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Complete characteristics of the deformations of a tapered cantilever due to self weight are studied. Explicit stability criteria for pointy tapered columns and numerical results for the blunt columns are given. Asymptotic formulas for large deformations are derived, and the results compare well with those from numerical integration. It is found that the deformation depends heavily on a non-dimensional gravity parameter, the degree of taper and the cross sectional shape of the cantilever.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
207--220
Opis fizyczny
Bibliogr. 17 poz.
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autor
Bibliografia
- 1. L. Euler, De Curvis Elasticis, 1744.
- 2. A.G. Greenhill, Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and of the greatest height to which a tree of given proportions can grow, Proc. Camb. Phil. Soc., 4, 65–73, 1881.
- 3. W.G. Bickley, The heavy elastica, Phil. Mag. Ser. 7, 17, 603–622, 1934.
- 4. C.Y. Wang, Large deformations of a heavy cantilever, Quart. Appl. Math., 39, 261–273, 1981.
- 5. C.Y. Wang, A critical review of the heavy elastica, Int. J. Mech. Sci., 28, 549–559, 1986.
- 6. S.B. Hsu, S.F. Hwang, Analysis of large deformation of a heavy cantilever, SIAM J. Math. Anal., 19, 854–866, 1988.
- 7. T. Belendez, M. Perez-Polo, C. Neipp, A. Belendez, Numerical and experimental analysis of large deflections of cantilever beams under a combined load, Phys. Scrip., T118, 61–65, 2005.
- 8. P.B. Goncalves, D.L.B.R. Jurjo, C. Magluta, N. Roitman, D. Pamplona, Large deflection behavior and stability of slender bars under self weight, Struct. Eng. Mech., 24, 709–725, 2006.
- 9. S.T. Santillan, R.H. Plaut, T.P. Witelski, L.N. Virgin, Large oscillations of beams and columns including self-weight, Int. J. Nonlinear Mech., 43, 761–771, 2008.
- 10. A.N. Dinnik, Buckling and Torsion, Acad. Nauk. CCCP, Moscow 1955 [in Russian].
- 11. C.A. Stuart, Buckling of a heavy tapered rod, J. Math. Pure Appl., 80, 281–337, 2001.
- 12. S.F. Hwang, L.R. Yeh, Analysis of large deformation of a nonprismatic beam, Taiwan. J. Math., 3, 89–106, 1999.
- 13. C.A. Stuart, G. Vuillaume, Buckling of a critically tapered rod, properties of some global branches of solutions, Proc. Roy. Soc. London A460, 3261–3282, 2004.
- 14. P.C. Raju, G. Venkateswara Rao, Post-buckling of tapered cantilever columns, Comp. Meth. Appl. Mech. Eng., 15, 201–206, 1978.
- 15. B.K. Lee, J.F. Wilson, S.J. Oh, Elastica of cantilevered beams with variable cross sections, Int. J. Nonlinear Mech., 28, 579–589, 1993.
- 16. B.P. Madhusudan, V.R. Rajeev, B. Nageswara Rao, Post-buckling of cantilever columns having variable cross-section under a combined load, Int. J. Nonlinear Mech., 38, 1513–1522, 2003.
- 17. G.M. Murphy, Ordinary Differential Equations and Their Solutions, Van Nostrand, Princeton, New Jersey, 1960.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT4-0010-0028