Abstract
Large deflection of a cantilever beam subjected to a tip-concentrated load is governed by a non-linear differential equation. Since it is hard to find exact or closed-form solutions for this non-linear problem, this paper investigates the aforementioned problem via the differential transformation method (DTM) and the variational iteration method (VIM), which are well-known approximate analytical solutions. The mathematical formulation is yielded to a non-linear two-point 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 problems.
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Pouya Salehi was born in 1984. He received his M.S. 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 methods.
Hessameddin 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 methods.
Mohsen Torabi received his M.S. in mechanical engineering from the Semnan University and his B.S. 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 non-Fourier conduction heat transfer. He has more than 25 publications in refereed journals and international conferences.
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Salehi, P., Yaghoobi, H. & Torabi, M. Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load. J Mech Sci Technol 26, 2879–2887 (2012). https://doi.org/10.1007/s12206-012-0730-y
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DOI: https://doi.org/10.1007/s12206-012-0730-y