Anisotropic elastic tubes of arbitrary cross section under arbitrary end loads:: Separation of beamlike and decaying solutions

First approximation analytical solutions are constructed for finite and semi-infinite, fully anisotropic elastic tubes of constant thickness h and arbitrary cross section, subject to purely kinetic or purely kinematic boundary conditions. Final results contain relative errors of O(root/h/R) where R is some equivalent cross sectional radius. Solutions are decomposed into the sum of an exact beamlike or Saint-Venant solution, treated in Ladeveze et al. (Int. J. Solids Struct., 41, pp. 1925-1944, 2004) and extended in an appendix; a rapidly decaying edge-zone solution; and a slowly decaying semi-membrane-inextensional-bending (MB) solution. Explicit conditions on the boundary data are given that guarantee decaying solutions. The MB solutions are expressed as an infinite series of complex-valued exponential functions times real-valued one-dimensional eigenfunctions which satisfy a fourth-order differential equation in the circumferential coordinate and depend on the pointwise cross sectional curvature only.