Vol. 3, No. 3, 2008

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The effect of taper on section constants for in-plane deformation of an isotropic strip

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

Vol. 3 (2008), No. 3, 425–440

The variational-asymptotic method is used to obtain an asymptotically-exact expression for the strain energy of a tapered strip-beam. The strip is assumed to be sufficiently thin to warrant the use of two-dimensional elasticity. The taper is represented by a nondimensional constant of the same order as the ratio of the maximum cross-sectional width to the wavelength of the deformation along the beam, and thus its cube is negligible compared to unity. The resulting asymptotically-exact section constants, being functions of the taper parameter, are then used to find section constants for a generalized Timoshenko beam theory. These generalized Timoshenko section constants are then used in the associated one-dimensional beam equations to obtain the solution for the deformation of a linearly tapered beam subject to pure axial, pure bending, and transverse shear forces. These beam solutions are then compared with plane stress elasticity solutions, developed for extension, bending, and flexure of a linearly tapered isotropic strip. The agreement is excellent, and the results show that correction of the section constants using the taper parameter is necessary in order for beam theory to yield accurate results for a tapered beam.

beam theory, asymptotic methods, dimensional reduction, tapered beam
Received: 6 July 2007
Revised: 3 October 2007
Accepted: 8 October 2007
Published: 1 May 2008
Dewey H. Hodges
Daniel Guggenheim School of Aerospace Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0150
United States
Jimmy C. Ho
Daniel Guggenheim School of Aerospace Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0150
United States
Wenbin Yu
Wenbin Yu
Mechanical & Aerospace Engineering Department
Utah State University
Logan, UT 84322-4130
United States