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

2013 ◽  
Author(s):  
Teruhiro Nakashima ◽  
Tomoyo Taniguchi
Keyword(s):  
Finite Elements ◽  
Dynamic Pressure ◽  
Displacement Function ◽  
Bottom Plate ◽  
Inertia Force ◽  
Flat Bottom ◽  
Ring Element ◽  
Spring Element ◽  
Rocking Motion ◽  
Tank Bottom

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.

A Static Analysis of Uplift During Strong Earthquakes of Unanchored Flat-Bottom Cylindrical Shell Tanks

2016 ◽  
Author(s):  
Teruhiro Nakashima ◽  
Tomoyo Taniguchi
Keyword(s):  
Dynamic Pressure ◽  
Shell Element ◽  
Bottom Plate ◽  
Inertia Force ◽  
Flat Bottom ◽  
Physical Conditions ◽  
Ring Element ◽  
Spring Element ◽  
Rocking Motion ◽  
Tank Bottom

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. Moreover in analyzing uplift of the tank bottom plate precisely, 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. Dead load, hydro-pressure and inertia force due to earthquakes acceleration as well as dynamic pressure of fluid induced by bulging and rocking motions of the tank are applied statically. Comparison of results by the proposed method and that computed by the explicit FE Analysis reveals that the accurate uplift displacement is not obtained until all physical conditions involved in the tank rocking motion and the inward deformation of the tank shell is properly considered.

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

2012 ◽  
Author(s):  
Teruhiro Nakashima ◽  
Tomoyo Taniguchi
Keyword(s):  
Shell Element ◽  
Displacement Function ◽  
Bottom Plate ◽  
Flat Bottom ◽  
Ground Acceleration ◽  
Ring Element ◽  
Spring Element ◽  
Rocking Motion ◽  
Analytical Accuracy ◽  
Tank Bottom

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.

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

2016 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Teruhiro Nakashima ◽  
Yuuichi Yoshida
Keyword(s):  
Cylindrical Shell ◽  
Significant Influence ◽  
Bending Stiffness ◽  
Bottom Plate ◽  
Flat Bottom ◽  
Fluid Surface ◽  
Rocking Motion ◽  
Tank Bottom

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.

Effective Mass of Fluid for Rocking Motion of Flat-Bottom Cylindrical Tanks

2009 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Toru Segawa
Keyword(s):  
Effective Mass ◽  
Fluid Pressure ◽  
Angular Acceleration ◽  
Inertia Force ◽  
Bottom Edge ◽  
Flat Bottom ◽  
Effective Moment ◽  
Rocking Motion ◽  
Tank Bottom ◽  
Cylindrical Tanks

In analyzing the rocking motion of the flat-bottom cylindrical tanks subjected to severe earthquakes, the effective mass of fluid for the rocking motion and its moment inertia around the pivoting bottom edge of the tank would be indispensable dynamical properties, because they couples the fluid-shell interaction motion, the so-called bulging motion, with the rocking motion. This paper quantifies them based on the equilibrium of the fluid pressure and inertia force accompanying the angular acceleration acting on the pivoting bottom edge of the tank. Employing a general mathematical solution for the fluid pressure that can calculate either fully or partially uplifted tank bottom, this paper presents mathematical formulae of the effective mass of fluid for the rocking motion and its moment inertia. These quantities are given by an explicit function of dimensional variables of the tank but with Fourier series. For designer’s convenience, the effective moment inertia and effective mass of fluid for the rocking motion and its center of gravity from the pivoting bottom edge are normalized accordingly and are depicted on diagrams.

Approximation of Fluid Pressure on the Cylindrical Tanks in Rock With the Crescent-Like Uplift Part in the Bottom Plate by Radially Sliced Tank Model

2013 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Takumi Shirasaki
Keyword(s):  
Fluid Pressure ◽  
Bottom Plate ◽  
Mathematical Treatment ◽  
Cylindrical Tank ◽  
Flat Bottom ◽  
Tank Model ◽  
Rectangular Tank ◽  
Tank Bottom ◽  
Cylindrical Tanks ◽  
Earthquake Effects

Flat-bottom cylindrical shell tanks may rock and have a crescent-like uplift part in the bottom plate at the event of a severe earthquake. Effects of the deformed tank bottom plate on the fluid pressure on the cylindrical tank have not been, however, quantified yet. Since the crescent-like uplift part appears eccentrically on the periphery of the tank bottom plate, its mathematical treatment would be troublesome. Regarding a cylindrical tank as a set of pieces of a thin rectangular tank with a deformed bottom plate that correspond radially sliced parts of the cylindrical tank with the crescent-like uplift part in the bottom plate, this paper defines the fluid pressure on the cylindrical tank by calculating that on the rectangular tank. For designer’s convenience, the fluid pressure computed are normalized and depicted in accordance with the aspect of the cylindrical tank and the uplift ratio of the tank bottom plate.

A Numerical Study of Uplift Motion of Flat-Bottom Cylindrical Shell Model Tank Subjected to Harmonic Excitation

2010 ◽  
Author(s):  
Teruhiro Nakashima ◽  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Numerical Study ◽  
Harmonic Excitation ◽  
Fe Analysis ◽  
Experimental Result ◽  
Bottom Plate ◽  
Flat Bottom ◽  
Tank Model ◽  
Rocking Motion ◽  
The Impact

In analyzing the rocking motion of unanchored flat-bottom cylindrical shell tanks, the fluid-structure interaction and the impact between the tank bottom plate and tank foundation should be treated adequately. Employing harmonic excitation, this paper examines the applicability of the explicit FE-Analysis technique for analyzing the rocking motion of a flat-bottom cylindrical shell tank model. Since the tank model possesses a thick and elastic bottom plate, the model tank pivots upon from an edge of the bottom plate to another edge of that reciprocally. The rocking motion of the model tank to the harmonic excitation is numerically computed and the uplift displacement of the tank is compared with experimental result. Agreement between the numerical and experimental results implies that the explicit FE-Analysis is capable of analyzing the rocking motion of cylindrical shell tanks subjected to the earthquake excitation.

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

2006 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Teruhiro Nakashima ◽  
Yoshinori Ando
Keyword(s):  
Analytical Procedure ◽  
Coefficient Of Restitution ◽  
Senior Author ◽  
Analysis Procedure ◽  
Bottom Plate ◽  
Simple Analysis ◽  
Combined System ◽  
Flat Bottom ◽  
Empty Container ◽  
Rocking Motion

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.

Experimental and Analytical Studies of Rocking Mechanics of Unanchored Flat-Bottom Cylindrical Shell Model Tanks

2004 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Shell Model ◽  
Effective Mass ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Bottom Plate ◽  
Base Shear ◽  
Flat Bottom ◽  
Rocking Motion ◽  
Physical Quantities

Employing a few feasible physical quantities of liquid related to the rocking motion of tanks, this paper tries to understand the fundamental dynamics of the rocking motion of tanks. Introducing the effective mass of liquid for rocking motion and for rocking-bulging interaction motions, the equations of motion are derived by analogue of rocking motion between rigid bodies and tanks. Using the exclusive tanks that possess the rigid-doughnuts-shape bottom plate that guarantees the uplift region of the bottom plate and the extent of the effective mass of liquid for rocking motion, the harmonic shaking tests are carried out. The proposed procedures can stepwise trace the base shear and the uplift displacement of the model tanks used herein.

Applicability of the Simplified Analysis and Relevant Calculations to Evaluating Uplift Displacement of Unanchored Tanks

2018 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yuichi Yoshida ◽  
Ken Hatayama
Keyword(s):  
Seismic Vulnerability ◽  
Thought Experiment ◽  
Tohoku Earthquake ◽  
Bottom Plate ◽  
Ground Acceleration ◽  
The Pacific ◽  
Rocking Motion ◽  
Tank Bottom ◽  
Cylindrical Tanks ◽  
Constraint Effects

Evaluation of the rocking motion of unanchored cylindrical tanks subjected to the ground acceleration is a main topic in the framework of the seismic vulnerability assessment of this particular kind of structures. However, despite the anchored or unanchored tanks, any calculation that attempts fully evaluate tank uplift has not been presented, while many of the analyses of the tank rocking motion and the deformation of the tank bottom plate have been respectively presented. This paper carries out a thought experiment of applicability of these analyses to evaluating uplift of the unanchored tanks. First, this paper focuses on an anchored tank at a chemical plant whose anchor bolts were pulled-out during the 2011 off the pacific coast of Tohoku Earthquake. Second, combine a few analyses of uplift of the unanchored tanks being available to date; then, calculate the uplift displacement of an anchored tank of interest as if it were an unanchored tank. Next, infer the pulling-out length of anchor bolt of the anchored tank of interest from a photo in a reconnaissance report; then, compare it with the uplift displacement calculated. Since the uplift displacement calculated is larger than that inferred. Since a discrepancy between them would be responsible for the constraint effects of anchors that have not been clearly quantified, the present analyses of the tank rocking motion and the deformation of the tank bottom plate may have a potential to give an appropriate uplift of unanchored tanks.

scholarly journals Masses of Fluid for Cylindrical Tanks in Rock With Partial Uplift of Bottom Plate

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yukihiro Katayama
Keyword(s):  
Effective Mass ◽  
Bottom Plate ◽  
Effective Moment ◽  
Rocking Motion ◽  
Tank Bottom ◽  
Cylindrical Tanks ◽  
The Masses

This study proposes the use of a slice model consisting of a set of thin rectangular tanks for evaluating the masses of fluid contributing to the rocking motion of cylindrical tanks; the effective mass of fluid for rocking motion, that for rocking–bulging interaction, effective moment inertia of fluid for rocking motion and its centroid. They are mathematically or numerically quantified, normalized, tabulated, and depicted as functions of the aspect of tanks for different values of the ratio of the uplift width of the tank bottom plate to the diameter of tank for the designer's convenience.

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