Efficient Mesh Updating Scheme for the ALE Corotational Formulation of an Arbitrarily Curved Beam

This paper presents an efficient mesh updating scheme (MUS) for the arbitrary Lagrangian–Eulerian (ALE) formulation of an arbitrarily curved beam based on the corotational method. By discretizing the beam using both Lagrangian elements and ALE elements, the proposed MUS can take full advantage of the simple expression form of the Lagrangian formulation and the accurate moving-load description of the ALE node. The deleting-node and adding-node procedures of the MUS can avoid the negative influence of the variation of the ALE element length on the element accuracy and stiffness matrix singularity. In contrast to the adding-node procedure for Lagrangian elements, interpolation cannot be used directly. Inserting a Lagrangian node in an ALE element is investigated, and the displacement, velocity, and acceleration of the newly added node are evaluated accurately based on the corotational method. Three examples are investigated to verify the validity, computational accuracy and computational efficiency of the proposed MUS by comparing the results of the MUS with those from literature that utilized traditional ALE formulation. These examples show that the proposed MUS has significant advantages in terms of computational time and computer memory.