Authors: Pouya Salehi Hessameddin Yaghoobi Mohsen Torabi
Publish Date: 2012/09/15
Volume: 26, Issue: 9, Pages: 2879-2887
Abstract
Large deflection of a cantilever beam subjected to a tipconcentrated load is governed by a nonlinear differential equation Since it is hard to find exact or closedform solutions for this nonlinear problem this paper investigates the aforementioned problem via the differential transformation method DTM and the variational iteration method VIM which are wellknown approximate analytical solutions The mathematical formulation is yielded to a nonlinear twopoint boundary value problem In this study we compare the DTM and VIM results with those of Adomian decomposition method ADM and the established numerical solution obtained by the Richardson extrapolation in order to verify the accuracy of the proposed methods As an important result it is depicted from tabulated data that the DTM results are more accurate in comparison with those obtained by the VIM and ADM which is one of the objectives of this article Moreover the effects of dimensionless end point load α on the slope of any point along the arc length and the dimensionless vertical and horizontal displacements are illustrated and explained The results reveal that these methods are very effective and convenient in predicting the solution of such problems and it is predicted that the DTM and VIM can find a wide application in new engineering problemsPouya Salehi was born in 1984 He received his MS in mechanical engineering from Semnan State University He has conducted different papers which are related to fuzzy logic optimization analytical solutions heat transfer etc Moreover he has some papers which were released in different conferences and journals He is also interested to work in new topics such as biomechanics aerospace energy optimization and new numerical methods analytical methodsHessameddin Yaghoobi received his Bachelor’s degree in mechanical engineering from the Islamic Azad University Central Tehran Branch Tehran Iran and MSc degree from Semnan University His research interests include formulation and analysis of problems in solid and structural mechanics functionally graded materials FGMs and analytical methodsMohsen Torabi received his MS in mechanical engineering from the Semnan University and his BS in solid mechanics from the Azad University Tehran Branch He has authored several technical papers in the field of heat transfer His current research focuses on analytical and computational analysis of heat transfer and nonFourier conduction heat transfer He has more than 25 publications in refereed journals and international conferences
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