Elasticas and buckling loads of shear deformable tapered columns

International Journal of Structural Stability and Dynamics

Volumn 5, Issue 3, 2005, Pages 317-335

  Lee, Byoung Koo ^a,b   Carr, Athol J ^b   Lee, Tab Eun ^a   Ahn, Dae Soon ^a  

^a Wonkwang University   (South Korea)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Bernoulli Euler beam theory; Buckling load; Elastica; Elastica arch; Experiment; Shear deformation; Tapered column

Indexed keywords

BUCKLING; DIFFERENTIAL EQUATIONS; LOADS (FORCES);

BERNOULLI-EULER BEAM THEORY; BUCKLING LOAD; ELASTICA; ELASTICA ARCH; EXPERIMENT; TAPERED COLUMN;

SHEAR DEFORMATION;

EID: 24144482806     PISSN: 14658763     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0219455405001684     Document Type: Article

References (21)

1. J. M. Gere and S. P. Timoshenko, Mechanics of Materials (Books/Cole Engineering Division, Monterey, CA, 1984).
2. R. T. Haftka, Z. Gurdal and M. P. Kamat, Elements of Structural Optimization (Kluwer Academic Publishers, Dordrecht, 1990).
3. L. Euler, Methodus inveniendi lineas curves maxima minimive proprietate gaudentes, Additamentum I, De Curvis Elasticis, Lausanne and Geneva (1774).
4. C. Rojahn, Large deflections of elastic beams, Thesis for Engineers, Stanford University, USA (1968).
5. R. Schmidt and D. A. Da Deppo, A survey of literature on large deflection of non-shallow arches, bibliography of finite deflections of straight and curved beams, rings and shallow arches, J. Ind. Math. Soc. 21 (1971) 91-114.
6. J. F. Wilson, D. M. Holloway and S. B. Biggers, Stability experiments on the strongest columns and circular arches, Exp. Mech. 11 (1971) 303-308.
7. J. V. Huddleston, Effect of shear deformation on the elastica with axial strain, Int. J. Numer. Methods Eng. 4 (1972) 433-444.
8. C. Y. Wang, Large deflections of an inclined cantilever with an end load, Int. J. Non-Linear Mech. 16 (1981) 155-164.
9. P. S. Theocaris and D. E. Panayotounakos, Exact solutions of non-linear differential equations concerning the elastic line of a straight rod due to terminal loading, Int. J. Non-Linear Mech. 17(5-6) (1982) 395-402.
10. I. Sheinman and M. Adam, The effect of shear deformation on the post-buckling behavior of laminated beams, J. Appl. Mech., ASME 54 (1987) 558-562.
11. J. F. Wilson and J. M. Snyder, The elastica with end-load flip-over, J. Appl. Mech., ASME 55 (1988) 845-848.
12. B. K. Lee, Numerical analysis of large deflections of cantilever beams, J. Korean Soc. Civ. Eng. 10 (1990) 1-7.
13. Y. Goto, T. Yoshimitsu and M. Obata, Elliptic integral solutions of plane elastica with axial and shear deformations, Int. J. Solids Struct. 26(4) (1990) 375-390.
14. B. K. Lee and J. F. Wilson, Elastica of cantilevered beam with variable cross-section, Int. J. Non-Linear Mech. 28(5) (1993) 579-589.
15. S. Chucheepsakul, S. Bunchareon and T. Huang, Elastica of simple-variahle-arc-length beam subjected to end moment, J. Eng. Mech., ASCE 121 (1995) 762-767.
16. B. K. Lee and S. J. Oh, Elastica and buckling load of simple tapered columns with constant volume, Int. J. Solids Struct. 37 (2000) 2507-2518.
17. B. K. Lee, S. J. Oh and G. Li, Buckling loads of columns of regular polygon cross-section with constant volume and clamped ends, Electron. J. Struct. Eng. 2 (2002) 76-84.
18. A. B. Sotiropoulou and D. E. Panayotounakos, Exact parametric analytic solutions of the elastica ODEs for bars including effects of the transverse deformation, Int. J. Non-Linear Mech. 39 (2004) 1555-1570.
19. A. K. Gupta, Vibration of tapered beams, J. Struct. Div., ASCE 121 (1985) 762-767.
20. A. W. Al-Khagaji and J. R. Tooley, Numerical Methods in Engineering Practice (Holt, Reinhart and Winston, New York, NY, 1986).
21. J. F. Wilson, Experiments of the Strength of Solids (McGraw-Hill, Inc., New York, NY, 1993).