Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2754

Full Length Research Paper

The solution of Euler-Bernoulli beams using variational derivative method

  Atilla Özütok1* and Arife Akin1        
Department of Civil Engineering, Faculty of Engineering Architectural, Selcuk University, 42031 Konya, Turkey.
Email: [email protected]

  •  Accepted: 07 April 2010
  •  Published: 31 May 2010



Finite difference methods are often used for analyzing structures governed by complex differential equations. The finite difference method, well known as an efficient numerical method, was formerly applied to the case of beam and plate problems. The basic disadvantages of this method are the requirement of out-of-region points during the solution process and the difficulty of implementing the boundary conditions along irregular boundaries. In this study, the variational derivative method was proposed to solve the functional of the Euler–Bernoulli beam obtained by Gâteaux differential method. The main reason for the preference of this method over the finite difference method was the elimination of the need for the out-of-region domain points that complicate the application of the finite difference method. The moments and deflections of beams with constant and varying cross-sections and various support types were calculated in order to demonstrate the applicability of the method. The performance of this formulation is verified by comparing the obtained results with the results of the numerical examples in the literature.


Key words: Finite difference, variational derivative, beams.