Nonlinear computational methods for hydroelastic effects of ships in extreme seas

Assessing the structural integrity of ship hull structures needs a reliable prediction of loads in extreme seas. Hydroelastic effects on wave-induced loads and structural response have gained great importance recently because they contribute to the life cycle load spectra of wave-induced hull girder stresses. The risk associated with ships encountering extreme waves is not negligible. The ship’s structural integrity and stability may be endangered when the master cannot avoid the extreme seas. The effects of hydroelastic effects of maritime structures has been investigated and hydroelastic theory developed based on linear fluid structure interaction. A Timoshenko beam model to idealize the ship structure was used.

Researchers led by Professor Ould el Moctar from University of Duisburg-Essen in Germany presented computational methods to assess hydroelasticity effects on wave-induced sectional loads of ships in extreme irregular waves.  Further on, they determined wave sequences based on the Most Likely Response Wave concept. Their work is now published in peer-reviewed journal, Ocean Engineering.

The researchers adopted a straight forward and intuitive approach to solve the fluid-structure interaction problems. The approach entailed separating the solution domain into fluid domain and a structural domain then solving both domains alternatingly. They adopted structure dynamics method that computed body ship motions separately from elastic hull girder deformations. These rigid body ship motions were of finite amplitude and, consequently, they were formulated nonlinearly, while elastic hull deformations were of small amplitude and were, therefore, linearized.

Separating large amplitude motions from small elastic deformations yields a consistent formulation of rigid body motions. However, this is derived from an assumption that elastic deformations do not affect the translational and the angular momentum of the body. This translates that the overall sums of external forces and moments equal the change of rigid body momentum and angular momentum, while the inhomogeneous distribution of external forces and moments causes deformations. However, to understand the distinction between rigid and elastic motions requires you to consider the time variation of the mass inertia tensor and the effect of deformation velocities when calculating the angular momentum.

The results obtained from physical model tests in regular and irregular waves were used to validate the numerical methods and procedures adopted for this study. The measurements comprised ship motions, sectional loads, and accelerations. Physical models for three modern containerships were performed. To measure sectional loads, these models had to be segmented. Model 1 consisted eight segments, while models 2 and 3 had six segments.

These containership models were equipped with a backbone that reflected the basic vibration modes and natural frequencies of the full-scale ships. Model tests were composed of runs in regular and irregular long-crested waves. Irregular waves were obtained from random realizations of sea states. Runs in dedicated deterministic sequences were done to produce ship responses of given magnitudes.

The loads as well as structural vibrations caused by irregular waves were consistent with experiments since the whipping effects were covered comprehensively. Long simulation runs of 5000s of the irregular waves were carried out and analyzed statistically. Besides deviations in tail distribution, short-term statistics  of motions and sectional loads considering hydroelasticity effects  were captured. The results obtained helped in assessing the feasibility of using transient Reynolds-averaged Navier-Stokes equations and computational structure dynamics methods in predicting  non-linear ship responses in extreme steep and irregular waves.