Dynamic Modeling of Multiple Line Structures Subject to Large Deformation and Elongation Using an Absolute Nodal Coordinate Formulation (ANCF) Approach

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This research focuses on the development of a robust numerical model to perform dynamic analysis of line structures in time domain. The dynamic analysis of elastic line structures introduced here is based on the gradient deficient Absolute Nodal Coordinate Formulation (ANCF) method, which is an enhancement from the traditional rod theory. Large elongation assumption of elastic line structures is implemented both in constitutive model and in motion equations. Also, the rotary inertia and Poisson’s effects are taken into consideration. The line model developed in this research includes the variation in strain and takes a full account of the bending effect with large stretching. The ANCF method, based on the energy conservation, is a non-incremental Finite Element Method. All physical terms in line system’s motion equations of the traditional rod theory are retained, but expanded with full-size coefficient matrices. Handling simulations of mechanical interactions with constraints and connectors are included. The Jacobian matrix for constraints and stiffness matrix for connectors are introduced with systematically assembled mechanical interaction equations combined into the integrated system equations. The unified model equations are formulated and an object-oriented based FORTRAN solver is developed. Numerically, the explicit scheme with predictor corrector method and the implicit scheme according to the Newmark-beta method are employed to solve the model equations for dynamic simulations. Three cases are simulated to verify the developed model, which are (1) elastic beam falling in air with two different gravity constants, (2) fallings of a submerged horizontal tether and applied motions of a submerged vertical tether, and (3) moored line structures in a wave basin test. The numerical results in tension and strains calculated from either the small stretching or large stretching based models are presented. For the three study cases, the model predicted solutions are compared with other published numerical, experimental , or wave basin test results to validate and examine the performance of the developed model. Fairly good agreements between the present model solutions and those from published literatures are obtained. The simulated results also confirm that the large stretching model can generate more accurate and much improved predictions, especially the tensions and strains, when compared to those from the small stretching model. With the comprehensive verification based on the model test cases, this program can serve as a powerful design and evaluation tool for mooring line, and can be augmented to a fully coupled floating system.

Numerical models, Line structure, Large Elongation, Poisson's effect, ANCF