, 2011). In this part, the coupling method is briefly described without any figures and equations. The details were introduced by the works of Kim et al., 2009a, Kim et al., 2009b and Kim et al., 2009c. It should be noted that the beam and the fluid panel modes are coupled based on nodal motions in the Cartesian coordinate system. Most fluid–structure coupling has been performed in a

generalized coordinate system. Handling of the so-called m-term and restoring force in the node-based coupling is different from that in mode-based coupling. For example, the fluid restoring force is composed 5-Fluoracil chemical structure of pressure, normal vector, and mode variations in a generalized coordinate system ( Senjanović et al., 2008). Their contributions depend on the wetted hull surface. In general, pressure variation is predominant, and mode variation has the smallest portion. Pressure and normal vector variations in the Cartesian coordinate system have the similar form as those in the generalized coordinate system, but mode variation has a different form in the Cartesian coordinate system, which corresponds to geometric stiffness. It can be understood as moment arm variation. Moment arm variation

is missing in the current state of the nodal-based coupled method. Explicit expressions for restoring force in both Cartesian and generalized coordinate systems were discussed in the work of Senjanović et al. (2013). In the coupling of the 3-D Rankine panel model, 2-D slamming model, and the beam model, it is essential to exchange the motion and pressure between the models. Selleckchem Alectinib The dynamic, static, and slamming pressures are distributed to two adjacent nodes as nodal force using shape function of beam element. The motions of the body surface and slamming sections are calculated by motions of the two adjacent node and the shape function. The details follow the works of Kim et al., 2009a, Kim et al., 2009b and Kim et al., 2009c. A modified beam model is proposed to utilize eigenvectors of the 3-D FE model in the beam theory model when modal superposition

method is used. It is a hybrid model in transition from beam theory model to 3-D FE model. The purpose is to confirm whether the hybrid model has both advantages of the fast computation speed Quinapyramine of beam model and the accuracy of 3-D FE model or not. The model approximates a ship structure as a beam, but beam theory is not used because the eigenvectors at beam nodes are obtained from the 3-D FE model using linear interpolation. Eigenvalue analysis of the 3-D FE model can be performed by commercial FEM software. It should be noted that stiffness and mass matrices of the beam element are not formulated, but the inertial properties of the 3-D FE model are modeled by lumped mass distribution along the longitudinal axis for gravity restoring and sectional force calculation.