An anisotropic heterogeneous beam with overspecified boundary conditions

Lyons, Kevin

doi:10.2140/jomms.2008.3.1549

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An anisotropic heterogeneous beam with overspecified boundary conditions

C. Kevin Lyons

Vol. 3 (2008), No. 8, 1549–1559

DOI: 10.2140/jomms.2008.3.1549

Abstract

In this paper a heterogeneous anisotropic cylindrical beam with a rigidly fixed base is considered as an alternative to the relaxed Saint-Venant’s problem. The rigidly fixed base results in a problem with overspecified boundary conditions for which a proof of existence is given. The results of this paper indicate that the relaxed Saint-Venant’s problem, for loads independent of the axial coordinate, ignores the dependence of the stress field on the axial coordinate. Dependence of the stress field on the axial coordinate could result in warping of transverse cross sections and nonzero in-plane stresses, which is significant for understanding the behavior of natural structures such as wood and mammalian bone.

Keywords

Anisotropic, heterogeneous, dynamic, cantilever beam

Milestones

Received: 5 March 2008

Revised: 2 August 2008

Accepted: 11 August 2008

Published: 1 October 2008

Authors

C. Kevin Lyons
Faculty of Forestry University of British Columbia Department of Forest Resources Management Forest Sciences Centre Vancouver B.C. V6T 1Z4 Canada

Vol. 3, No. 8, 2008

C. Kevin Lyons

Abstract

Keywords

Milestones

Authors