Dimensionless numerical analysis method for flexible body with large deformation, displacement and time-varying length

Abstract

A tethered system, which is a multibody system in which multiple rigid bodies are connected via a flexible tether, is currently used for space and deep-sea exploration. In order to perform accurate work with such tethered systems, the ability to comprehend tether dynamics behavior with large deformation/displacement and time-varying length is crucial. Numerical analyses are beneficial in that it is difficult to carry out experiments in such environment. In this paper, an efficient numerical approach is proposed for a flexible body motion with time-varying length using a dimensionless equation of motion. Generally Absolute Nodal Coordinate Formulation (ANCF), which is a nonlinear finite element method is effective for dynamic simulation of a flexible body motion. VFE-ANCF, which applies variable-domain finite element (VFE) as a method of expressing time-varying length to ANCF, was proposed to represent the motion of a flexible body with large deformation, displacement and time-varying length. However, conventional approach using VFE-ANCF has a problem that the accuracy changes depending on the length change. So in this paper, to avoid this problem, dimensionless variables are introduced using representative value that changes with time-varying length. In addition, the usefulness of this method is shown by comparing the numerical results using this method and the conventional method.

Numerical approach for flexible body with internal boundary movement

“…By making the equation of motion dimensionless, the physical factors that govern complex behavior are normalized and movements can be more appropriately evaluated. In addition, as shown in a previous study 23 , by setting the representative length to the length of each body that changes in time, flexible body is converted to the dimensionless system consisting of two bodies with constant length. Furthermore, by setting the representative time using the time-varying length of the shorter body, the time step is set according to the higher frequency of bodies A and B at each time step.…”

“…This study proposes a numerical approach for the analysis of a flexible body motion with an internal variable boundary. In addition, the dimensionless approach we proposed in a previous paper 23 is applied to it. In conventional dimensionless approaches, constant representative values are generally used 24 .…”