Approaches for Addressing Hydrostatic Nonlinearity in Cylindrical Floating Platforms and Their Influence on Hydrostatic Equilibrium and Undamped Natural Period Estimation

Abstract Hydrostatic restoring forces have a decisive influence on the static and dynamic behavior of floating structures. They exert a significant impact on the stability, integrity and functionality of such structures. Although these forces and the stiffness they induce can be considered linear for small displacements, they are generally nonlinear and the nonlinearity must be taken into account for certain structures that might experience large displacements, where even the external forces are nonlinearly dependent on the displacement. A common approach to account for hydrostatic stiffness nonlinearity in hydrostatic equilibrium analysis is to use the conventional linear hydrostatic stiffness matrix in an iterative method and update it at each iteration till equilibrium is reached. However, the use of a fully nonlinear stiffness matrix is expected to improve accuracy. This paper proposes a comprehensive methodology for deriving the general nonlinear hydrostatic stiffness matrix for cylindrical floating structures and examines its impact on determining the equilibrium position and undamped natural periods compared to the conventional linear stiffness matrix.