Abstract
In this study, large deflection of cantilever beams of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. In calculations, both material and geometrical non-linearity have been considered. Horizontal and vertical deflections magnitudes were calculated throughout Euler-Bernoulli curvature-moment relationship assuming different arc lengths. Vertical deflections were calculated by using Runge-Kutta method. More simple and easily understandable results have been obtained compared to the previous studies about the issue and compatible values have been obtained for most of the compared values.
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References
Baker G 1993 On the large deflections of non-prismatic cantilevers with a finite depth. Comput. Struct. 46: 365–370
Bisshopp K E, Drucker D C 1945 Large deflections of cantilever beams. Q. Appl. Math. 3: 272–275
Eren I, 2006 Some newsolutions on large deflections of beams (in Turkish). PhD Dissertation, Institute of Science, Yildiz Technical University, Istanbul
Fertis D G 1999 Nonlinear Mechanics, (New York: CRC Pres)
Frisch-Fay R 1962 Flexible Bars, (London: Butter Worths)
Lau J H 1982 Large deflections of beams with combined loads. J. Eng. Mech. 108: 180–185
Lee B K, Wilson J F, Oh S J 1993 Elastica of cantilevered beams with variable cross sections. Int. J. Non-Linear Mech. 28: 579–589
Lee K 2002 Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int. J. Non-Linear Mech. 37: 439–443
Lewis G, Monosa F 1981 Large deflections of cantilever beams of non-linear materials. Comput. Strct. 14: 357–360
Lewis G, Monosa, F 1982 Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment. Int. J. Non-Linear Mech. 17: 1–6
Lo C C, Gupta, S D 1978 Bending of a non-linear rectangular beam in large deflection. J. Appl. Mech. 45: 213–215
Prathap G, Varadan T K 1976 The inelastic large deformation of beams, J. Appl. Mech. 43: 689–690
Rao BN, Rao G V 1986 On the large deflection of cantilever beams with end rotational load. Z. Angew-Math. Mech. 66: 507–509
Scott E J, Carver D R, Kan M 1955 On the linear differential equation for beam deflection. J. Appl. Mech. 22: 245–248
Varadan T L, Joseph D 1987 Inelastic finite deflections of cantilever beams. J. Aeronaut. Soc. India 39: 39–41
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Eren, I. Determining large deflections in rectangular combined loaded cantilever beams made of non-linear Ludwick type material by means of different arc length assumptions. Sadhana 33, 45–55 (2008). https://doi.org/10.1007/s12046-008-0004-7
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DOI: https://doi.org/10.1007/s12046-008-0004-7