Nonlinear dynamic deformation simulation for helical rod like objects


  • Hongwang Du
  • Wei Xiong
  • Haitao Wang
  • Zuwen Wang
  • Bin Yuan


helical rod, Kirchhoff dynamic analogy, cylindrical coordinates, deformation simulation


In this paper, dynamic deformation simulation of an elastic helical rod with circular cross-section under axial tension is discussed on the basis of the Kirchhoff dynamic analogy. Firstly, equilibrium equations of an elastic rod described by Euler angles are established in the Frenet coordinates of the centerline. To get solutions of the equations, through a cylindrical coordinate system founded by end constraint, mathematical analytical formulations were used to describe elastic rod configuration are gained on the basis of Saint-Venant Principle of Elasticity, in the form of Elliptic functions. Then, based on the conclusions of static analysis, the relationship between geometric parameters and end constraint of helical rods is qualitatively analyzed. Finally, nonlinear dynamic deformation simulation with constraint force change is realized in a virtual environment to verify the effectiveness of the above algorithm..