Applying Sectional Seakeeping Loads to Full Ship Structural Models Using Quadratic Programming

Interest in the seakeeping loads of vessels has increased dramatically in recent years. In current design practice, methods for predicting seakeeping motions and loads are mainly in two categories, strip theory methods and 3Dpanel methods. Methods based on strip theory provide reasonable motion prediction and are computationally efficient. However, many strip theory methods provide only hull girder sectional forces and moments, such as vertical bending moment and vertical shear force, which cannot be directly applied to a 3D finite element structural model. For panel based methods, the outputs include not only the global hull girder loads, but also panel pressures, which are well suited for 3D finite element analysis. However, because the panel based methods are computationally expensive, meshes used for hydrodynamic analyses are usually coarser than the mesh used for structural finite element analyses. Consequently, the panel pressure calculated from a hydrodynamic model mesh has to be transferred to the structural model mesh. The resulting discrepancy of the pressure map, regardless of what interpolation method is used, causes an imbalanced structural model. To obtain equilibrium of an imbalanced structural model, a common practice is to use the “inertia relief” approach [1] . However, this type of balancing causes a change in the hull girder load distribution, which in turn could cause inaccuracies in an extreme load analysis (ELA) and a spectral fatigue analysis (SFA). This paper presents a method to balance the structural model without using inertia relief. The method uses quadratic programming to calculate corrective nodal forces such that the resulting hull girder sectional loads match those calculated by seakeeping analyses, either by strip theory methods or 3Dpanel methods. To validate the method, a 3D panel linear code, MAESTRO-Wave [2] , was used to generate both panel pressures and sectional loads. A model is first loaded by a 3D-panel pressure distribution with a perfect equilibrium. The model is then loaded with only the accelerations and sectional forces and moments. The sectional forces and moments are converted to finite element nodal forces using the proposed quadratic programming method. For these two load cases, the paper compares the hull girder loads, the hull deflection and the stresses, and the accuracy proves the validity of this new method.