|
|||||
 |
|
|
|
|
|
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 |
|
|
