Vol. 4, No. 7-8, 2009

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ISSN: 1559-3959
Stability studies for curved beams

Chong-Seok Chang and Dewey H. Hodges

Vol. 4 (2009), No. 7-8, 1257–1270
Abstract
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The paper presents a concise framework investigating the stability of curved beams. The governing equations used are both geometrically exact and fully intrinsic; that is, they have no displacement and rotation variables, with a maximum degree of nonlinearity equal to two. The equations of motion are linearized about either the reference state or an equilibrium state. A central difference spatial discretization scheme is applied, and the resulting linearized ordinary differential equations are cast as an eigenvalue problem. The scheme is validated by comparing predicted numerical results for prebuckling deformation and buckling loads for high arches under uniform pressure with published analytical solutions. This is a conservative system of forces despite their being modeled as distributed follower forces. The results show that the stretch-bending coupling term must be included in order to accurately calculate the prebuckling curvature and bending moment of high arches. In addition, the lateral-torsional buckling instability of curved beams under tip moments is investigated. Finally, when a curved beam is loaded with nonconservative forces, resulting dynamic instabilities may be found through the current framework.

Keywords
elastic stability, structural stability, buckling, elastica, fully intrinsic
Milestones
Received: 22 December 2008
Revised: 31 December 2999
Accepted: 28 May 2009
Published: 26 December 2009
Authors
Chong-Seok Chang
Advanced Rotorcraft Technology
1330 Charleston Road
Mountain View, CA 94043
United States
Dewey H. Hodges
Georgia Institute of Technology
Daniel Guggenheim School of Aerospace Engineering
270 Ferst Drive
Atlanta, GA 30332-0150
United States
http://www.ae.gatech.edu/~dhodges/