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Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load
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  • Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load
  • Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load
저자명
Salehi. Pouya,Yaghoobi. Hessameddin,Torabi. Mohsen
간행물명
Journal of mechanical science and technology
권/호정보
2012년|26권 9호|pp.2879-2887 (9 pages)
발행정보
대한기계학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

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, ${alpha}$, 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.