Deformation of Thin Elastic Rod Under Large Deflections

  • V. S. Zhernakov
  • V. P. Pavlov
  • V. M. KudoyarovaEmail author
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The flexible elastic rods undergoing large deflections are widely used in the engineering practice. Analytic solutions for flexible rods are known for some special cases but there are cases when the exact solution does not exist. In such cases, it is expedient to use numerical methods, and the most known is a finite element method (FEM). This paper presents a new numerical method based on second-degree splines of the defect 1 allowing to solve the linearized nonlinear equations with high accuracy for large deflections of a thin elastic rod. The method efficiency is evaluated on the test problem of a pure bending (not shear) of a thin elastic rod. This paper shows that the method ensures the accuracy with a relative error does not exceed 1 × 10−6 for a sufficiently dense number of nodes.


Large deflections Rod deformation Mathematical modeling Numerical methods Splines 



The authors acknowledge receiving support base part of funded research program of Russian Foundation for Basic Research (RFBR) and Government of the Republic of Bashkortostan in the framework of a scientific project No. 17-48-020824_p_a.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. S. Zhernakov
    • 1
  • V. P. Pavlov
    • 1
  • V. M. Kudoyarova
    • 1
    Email author
  1. 1.Ufa State Aviation Technical UniversityUfaRussia

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