Study On Wave-Structure Interaction Based On SBFEM

The scaled boundary finite-element method (SBFEM) is a novel semi-analytical and semi-numerical method combining the advantages of the finite element method (FEM) and the boundary element method (BEM), which was initially proposed and applied in the field of solid mechanics. A new co-ordinate system composing of a circumferential local co-ordinate and a radial co-ordinate is established when using the SBFEM. Compared with FEM, the boundary is only spatially discretised in SBFEM, leading to a reduction of the spatial dimension by one. In the radial direction, the solution is analytical, so that high accuracy can be achieved. Compared with BEM, SBFEM does not require the fundamental solution, thus the problem of singular integral can be avoided.Firstly, the problems of wave interaction with bottom amounted cylinder and square cylinder are solved by SBFEM, where the 2D Helmholtz equation is taken as the governing equation. Combining with the domain decomposition technique, the fluid domain is divided into bounded domains and unbounded domains. In the bounded domains, matrix power series is chosen as the basic solution of the scaled boundary finite-element equation. In the unbounded domains, Hankel function is chosen as the basic solution of the scaled boundary finite-element equation. According to the principle that the velocity potential and its derivatives in the interface of sub-domains are continuous, the velocity potential of the whole domain is determined by matching at the interface of bounded domain and unbounded domain.Secondly, wave interaction with a bottom-mounted uniform porous cylinder of arbitrary shape is solved by using SBFEM. The non-homogenous equation due to the complex configuration of the structure is processed and transformed into homogenous equation by introducing a porous effect parameter G. The resulting final scaled boundary finite-element equation is homogenous and can be solved in conventional manners. In addition, the relationship between the wave run-up, wave loads and the wave number and the porous effect parameter are investigated.Thirdly, the problems of radiation and diffraction of wave by an infinite long horizontal floating structure near a sidewall are solved by SBFEM and domain decomposition technique. Here, since the unbounded domain consists of the free surface, the seabed and the virtual boundary at infinity, the scaled center can not be defined by the traditional scaled boundary co-ordinate system. Therefore, a new scaled boundary coordinate system suitable for this case is defined. It should be noted that the scaled boundary finite element equation corresponding to the radiation problem is non-homogenous; therefore the considered governing equation with power function in right hand side is solved by seeking the special solution for it. Through the linear superposition of the special solution and generation solution, the non-homogenous scaled boundary finite-element equation is solved and the velocity potential in the whole domain is determined. According to the corresponding formulas,the added mass and damping coefficient are obtained. The results compared with analytical results and numerical results demonstrate the accuracy of SBFEM.Finally, the hydro-elastic problem of a floating ring-shaped plate is solved by SBFEM. The governing equation of six-order partial differential equation is transformed into three Helmholtz-type equations. Through matching the boundary conditions at the edges of the plate, the velocity potential in the whole fluid domain is determined, then the 3D deflection of the whole plate and the free surface elevation are obtained.This thesis has applied SBFEM to solve the 2D wave-structures interaction problem successfully. Through studying on the results of several cases, high accuracy and high efficiency of SBFEM have been demonstrated. In the future, the SBFEM may be further extended to solve more complicated hydrodynamic problems in ocean engineering.