A mesh insensitive finite element method to compute statical stability curve of floating bodies with arbitrary configurations based on a force‐oriented approach

Abstract

For any floating body, statical stability curves play a critical role in its stability analysis. In this article, a force‐oriented approach, in conjunction with finite element procedure, is proposed in order to compute those curves of floating bodies with complicated hull forms. The hull surface is meshed by triangular elements. The buoyant force and restoring moments are directly computed through the load redistribution of the hydrostatic pressure over the facet of each triangular element. Computations of a statical stability curve require a series of floating conditions that lead to the change of waterline with respect to the hull surface. In order to do all computations by using a unique finite element mesh, techniques regarding nodal coordinate update and non‐matching element treatment are developed. The procedure has been established and the algorithm has been developed. Results from three examples with simple but representative geometries are compared to those by hand calculations to verify the accuracy of the approach. Then, two standard reference hull forms, a very large crude carrier (KRISO KVLCC2) and a trimaran (NPL Round Bilge 4a), have been investigated to demonstrate the validation of the approach. Results of all examples show that the proposed approach is insensitive to the mesh pattern.