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TECHNICAL PAPERS

Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams

[+] Author and Article Information
Wenbin Yu, Dewey H. Hodges

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150

J. Appl. Mech 71(1), 15-23 (Mar 17, 2004) (9 pages) doi:10.1115/1.1640367 History: Received August 30, 2002; Revised June 16, 2003; Online March 17, 2004
Copyright © 2004 by ASME
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References

Le, K. C., 1999, Vibrations of Shells and Rods, 1st Ed., Springer, Berlin.
Ciarlet,  P. G., and Destuynder,  P., 1979, “A Justification of a Nonlinear Model in Plate Theory,” Comput. Methods Appl. Mech. Eng., 17/18, pp. 227–258.
Berdichevsky,  V. L., 1979, “Variational-Asymptotic Method of Constructing a Theory of Shells,” Prikl. Mat. Mekh., 43(4), pp. 664–687.
Hodges,  D. H., Atilgan,  A. R., Cesnik,  C. E. S., and Fulton,  M. V., 1992, “On a Simplified Strain Energy Function for Geometrically Nonlinear Behavior of Anisotropic Beams,” Composites Eng., 2(5–7), pp. 513–526.
Cesnik,  C. E. S., and Hodges,  D. H., 1993, “Stiffness Constants for Initially Twisted and Curved Composite Beams,” Appl. Mech. Rev., 46(11, Part 2), pp. S211–S220.
Cesnik,  C. E. S., and Hodges,  D. H., 1997, “VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling,” J. Am. Helicopter Soc., 42(1), pp. 27–38.
Popescu,  B., and Hodges,  D. H., 1999, “On Asymptotically Correct Timoshenko-Like Anisotropic Beam Theory,” Int. J. Solids Struct., 37(3), pp. 535–558.
Popescu,  B., Hodges,  D. H., and Cesnik,  C. E. S., 2000, “Obliqueness Effects in Asymptotic Cross-Sectional Analysis of Composite Beams,” Comput. Struct., 76(4), pp. 533–543.
Yu,  W., Hodges,  D. H., Volovoi,  V. V., and Cesnik,  C. E. S., 2002, “On Timoshenko-Like Modeling of Initially Curved and Twisted Composite Beams,” Int. J. Solids Struct., 39(19), pp. 5101–5121.
Yu,  W., Volovoi,  V. V., Hodges,  D. H., and Hong,  X., 2002, “Validation of the Variational Asymptotic Beam Sectional Analysis,” AIAA J., 40(10), pp. 2105–2112.
Trabucho, L., and Viano, J., 1996, “Mathematical Modeling of Rods,” Handbook of Numerical Analysis, Vol. IV, P. Ciarlet and J. Lions, eds., Elsevier, New York, pp. 487–974.
Volovoi,  V. V., Hodges,  D. H., Cesnik,  C. E. S., and Popescu,  B., 2001, “Assessment of Beam Modeling Methods for Rotor Blade Applications,” Math. Comput. Modell., 33(10–11), pp. 1099–1112.
Danielson,  D. A., and Hodges,  D. H., 1987, “Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor,” ASME J. Appl. Mech., 54(2), pp. 258–262.
Hodges,  D. H., 1999, “Non-linear Inplane Deformation and Buckling of Rings and High Arches,” Int. J. Non-Linear Mech., 34(4), pp. 723–737.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, McGraw-Hill, Maidenhead, UK.
Renton,  J. D., 1991, “Generalized Beam Theory Applied to Shear Stiffness,” Int. J. Solids Struct., 27(15), pp. 1955–1967.
Berdichevsky,  V. L., and Kvashnina,  S. S., 1976, “On Equations Describing the Transverse Vibrations of Elastic Bars,” Prikl. Mat. Mekh., 40, pp. 120–135.

Figures

Grahic Jump Location
Schematic of beam deformation
Grahic Jump Location
Sketch of a clamped prism
Grahic Jump Location
Sketch of a rectangular cross section

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