Nonlinear finite element analysis of elastic water storage tanks

• This paper presents a nonlinear hydrodynamic analysis of elastic water tank of different lengths against horizontal harmonic excitation of various frequencies and amplitudes.
• The numerical exercises show that the amplitude, frequency and the length of the tank may alter the responses of the water domain.
• The outcome of the analysis results show that the nonlinear convective term should not be neglected when excitation frequencies are lower than the first fundamental frequency of the water domain.
• Also, the nonlinear effect should not be ignored for relatively narrow water tank.
• The differences between linear and nonlinear hydrodynamic pressure become more if the magnitude of the acceleration is higher.
• However, the linear and nonlinear hydrodynamic pressure are almost of same magnitude in case of earthquake excitation.

The present paper deals with the nonlinear finite element analysis of elastic water tanks. Both fluid and tank walls are discretized and modeled by two dimensional eight-node isoperimetric elements. In the governing equations, displacement for tank walls and pressure for the fluid domain are considered as independent nodal variables. The nonlinear term for the convective acceleration in Navier–Stokes equations is incorporated in the present analysis. The nonlinearity effects of the fluid are studied considering excitations both harmonic of various frequencies and random. The hydrodynamic pressure on tank wall is presented both from linear and nonlinear analysis for a comparison. The results show that the convective nonlinearity increases the magnitude of hydrodynamic pressure to a considerable amount when the excitation frequency approaches to the fundamental frequency of the water tank. The magnitude of hydrodynamic pressure in nonlinear analysis is quite large compare to that in linear analysis when the distance between the two vertical walls are relatively closer. However, the increase in pressure is insignificant when the tank is vibrated with a frequency higher than the frequency of the fluid domain. The seismic analysis results show that the distribution of nonlinear hydrodynamic pressure is almost similar to the linear pressure due to ground excitation.