and extension of a cylindrically anisotropic elastic circular tube or bar. Proc. Roy. Soc. Lond, to appear.] rederived the solutions based on a modified formalism of Lekhnitskii, in which the solutions are in terms of elastic compliances, reduced elastic compliances as well as doubly reduced compliance. The results are much more compact and simpler than those of the earlier one. Independently, in this work, we construct the governing system also under the Lekhnitskii's framework. Nevertheless, the present work and Ting's formulation (1999) are not alike. Besides the loads considered in Ting (1996, 1999), we add the effect of a uniform temperature change in the formulation. The assumption that the stresses depend only on r makes it possible to incorporate the various loading cases considered. In addition to the explicit forms of admissible stresses, we derive the admissible displacements which are ensured to be single-valued for a multiply-connected domain. In contrast to the Ting's works (1996, 1999), which often require superpositions of two or more basic solutions, the present solutions offer complete forms of solutions ready for direct calculations. We also report that, as in rectilinearly anisotropic solids, an entire analogy is observed between the fields of a uniform axial extension and a uniform temperature change in cylindrically anisotropic solids.

Original languageEnglish
Pages (from-to)5143-5159
Number of pages17
JournalInternational Journal of Solids and Structures
Volume37
Issue number37
DOIs
Publication statusPublished - 2000 Sep 11

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A revisit of a cylindrically anisotropic tube subjected to pressuring, shearing, torsion, extension and a uniform temperature change'. Together they form a unique fingerprint.

Cite this