Scaled Boundary Finite Element Method Analysis of Sloshing in Axi-symmetric Vessels

摘要

This paper describes the development of a new efficient semi-analyticalmethod, namely scaled boundary finite-element method (SBFEM) forthe analysis of sloshing in axi-symmetric vessels based on multimodalanalysis, and the governing Laplace equations and linear free surfaceboundary condition are also applied to the proposed model. A twodimensionaleigenvalue problem is obtained by using the scaledboundary finite element method for zero external excitation, which issolved through a variational (Garlerkin) formulation that uses threenodefinite elements by only discreting the boundary of the watersurface and walls, then the dimension of the problem is reduced by one.Subsequently, based on an appropriate decomposition of the containerfluidmotion, and considering the eigenmodes of the correspondingeigenvalue problem, an efficient methodology is proposed forexternally-induced sloshing, through the calculation of thecorresponding sloshing (or convective) masses. Numerical results areobtained for sloshing frequencies and masses in spherical vessels and aconical vessel, and the dynamic response of the sloshing is alsoobtained under different seismic waves. The numerical results are invery good comparison with other analytical or numerical solutions.