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Research Papers

Analytical Modeling of Trapeze and Poynting Effects of Initially Twisted Beams

[+] Author and Article Information
Fang Jiang

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: jiang302@purdue.edu

Wenbin Yu

Associate Professor
Fellow ASME
School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: wenbinyu@purdue.edu

Dewey H. Hodges

Professor
Fellow ASME
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0150
e-mail: dhodges@gatech.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 19, 2015; final manuscript received April 9, 2015; published online April 30, 2015. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 82(6), 061003 (Jun 01, 2015) (11 pages) Paper No: JAM-15-1028; doi: 10.1115/1.4030362 History: Received January 19, 2015; Revised April 09, 2015; Online April 30, 2015

An asymptotically correct, nonlinear, analytical cross-sectional analysis is developed for pretwisted, isotropic beams under axial load and torsion. A comprehensive model is presented that for the first time simultaneously counts for both trapeze and Poynting effects (either positive or negative). Several material models are used and differences are discussed in detail. The limitations of the uniaxial stress assumption and Saint-Venant/Kirchhoff materials are illustrated. Compared to the widely accepted results in the literature, the present theory demonstrates improved results without introducing assumptions commonly used in other works. It is concluded that the trapeze and Poynting phenomena are governed by the material models and warping functions, and nonlinearly coupled extension and torsion can be eliminated by properly selecting the thickness-to-width ratio.

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Figures

Grahic Jump Location
Fig. 1

Schematic of slightly twisted trapeze being restored to untwisted state by indicated force components (Reprinted with permission from Hodges [1]. Copyright 2006 by American Institute of Aeronautics and Astronautics, Inc).

Grahic Jump Location
Fig. 2

Schematic of undeformed and deformed beam

Grahic Jump Location
Fig. 4

Plot of Eq. (64) for a rectangular section

Grahic Jump Location
Fig. 3

Plot of Eq. (61) for an elliptical section

Grahic Jump Location
Fig. 5

Plot of Eq. (66) for an elliptical section (F1/EA = 0.005): (a) G/E = 0.4 and (b) G/E = 0.025

Grahic Jump Location
Fig. 6

u1 of the middle position of a solid elliptical section beam. (a) Rubber beam with μ = 1.5 MPa and K = 0.5 GPa (κ1 = 0.171 rad/m) and (b) aluminum beam with E = 68.9 GPa and ν = 0.33 (κ1 = 0.038 rad/m).

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