Nonlinear dynamics analysis of variable length flexible beams using the ALE-ANCF method

Abstract

For the flexible slender structure with time-variation of its length, the tip could vibrate violently. In recent years, flexible multibody dynamics has been used to analyze this phenomenon. On the other hand, when analyzing this phenomenon by the finite element method, the analysis becomes complicated because the nodes across the boundaries between constrained and unbounded areas, so it is necessary to discriminate the area for each node. For this problem, using the ALE (Arbitrary Lagrangian-Eulerian) finite element method, some nodes can be fixed at boundaries and the others can be arranged arbitrarily in each area. This will make it easier to analyze the flexible body with time-varying length. This study presents an analytical method for flexible bodies with time-varying length by using the ALE-ANC method. The ALE-ANC method, which is a combination of the ALE finite element method and the ANCF (Absolute Nodal Coordinate Formulation) that is one of the formulations of flexible multibody dynamics can place nodes independently of the motion. In this method, the element coordinates of nodes are used as the generalized coordinates. It is possible to express the length variation of the flexible body by changing these coordinates with time. In addition, we developed a numerical method that introduces an energy-momentum conservation scheme. This avoids complications in the analysis due to the time dependence of the mass matrix caused by the length variation of the element. In order to verify the validity of the proposed method, this study simulates variable length flexible beams using the presented model and compares the result with previous research.