Spectral Collocation Method in the Large Deformation Analysis of Flexible Beam

The traditional numerical methods in the study of large deformation of thin elastic beam usually show limited accuracy or are complicated to implement. In this paper, we propose a highly accurate and easily coded algorithm based on the polynomial collocation spectral method, for the study of beam bending, twisting and stretching. Ten nonlinear governing differential equations corresponding to Kirchhoff’s rod theory are discretized on the Chebyshev or Legendre Guass-Lobatto points. The solutions are obtained through the modified Newton-Raphson method and verified by the existing solutions. This polynomial collocation spectral method is demonstrated for various types of loading conditions, boundary conditions and intrinsic configurations. The analysis of the solutions reveals that the method could dramatically increase the accuracy of the simulation.