Development of Monolithic Method for Shell-fluid Interaction Based on Consistent Pressure Poisson Equation

This paper describes an efficient monolithic method for shell-fluid interaction problems based on the fluid pressure Poisson equation (PPE). The PPE is derived so as to be consistent with the coupled equation system for the shell-fluid interaction. In the proposed method, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all the other unknown variables except those for the shell are derived explicitly. The coefficient matrix of the PPE is well-conditioned even if the structure is very stiff or heavy compared to the fluid, and even if the ill-conditioned submatrix is generated due to the shell elements. These characteristics are successfully utilized to combine the proposed method with the standard conjugate gradient method. To demonstrate fundamental perfermances of the proposed method, it is applied to evaluate the vibration characteristics of a thin elastic cantilever plate in a quiescent fluid.