Teruhiro Nakashima

Numerical Investigation Into Significant Reduction in Coefficient of Restitution for Fluid-Container Combined Systems

The analysis procedure of rocking motion of unanchored flat-bottom cylindrical shell tanks should include an impact problem between the tank bottom plate and tank foundation. To evaluate the rocking motion of tanks based on a simple analytical procedure developed by a senior author, adequate estimation of a coefficient of restitution is necessary. This paper numerically examines the coefficient of restitution suitable for the fluid-container combined system used in such simple analysis procedure. Employing free rocking motion, an empty container and fluid-container combined system are computed. The velocity vectors of the empty container turn their direction simultaneously just after the uplifted edge hits the ground, while those of the fluid-container combined system need a time to turn their direction. This implies that the coefficient of restitution should be evaluated with effects of fluid stored in the tank.Copyright

Contribution of the Bending Stiffness of the Tank Bottom Plate and Out-of-Round Deformation of Cylindrical Shell to the Tank Rocking Motion

Effects of bending stiffness of the tank bottom plate and out-of-round deformation of cylindrical shell on uplift of the un-anchored flat-bottom cylindrical shell tanks are investigated. Numerical tank models whose bottom plate has different bending stiffness reveal that changes in bending stiffness of the tank bottom plate may have little influence on uplift of the tanks. Contrary, numerical tank models whose cylindrical shell is stiffed differently reveal that out-of-round deformation of the cylindrical shell may have significant influence on uplift of the tanks. In addition, uplift of the tanks may have little influence on development of waves on the fluid surface like sloshing.Copyright

Approximation of Uplift of Flat-Bottom Cylindrical Tanks and Effects of Out-of-Plane Deformation of Cylindrical Shell on it

For the unanchored flat-bottom cylindrical tanks located in the seismic prone area, uplift of the tank bottom plate is inevitable. Besides the work of Nakashima, effects of out-of-plane deformation of the cylindrical shell on uplift of the tank bottom plate have been paid little attention. In analyzing uplift of the tank bottom plate, for design purpose in particular, its effects should be included. First, employing a cylindrical shell tanks with multistage rigid or elastic stiffeners, their uplift responses to the horizontal sinusoidal base acceleration are compared to highlight effects of out-of-plane deformation on uplift of the tank bottom plate. Next, employing the numerical results of the cylindrical shell tank with multistage rigid stiffeners, analytical accuracy of the simplified calculation for evaluating the angular acceleration accompanying the tank rock motion is examined.Copyright

A Study of Applicability of Finite Displacement Analyses With Semi-Analytical Finite Elements for Analyzing Uplift Displacement of Flat-Bottom Cylindrical Shell Tanks Statically

The rocking motion of tanks due to earthquakes causes the large uplift deformation of the tank bottom plate that has been considered to contribute to the various damages of the tanks. For analyzing the uplift displacement of the tank bottom plate statically and precisely, this paper develops a shell element, ring element and spring element partially attached to the ring element. These elements are defined as a semi-analytical finite element. Fourier series give its circumferential displacement function, while the polynomial gives its radial displacement function. In addition, the ring element can deal with effects of the large deformation, while the spring element enables to express the partial contact between the tank bottom plate and foundation. On the other hand, the loads considered are dead load, hydro-pressure and inertia force due to earthquakes acceleration as well as dynamic pressure of fluid induced by bulging and rocking motion of the tank. The numerical analyses model of the LNG Storage Tank was created using the semi-analytical finite elements shown here, and the uplift displacement of the tank bottom plate accompanying the tank rocking motion was calculated with the static analyses. For evaluating analytical accuracy of the proposed method, numerical results of the proposed method are compared with that of the explicit FE Analysis.Copyright

Applicability of Semi-Analytical Finite Elements for Analyzing Uplift Displacement of Flat-Bottom Cylindrical Shell Tanks Statically

The rocking motion of tanks due to earthquakes causes the uplift and partial deformation of the tank bottom plate that has been considered to contribute to damage of various tanks.For analyzing the uplift displacement of the tank bottom plate numerically and precisely, this paper develops the analytical finite shell element, ring element and spring element partially attached to the ring element. These elements are defined as semi-analytical finite element models. Fourier series give their circumferential displacement function, while polynomial gives their radial displacement function.Applicability of a set of these elements to analyze the shell deformation and contact between the tank bottom plate and the foundation subjected to ground acceleration induced loads is verified. For evaluating analytical accuracy of the proposed method, numerical results are compared with other numerical ones.Copyright