Numerical methods for hydro -static and -dynamic analysis of 3D elastic floating structures

Abstract

In this work, a numerical method for a 3D linear hydroelastic analysis of floating structures with liquid tanks subjected to surface regular water waves is developed and compare the numerical results with experimental tests. Considering direct couplings among structural motion, sloshing, and water waves, a mathematical formulation and a numerical method are developed. The finite element method is employed for the floating structure and internal fluid in tanks, and the boundary element method is used for the external fluid. The resulting formulation completely incorporates all the interaction terms including hydrostatic stiffness and the irregular frequency effect is removed by introducing the extended boundary integral equations. Important issues of the 3D hydroelastic problem are the complete inclusion of hydrostatic stiffness and hydrostatic equilibrium of elastic floating structures. The hydrostatic stiffness is composed of the sum of the hydrostatic pressure and initial stress effects. Therefore, an explicit expression of geometric stiffness that is related to the hydrostatic pressure is required, and the hydrostatic analysis should be pre-performed before the hydrodynamic analysis to obtain the initial stress fields. An updated Lagrangian finite element (FE) formulation for a geometrically nonlinear hydrostatic analysis of flexible floating structures subjected to buoyancy, self-weight, and various external static loads is developed. The nonlinear equation is linearized with respect to a reference configuration and the resulting FE formulation is iteratively solved using the Newton-Raphson method. A special numerical integration technique is developed to handle the wet-surface change without re-meshing. Through the proposed numerical method, the hydrostatic equilibrium can easily be calculated considering various static and quasi-static loading conditions and the stress field of elastic bodies is more accurately evaluated in a large deformation case.