An arbitrary Lagrangian-Eulerian corotational formulation for nonlinear dynamic analysis of arbitrarily curved viscoelastic beams

In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.