Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach

This paper presents the theory development and numerical implementation of a new gradient-deficient-based ANCF (Absolute Nodal Coordinate Formulation) model applied to perform the nonlinear dynamic analysis of elastic line structures subject to large stretching and deformation. The derivations of model equations, introduced numerical approaches, and result validations are the focuses of this study. Different from the traditional rod theory for small stretching consideration, the present model implements the line structures’ large elongation concepts into both the control mechanisms of constitutive formulations and equations of motion. The effect of external hydrodynamic forces on structures is also included in the model formulations. Based on the conservation of energy, the line model developed in this study covers the variation in strain and takes a full account of the bending effect with large stretching. A finite-element-based implicit scheme according to a modified Newmark-beta method is employed to solve the assembled system equations with unknown variables of nodal position vectors, their tangential derivatives, and strains. Selected cases with dynamic motions, such as nonlinear oscillation of a compound pendulum, free falling of a horizontal elastic beam in air with two different settings of gravity, free falling of a submerged horizontal tether with and without an attached concentrated mass, and a submerged vertical tether with a prescribed translational motion, are simulated to verify the developed model by comparing the results with analytical solutions and published experimental data and numerical results. It is found the present ANCF model, as noticed with good matched results with analytical solutions, measurements and other published solutions, is demonstrated to be able to provide converged and reasonably accurate predictions on the responses of line structures subject to large dynamic motions.