A New Approach for the Non-linear Analysis of the Deflection of Beams Using Lie Symmetry Groups


Changizi M. A. , Stiharu I., ŞAHİN D. E.

1st International Conference of Mechatronics and Cyber-MixMechatronics (ICOMECYME), Bucharest, Romania, 7 - 08 September 2017, vol.20, pp.138-148 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 20
  • Doi Number: 10.1007/978-3-319-63091-5_17
  • City: Bucharest
  • Country: Romania
  • Page Numbers: pp.138-148

Abstract

The linear formulation does not yield acceptable results when is used to the beams that experience large deflections. Further, the linear models could accommodate large deflections such as those encountered in some machinery where bending does not exceed three times the thickness of the beam. However, the defection of beams subjected to arbitrary loads that yield non-linear deflection has been solved so far only for two loading conditions; point moment and point force. The present work presents a general method based on Lie symmetry groups that yields an exact solution to the general problem involving any arbitrary loading.