A Hybrid Arbitrary Lagrangian Eulerian Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

Abstract

This work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two-dimensional beam finite element is presented, based on the absolute nodal coordinate formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as the arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for comoving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as in the case of beams with evenly distributed mass.