Generalized Timoshenko theory of the variational asymptotic beam sectional analysis

Journal of the American Helicopter Society

Volumn 50, Issue 1, 2005, Pages 46-55

  Yu, Wenbin ^a,b   Hodges, Dewey H ^b  

^a UTAH STATE UNIVERSITY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AIRCRAFT PARTS AND EQUIPMENT; ASYMPTOTIC STABILITY; BUCKLING; COMPUTER SIMULATION; ELASTIC MODULI; ELASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; STIFFNESS; VARIATIONAL TECHNIQUES; VIBRATIONS (MECHANICAL);

TIMOSHENKO THEORY; VARIATIONAL ASYMPTOTIC BEAM SECTIONAL ANALYSIS;

AEROSPACE ENGINEERING;

EID: 14044255810     PISSN: 00028711     EISSN: None     Source Type: Journal    
DOI: 10.4050/1.3092842     Document Type: Article

References (27)

1. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity 4th ed., Dover Publications, New York, pp. 1-3.
2. Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S., and Fulton, M. V., "On a Simplified Strain Energy Function for Geometrically Nonlinear Behaviour of Anisotropic Beams," Composites Engineering, Vol. 2, (5-7), 1992, pp. 513-526.
3. Cesnik, C. E. S., Hodges, D. H., and Sutyrin, V. G., "Cross-Sectional Analysis of Composite Beams Including Large Initial Twist and Curvature Effects," AIAA Journal, Vol. 34, (9), September 1996, pp. 1913-1920.
4. Volovoi, V. V., Hodges, D. H., Cesnik, C. E. S., and Popescu, B., "Assessment of Beam Modeling Methods for Rotor Blade Applications," Mathematical and Computer Modelling, Vol. 33, (10-11), 2001, pp. 1099-1112.
5. Hodges, D. H., "A Review of Composite Rotor Blade Modeling," AIAA Journal, Vol. 28, (3), March 1990, pp. 561-565.
6. Cesnik, C. E. S., "Cross-Sectional Analysis of Initially Twisted and Curved Composite Beams," Ph.D. Thesis, Aerospace Engineering, Georgia Institute of Technology, May 1994.
7. Jung, S. N., Nagaraj, V. T., and Chopra, I.,"Assessment of Composite Rotor Blade Modeling Techniques," Journal of the American Helicopter Society, Vol. 44, (3), July 1999, pp. 188-205.
8. Cesnik, C. E. S., and Hodges, D. H., "Stiffness Constants for Initially Twisted and Curved Composite Beams," Applied Mechanics Reviews, Vol. 46, (11, Part 2), 1993, pp. S211-S220.
9. Cesnik, C. E. S., and Hodges, D. H., "Variational-Asymptotical Analysis of Initially Twisted and Curved Composite Beams," International Journal for Engineering Analysis and Design, Vol. 1, (2), April 1994, pp. 177-187.
10. Cesnik, C. E. S., and Hodges, D. H., "Stiffness Constants for Composite Beams Including Large Initial Twist and Curvature Effects," Applied Mechanics Reviews, Vol. 48, (11, Part 2), 1995, pp. S61-S67.
11. Cesnik, C. E. S., and Hodges, D. H., "VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling," Journal of the American Helicopter Society, Vol. 42, (1), January 1997, pp. 27-38.
12. Popescu, B., and Hodges, D. H., "On Asymptotically Correct Timoshenko-like Anisotropic Beam Theory," International Journal of Solids and Structures, Vol. 37, (3), 1999, pp. 535-558.
13. popescu, B., Hodges, D. H., and Cesnik, C. E. S., "Obliqueness Effects in Asymptotic Cross-Sectional Analysis of Composite Beams," Computers and Structures, Vol. 76, (4), 2000, pp. 533-543.
14. Yu, W., Hodges, D. H., Volovoi, V. V., and Cesnik, C. E. S., "On Timoshenko-like Modeling of Initially Curved and Twisted Composite Beams," International Journal of Solids and Structures, Vol. 39, (19), 2002, pp. 5101-5121.
15. Yu, W., Volovoi, V. V., Hodges, D. H., and Hong, X., "Validation of the Variational Asymptotic Beam Sectional Analysis," AIAA Journal, Vol. 40, (10), October 2002, pp. 2105-2113.
16. Berdichevsky, V. L., "Variational-Asymptotic Method of Constructing a Theory of Shells," Journal of Applied Mathematics and Mechanics, Vol. 43, (4), 1979, pp. 664-687.
17. Yu, W., and Hodges, D. H., "Elasticity Solutions versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams," Journal of Applied Mechanics, Vol. 71, (1), 2004, pp. 15-23.
18. Berdichevsky, V. L., and Staroselskii, L. A., "On the Theory of Curvilinear Timoshenko-Type Rods," Journal of Applied Mathematics and Mechanics, Vol. 47, (6), 1983, pp. 809-817.
19. Hodges, D. H., "A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams," International Journal of Solids and Structures, Vol. 26, (11), 1990, pp. 1253-1273.
20. Renton, J. D., "Generalized Beam Theory Applied to Shear Stiffness," International Journal of Solids and Structures, Vol. 27, (15), 1991, pp. 1955-1967.
21. Pai, P. F., and Schulz, M. J., "Shear Correction Factors and an Energy-Consistent Beam Theory," International Journal of Solids and Structures, Vol. 36, (14), 1999, pp. 1523-1540.
22. Stephen, N. G., "Considerations on Second Order Beam Theories," International Journal of Solids and Structures, Vol. 17, (3), 1981, pp. 325-333.
23. Cowper, G. R., "The Shear Coefficient in Timoshenko's Beam Theory," Journal of Applied Mechanics, Vol. 33, (2), June 1966, pp. 335-340.
24. Gruttmann, F., and Wagner, W., "Shear Correction Factors in Timoshenko's Beam Theory for Arbitrary Shaped Cross-sections," Computational Mechanics, Vol. 27, (3), 2001, pp. 199-207.
25. Giavotto, V., Borri, M., Mantegazza, P., Ghiringhelli, G., Carmaschi, V., Maffioli, G. C., and Mussi, F., "Anisotropic Beam Theory and Applications," Computers and Structures, Vol. 16, (1-4), 1983, pp. 403-413.
26. Paz, M., Strehl, C. P., and Schrader, P., "Computer Determination of the Shear Center of Open and Closed Sections," Computers and Structures, Vol. 6, (2), 1976, pp. 117-125.
27. Bauchau, O., "Computational Schemes for Flexible, Nonlinear Multi-Body Systems," Multibody System Dynamics, Vol. 2, (2), 1998, pp. 169-225.