A practical method to apply hull girder sectional loads to full-ship 3D finite-element models using quadratic programming

摘要

Interest in the seakeeping loads of vessels has increased dramatically in recent years. While many studies focused on predicting seakeeping loads, little attention was given on how loads are transferred to 3D finite-element models. In current design practice, methods for predicting seakeeping motions and loads are mainly based on the potential flow theory, either strip theory methods or 3D-panel methods. Methods based on strip theory provide reasonable motion prediction for ships and are computationally efficient. However, the load outputs of strip theories are 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. Methods-based 3D panel methods can be applied to a wide range of structures, but are computationally expensive. The seakeeping load outputs of panel methods 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. When pressure loads are mapped from one mesh to another, a small discrepancy at the element level will occur regardless of what interpolation method is used. The integration of those small pressure discrepancies along the whole ship inevitably causes an imbalanced structural finite-element model. To obtain equilibrium of an imbalanced structural model, a common practice is to use the 'inertia relief approach. 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 practical method to balance the structural model without using inertia relief. The method uses quadratic programming to calculate equivalent nodal forces such that the resulting hull girder sectional loads match those calculated by seakeeping analyses, either by strip theory methods or 3D-panel methods. To validate the method, a 3D panel linear code, MAESTRO-Wave, 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.