Dynamics of offshore risers using a geometrically-exact beam model with hydrodynamic loads and contact with the seabed

During the operation of moored, floating devices in the renewable energy sector, the tight coupling between the mooring system and floater motion results in snap load conditions. Before snap events occur, the mooring line is typically slack. Here, the mechanism of energy propagation changes from axial to bending dominant, and the correct modelling of the rotational deformation of the lines becomes important. In this paper, a new numerical solution for modelling the mooring dynamics that includes bending and shearing effects is proposed for this purpose. The approach is based on a geometrically exact beam model and quaternion representations for the rotational deformations. Further, the model is coupled to a two-phase numerical wave tank to simulate the motion of a moored, floating offshore wind platform in waves. A good agreement between the proposed numerical model and reference solutions was found. The influence of the bending stiffness on the motion of the structure was studied subsequently. We found that increased stiffness increased the amplitudes of the heave and surge motion, whereas the motion frequencies were less altered.

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On the geometrically exact beam model: A consistent, effective and simple derivation from three-dimensional finite-elasticity

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2008.04.015 ◽

2008 ◽

Vol 45 (17) ◽

pp. 4766-4781 ◽

Cited By ~ 35

Author(s):

F. Auricchio ◽

P. Carotenuto ◽

A. Reali

Keyword(s):

Finite Elasticity ◽

Three Dimensional ◽

Beam Model ◽

Simple Derivation ◽

Geometrically Exact Beam

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Horizontal and Torsional Modes of an Ultra Large Container Ship (ULCS)

Volume 6B: Ocean Engineering ◽

10.1115/omae2020-18659 ◽

2020 ◽

Author(s):

P. P. Vijith ◽

Suresh Rajendran

Keyword(s):

Numerical Model ◽

Numerical Method ◽

Natural Frequency ◽

Flexible Structures ◽

Complex Problem ◽

Mode Shapes ◽

Beam Model ◽

Torsional Vibrations ◽

Hydrodynamic Loads ◽

Structural Responses

Abstract The hydro elastic responses of flexible structures under fluid loading is an important concern during the design of large ocean structures. The two-way coupling between the structural responses and the hydrodynamic loads is a complex problem in large flexible floating structures since the structures can vibrate in longitudinal, vertical, horizontal, or torsional modes. The antisymmetric distortion modes may be coupled depending on the location of the centroid and the shear centre. In the case of thin walled open structures, horizontal and torsional vibrations are usually coupled due to the asymmetry of cross section as well as eccentricity between centroid of the section and shear deformation centres. The acurate estimation of dry natural frequency and modes shapes of structure is indispensable since it helps to validate the accuracy of the structural modelling. A numerical method available from one of the existing literatures is used for the estimation of dry and wet natural frequencies, and mode shapes of horizontal and torsional vibrations of an ULCS. The natural frequency and modes are essential parameters for the analysis of interaction between structural responses and hydrodynamic loads. The numerical method is based on a 1D FEM beam model. Distortion due to warping is included in the numerical model since it is well known that containerships with large hatch opening are susceptible to warping. The numerical model is subdivided into 50 stations and the mass distribution and the sectional properties are calculated in order to match the bending, shear, torsion and warping moduli of the experimental model. The dry and wet natural frequency and mode shapes for the horizontal and torsional vibrations of the ULCS is numerically calculated and compared with the experimental results.

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