FLUID PRESSURE ON RECTANGULAR TANK CONSISTING OF RIGID SIDE WALLS AND RECTILINEARLY DEFORMING BOTTOM PLATE DUE TO UPLIFT MOTION

摘要

Although the uplift motion of flat bottom cylindrical shell tanks has been considered to contribute toward various damage to tanks, the mechanics were not fully understood. As well as computing uplift displacement of the tanks, accurate prediction of fluid pressure accompanied with uplift motion is indispensable to prevent the tanks from severe damage. This paper mathematically derives the fluid pressure on a rectangular tank with unit depth consisting of rigid walls and rectilinearly deforming bottom plate accompanied with the uplift motion. Assuming perfect fluid and velocity potential, the continuity equation is given by Laplace equation. The fluid velocity imparted by motion of rigid walls, immobile bottom plate and rectilinearly deformed bottom plate of tank accompanied with uplift of the tank constitutes boundary conditions. Since this problem is set as the parabolic partial differential equation of Neumann problem, the velocity potential is solved with Fourier-cosine expansion. Derivatives of the velocity potential with respect to time give the fluid pressure at arbitrary point inside the tank. The proposed mathematical solution well converges with a first few terms of Fourier series. Diagrams that depict the fluid pressure normalized by product of angular acceleration and diagonals of the tank are presented.