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# Anisotropic Elastic Tubes of Arbitrary Cross Section Under Arbitrary End Loads: Separation of Beamlike and Decaying Solutions

[+] Author and Article Information

Laboratoire de Mecanique et Technologie, ENS de Cachan,  CNRS-Paris VI, Paris, France

J. G. Simmonds1

Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904-4742

1

Some of this work was performed while JGS was a visitor at ENS de Cachan.

J. Appl. Mech 72(4), 500-510 (Jul 29, 2004) (11 pages) doi:10.1115/1.1934532 History: Received February 06, 2004; Revised July 29, 2004

## Abstract

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 $O(h∕R)$, where $R$ is some equivalent cross sectional radius. Solutions are decomposed into the sum of an exact beamlike or Saint-Venant solution, treated in Ladevèze (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.

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