Linear and nonlinear hydroelasticity of mat-type very large floating structures: The Green-Naghdi theory

The hydroelastic response of mat-type Very Large Floating Structures (VLFS) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion and the dynamic loads on the VLFS due to these large waves. The goal of this dissertation is to develop a nonlinear theory to predict the hydroelastic response of VLFS and to compare with the linear response.; The nonlinear hydroelastic model developed in this dissertation is based on the Level-I Green-Naghdi theory for nonlinear shallow water waves, since the mat-type VLFS is typically moored in a shallow-water area near the coast line. Kirchhoff thin plate theory is used to describe the dynamic motion of the VLFS for the ratio between the horizontal and thickness dimensions is large. The fluid motion and the VLFS are coupled through the kinematic and dynamic boundary conditions at the fluid surface, and the plate edge boundary condition and mass continuity equations at the plate sides. A new set of jump conditions that are necessary for the continuity (or the matching) of the solutions between the open water region and the region under the structure is derived through the use of the postulated conservation laws of mass, momentum and mechanical energy. This nonlinear model is linearized, and the linear and nonlinear responses are compared. The resulting linear and nonlinear governing equations, subject to the boundary and jump conditions, are solved by the finite-difference method in the time domain. Second-order finite-difference methods are used to discretize the spatial derivatives and the Modified Euler Method is used for time-marching.; The theoretical and numerical models are verified by comparing the present results with previous experimental and numerical results, and good agreement is found. It is also shown that the present jump conditions connect the solutions in different regions very robustly and smoothly. The verified model is used to study the nonlinear response of VLFS to tsunami and hurricane waves which are modeled respectively using solitary wave and cnoidal wave theories. Parametric studies show that the nonlinearity of the water wave is very important in predicting the dynamic bending moment; wave run-up and slamming of VLFS. The increase of bending stiffness can reduce bending stress very efficiently for the nonlinear hydroelastic response.; The nonlinear model also is applied to study airplane landing and take-off from the mat-type VLFS. The loading due to the airplane is modeled by a moving pressure load on the VLFS. The drag force on the airplane due to hydroelastic deformation, and the deformation itself predicted by the present shallow-water theory are small, and have a similar magnitude to those calculated by the linear deep water potential wave theory reported in the literature.