Flexible multibody formulation using finite elements with 3 DoF per node with application in railway dynamics

Abstract

Flexible multibody formulations allow the dynamic analysis of mechanisms with slender or thin-walled structures that deform during their operation. However, the majority of the existing flexible multibody methodologies are formulated assuming finite element models featuring 6 nodal degrees of freedom, specifically 3 translations and 3 rotations. This work initially revises the existing flexible multibody methodology in which the modeling of the flexibility is independent of the modeling of the baseline multibody system while ensuring the coupling between the rigid and flexible components. The flexible multibody methodology includes the use of suitable reference conditions, the component mode synthesis, and the virtual bodies methodology. Commonly, solid elements found in finite element software exclusively have three nodal translation degrees of freedom, featuring no explicit angular degrees of freedom. In this work, we propose the enhancement of the existing formulation for a rigid-flexible joint to support the use of virtual bodies rigidly connected to the nodes of solid elements. The computational implementation of the methodology is demonstrated using a benchmark case. The methodology developed in this work is further applied to study the dynamics of a locomotive with a flexible bogie frame. Although not influencing the overall vehicle dynamics, the bogie flexible multibody model allows the evaluation of the PSD of the accelerations in different points of the bogie that are sensitive to structural defects. The comparison of the response of healthy and damaged bogie frames supports the development of tools to monitor the condition of bogie frames during the operation. This development will be explored in forthcoming works, thus expanding the use of flexible multibody methodologies to new applications.