Open Access Open Access  Restricted Access Subscription or Fee Access

Study of Asymmetric Elastic Beams in Off-Axis Four-Point Bending

John Constantine Venetis(1), Emilio Pavlos Sideridis(2*)

(1) School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Greece
(2) School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Greece
(*) Corresponding author


DOI: https://doi.org/10.15866/irease.v8i6.8369

Abstract


The intention of this paper is to study the mechanical behavior of asymmetric elastic beams in off – axis four point bending. The overall phenomenon is investigated for high rates of the curvature. An approximate analytical method to estimate the deflection is proposed, rendering it expressible in terms of a finite combination of elementary single – valued functions. The novel element here is the examination of the elastic behavior of the continuum beam without its separation in distinguished regions. Hence, the derived analytical representation of the deflection concerns both its positive and negative rates. Consequently, the proposed explicit solution enables us to draw firm qualitative information about a large category of rectangular continuum beams.
Copyright © 2015 Praise Worthy Prize - All rights reserved.

Keywords


Asymmetric Beams; Off-Axis Four Point Bending; Unit Step Function

Full Text:

PDF


References


Shvartsman, B.S., Large deflections of a cantilever beam subjected to a follower force. Journal of Sound and Vibration, 2007. 304(3-5): p. 969-973.
http://dx.doi.org/10.1016/j.jsv.2007.03.010

Nallathambi, A.K., C.L. Rao, and S.M. Srinivasan, Large deflection of constant curvature cantileverbeam under follower load. International Journal of Mechanical Sciences, 2010. 52(3): p. 440-445.
http://dx.doi.org/10.1016/j.ijmecsci.2009.11.004

Mutyalarao, M., D. Bharathi, and B.N. Rao, Large deflections of a cantilever beam under an inclined end load. Applied Mathematics and Computation, 2010. 217(7): p. 3607-3613.
http://dx.doi.org/10.1016/j.amc.2010.09.021

Karlson, K.N. and M.J. Leamy, Three-dimensional equilibria of nonlinear pre-curved beams using an intrinsic formulation and shooting, International Journal of Solids and Structures Volume 50, Issues 22–23, 15 October 2013, Pages 3491–3504
http://dx.doi.org/10.1016/j.ijsolstr.2013.05.016

Zakharov, Y.V. and A.A. Zakharenko, Dynamic instability in the nonlinear problem of a cantilever Vychysl. Tekhnol. (in Russian), 1999. 4(1): p. 48-54.

Zakharov, Y.V. and K.G. Okhotkin, Nonlinear Bending Of Thin Elastic Rods. Journal of Applied Mechanics and Technical Physics, 2002. 43(5): p. 739-744.
http://dx.doi.org/10.1023/a:1019800205519

Zakharov, Y.V., K.G. Okhotkin, and A.D. Skorobogatov, Bending of Bars Under a Follower Load. Journal of Applied Mechanics and Tehnical Phyisics, 2004. 45(5): p. 756-763.
http://dx.doi.org/10.1023/b:jamt.0000037975.91152.01

Kuznetsov, V.V. and S.V. Levyakov, Complete solution of the stability problem for elastica of Euler's column. International Journal of Non-Linear Mechanics, 2002. 37(6): p. 1003-1009.
http://dx.doi.org/10.1016/s0020-7462(00)00114-1

Levyakov, S.V. and V.V. Kuznetsov, Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads. Acta Mechanica, 2010. 211(1-2): p. 73-87.
http://dx.doi.org/10.1007/s00707-009-0213-0

Wang, J., J.K. Chen, and S.J. Liao, An explicit solution of the large deformation of a cantilever beam under point load at the free tip. Journal of Computational and Applied Mathematics, 2008. 212(2): p. 320-330.
http://dx.doi.org/10.1016/j.cam.2006.12.009

Kimiaeifar, A., G. Domairry, R. Mohebpour,. R. Sohouli,. G. Davodi Analytical Solution for Large Deflections of a Cantilever Beam Under Nonconservative Load Based on Homotopy Analysis Method. Numerical Methods for Partial Differential Equations, 2011. 27(3): p. 541-553.
http://dx.doi.org/10.1002/num.20538

Wang, Y.G., W.H. Lin, and N.Liu, A Homotopy Perturbation-Based Method for Large Deflection of a Cantilever Beam Under a Terminal Follower Force. International Journal for Computational Methods in Engineering Science and Mechanics, 2012. 13(2): p. 197-201.
http://dx.doi.org/10.1080/15502287.2012.660229

Batista M. Analytical Treatment of Equilibrium Configurations of Cantilever Under Terminal Loads using Jacobi Elliptical FunctionsInternational Journal of Solids and Structures Vol.51, 13, 15 pp. 2308–2326
http://dx.doi.org/10.1016/j.ijsolstr.2014.02.036

Kılıç, O., Aktaş, A., Dirikolu, M.H., 2001, An investigating of the effects of shear on the deflection of an orthotropic cantilever beam by use of anisotropic elasticity theory, Composites Science and Technology, 61, 2055-2061.
http://dx.doi.org/10.1016/s0266-3538(01)00101-4

Esendemir, Ü., Usal, M.R., Usal, M., 2006, The effects of shear on the deflection of simply supported composite beam loaded linearly, Journal of Reinforced Plastics and Composites, 25, 835-846.
http://dx.doi.org/10.1177/0731684406065133

M. Grediac, Four–point bending tests on off-axis composites. Composite Structures, 24, 89-98, 1993.
http://dx.doi.org/10.1016/0263-8223(93)90030-t

F. Mujika, I. Mondragon, On the displacement field for unidirectional off-axis composites in 3-point flexure – Part 1: Analytical approach. Journal of Composite Materials, 37, 1041-1066, 2003.
http://dx.doi.org/10.1177/0021998303037012001

F. Mujika, A. De Benito, I. Mondragon, On the displacement field for unidirectional off-axis composites in 3-point flexure – Part II: Numerical and experimental results. Journal of Composite Materials, 37, 1191-1217, 2003.
http://dx.doi.org/10.1177/0021998303037013004

H. Killic, H.-A. Rami, Elastic-degrading analysis of pultraded composite structures. Composite Structures, 60, 43-55, 2003.
http://dx.doi.org/10.1016/s0263-8223(02)00296-9

P. K. Majumdar, P. Fazzino, K. L. Reifsnider, Behavior of woven fabric composites in off-axis end-loaded bending. International SAMPE Symposium and Exhibition (Proceedings). Baltimore, MD, USA, Code 79037, Volume 54, May 18-21, 2009.

Mujika F [2006], “On the difference between flexural moduli obtained by three-point and four-point bending tests”, Polymer Testing 25 pp.214- 220.
http://dx.doi.org/10.1016/j.polymertesting.2005.10.006

Tari H [2013], On the parametric large deflection study of Euler – Bernoulli cantilever beams subjected to combined tip point loading”, Int. J. Non–Linear Mech. 49 pp.90-99.
http://dx.doi.org/10.1016/j.ijnonlinmec.2012.09.004

Mohyeddin A, Fereidoon A [2014], An analytical solution for the large deflection problem of Timoshenko beams under three-point bending”, Int. J. Mech. Sci. 78 pp.135-139 .
http://dx.doi.org/10.1016/j.ijmecsci.2013.11.005

Venetis, J., and Sideridis, E. [2015] Approximate solution to three point bending equation for a simply supported beam Scientific Research and Essays, 10(9), 339-347.
http://dx.doi.org/10.5897/sre2014.6148

Venetis, J., and Sideridis, E. Analytical Treatment to Three Point Bending Equation for Statically Determinate Continuum Beams, International Journal of Aerospace and Lightweight Structures Vol. 4 Number 4 (2014) 317–330

Sellakumar, S., Venkatasamy, R., Review of Structural Assessment of Pipe Bends, (2013) International Review of Mechanical Engineering (IREME), 7 (6), pp. 1180-1188.

Hashemi, S., Borneman, S., Alighanbari, H., Vibration of Cracked Composite Beams: a Dynamic Finite Element, (2013) International Journal on Numerical and Analytical Methods in Engineering (IRENA), 2 (3), pp. 88-98.

Borneman, S., Hashemi, S., Alighanbari, H., Vibration Analysis of Doubly Coupled Cracked Composite Beams: an Exact Dynamic Stiffness Matrix, (2014) International Journal on Numerical and Analytical Methods in Engineering (IRENA), 2 (4), pp. 124-135.

Theotokoglou E, Sideridis E. [2011] Study of Composite beams in asymmetric four – point bending. J. Reinf. Plast. Comp. 30(13):1125-1137.
http://dx.doi.org/10.1177/0731684411417199

Theotokoglou E, Sideridis E. [2014] Study of asymmetric glass reinforced plastic beams in off-axis four-point bending. J. Composite Mater. Proceedings the 3nd South–East European Conference on Computational Mechanics
http://dx.doi.org/10.1177/0021998314521260

Hilbebrandt F [1976] Advanced Calculus for Applications, (Second Edition), Prentice – Hall, New Jersey.

Krasnov M., Kiselov M., and Makarenko G., (1981), A Book of Ordinary Differential Equations, MIR Publ., Moskow.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2019 Praise Worthy Prize