3D finite-deformation beam model with viscous damping: Computational aspects and applications

A nonlinear finite-element formulation for the static and dynamic behavior of flexible beams was developed by appropriately modifying and extending the three-dimensional (3D) finite-deformation beam model originally developed by Simo. By introducing energy dissipation in a physically consistent way through a linear viscoelastic constitutive equation, the main contribution in this paper lies in the derivation of a tangent stiffness operator that includes the effect of damping. Moreover, a solution to issues concerning the interpolation of total rotation vectors of magnitude greater than π is proposed, along with an alternative approach for the update of curvatures based on total rotation vectors, taking advantage of special features of Lie groups and of the notion of right-trivialized derivative. Both two-dimensional (2D) and three-dimensional (3D) numerical examples are presented. In particular, static and dynamic analyses of an electrical conductor commonly used in power substations were performed. Energy balance calculations and the convergence rate of Newton's method illustrate the accuracy of the computed solutions.