The fractal finite element method for added-mass-type problems

Abstract

The fractal finite element method (FFEM), originally developed for calculating stress intensity factors in fracture mechanics problems, has been extended to analyse fluid-structure interaction in the form of added-mass-type problems. These include the free vibration of a submerged spherical shell and the interaction between a dam and a reservoir. For the former problem, the numerical solution from the FFEM agrees well with the analytical solution, and the FFEM performed better than conventional finite elements and infinite elements in terms of efficiency. For the latter problem, the FFEM predicted an added mass profile that is different from that based on Westergaard's parabolic solution.