The Nonlinear Hydrostatic Stiffness of Cylindrical Floating Platforms and Its Utilization in Static Stability Analysis

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 static stability analysis is to use the conventional linear hydrostatic stiffness matrix and update it at each position. However, the use of a nonlinear stiffness matrix can improve accuracy. This paper proposes a comprehensive methodology to derive the general nonlinear hydrostatic stiffness matrix for cylindrical floating structures and investigates its significance for determining the equilibrium position and undamped natural periods compared to the conventional linear stiffness matrix.