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

The problem of a cylindrically anisotropic tube or bar was seemed to be fir st examined by Lekhnitskii (1981) [Lekhnitskii, S.G., 1981. Theory of Elast icity of an Anisotropic Body. (Trans. from the revised 1977 Russian edition .) Mir, Moscow]. Recently, a thorough investigation of the subject was perf ormed 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. Sec. Lend. A452, 2397-2421] in which a formulation akin to that of Stroh's formalism is employed to resolve the boundary value problem sub jected to a uniform pressure, shearing, torsion and uniform extension. In a continuing paper, Ting (1999) [Ting, T.C.T., 1999. New solutions to pressu ring, shearing, torsion and extension of a cylindrically anisotropic elasti c circular tube or bar. Proc. Roy. Sec. Lend, to appear.] rederived the sol utions based on a modified formalism of Lekhnitskii, in which the solutions are in terms of elastic compliances, reduced elastic compliances as well a s doubly reduced compliance. The results are much more compact and simpler than those of the earlier one. Independently, in this work, we construct th e governing system also under the Lekhnitskii's framework. Nevertheless, th e present work and Ting's formulation (1999) are not alike. Besides the loa ds considered in Ting (1996, 1999), we add the effect of a uniform temperat ure 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 a dmissible displacements which are ensured to be single-valued for a multipl y-connected domain. In contrast to the Ting's works (1996, 1999), which oft en require superpositions of two or more basic solutions, the present solut ions offer complete forms of solutions ready for direct calculations. We al so report that, as in rectilinearly anisotropic solids, an entire analogy i s observed between the fields of a uniform axial extension and a uniform te mperature change in cylindrically anisotropic solids. (C) 2000 Elsevier Sci ence Ltd. All rights reserved.