Vol. 5, No. 6, 2010

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ISSN: 1559-3959
Stress and strain recovery for the in-plane deformation of an isotropic tapered strip-beam

Dewey H. Hodges, Anurag Rajagopal, Jimmy C. Ho and Wenbin Yu

Vol. 5 (2010), No. 6, 963–975
Abstract

The variational-asymptotic method was recently applied to create a beam theory for a thin strip-beam with a width that varies linearly with respect to the axial coordinate. For any arbitrary section, ratios of the cross-sectional stiffness coefficients to their customary values for a uniform beam depend on the rate of taper. This is because for a tapered beam the outward-directed normal to a lateral surface is not perpendicular to the longitudinal axis. This changes the lateral-surface boundary conditions for the cross-sectional analysis, in turn producing different formulae for the cross-sectional elastic constants as well as for recovery of stress, strain and displacement over a cross-section. The beam theory is specialized for the linear case and solutions are compared with those from plane-stress elasticity for stress, strain and displacement. The comparison demonstrates that for beam theory to yield such excellent agreement with elasticity theory, one must not only use cross-sectional elastic constants that are corrected for taper but also the corrected recovery formulae, which are in turn based on cross-sectional in- and out-of-plane warping corrected for taper.

Keywords
beam theory, elasticity, asymptotic methods
Milestones
Received: 1 May 2010
Revised: 10 July 2010
Accepted: 17 August 2010
Published: 1 January 2011
Authors
Dewey H. Hodges
Daniel Guggenheim School of Aerospace Engineering
Georgia Institute of Technology
270 Ferst Drive
Atlanta, GA 30332-0150
United States
http://www.ae.gatech.edu/~dhodges/
Anurag Rajagopal
Daniel Guggenheim School of Aerospace Engineering
Georgia Institute of Technology
270 Ferst Drive
Atlanta, GA 30332-0150
United States
Jimmy C. Ho
Science and Technology Corporation
Ames Research Center
Moffett Field, CA 94035
United States
Wenbin Yu
Department of Mechanical and Aerospace Engineering
Utah State University
Logan, UT 84322-4130
United States