Numerical analysis on springing and whipping using fully-coupled FSI models

This paper focuses on ship springing and whipping analysis using a three-dimensional (3-D) Rankine panel method combined with a beam-element-based 1-D structural model and a shell-element-based 3-D structural model. In addition, slamming loads are considered by 2-D generalized Wagner model (GWM). The beam model is a classical idealization of a ship structure, which is based on Timoshenko beam theory for bending and Vlasov beam theory for non-uniform torsion. The 3-D model consists of beam and shell elements, and its motions are approximated by a few of lower modes. Different coupling schemes are applied to couple the 3-D panel method and the different structure models. Whereas the 1-D beam model is coupled in a Cartesian coordinate system, the 3-D finite element (FE) model is coupled in a generalized coordinate system. The difference in coordinate systems leads to different numerical implementations of coupling. Agreement and discrepancy between the coupled models are discussed regarding results for a 60 m barge, a 6500 TEU containership, and an experimental model of a virtual 10,000 TEU containership. The bulkheads in the barge and the 6500 TEU containership are properly considered in beam modeling according to relative stiffness between the bulkheads and hulls. In linear responses to waves, good agreement is obtained between all the models. However, differences between the models are found in nonlinear springing and whipping responses.