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Research Papers: Seismic Engineering

Discrete Models for Seismic Analysis of Liquid Storage Tanks of Arbitrary Shape and Fill Height

[+] Author and Article Information
G. C. Drosos, D. L. Karabalis

Department of Civil Engineering, University of Patras, 26500 Patras, Greece

A. A. Dimas1

Department of Civil Engineering, University of Patras, 26500 Patras, Greeceadimas@upatras.gr

www.isesd.cv.ic.ac.uk.

1

Corresponding author.

J. Pressure Vessel Technol 130(4), 041801 (Sep 10, 2008) (12 pages) doi:10.1115/1.2967834 History: Received October 31, 2006; Revised May 16, 2007; Published September 10, 2008

A finite element method (FEM)-based formulation is developed for an effective computation of the eigenmode frequencies, the decomposition of total liquid mass into impulsive and convective parts, and the distribution of wall pressures due to sloshing in liquid storage tanks of arbitrary shape and fill height. The fluid motion is considered to be inviscid (slip wall condition) and linear (small free-surface steepness). The natural modal frequencies and shapes of the sloshing modes are computed, as a function of the tank fill height, on the basis of a conventional FEM modeling. These results form the basis for a convective-impulsive decomposition of the total liquid mass, at any fill height, for the first few (two or three at most) sloshing modes, which are by far the most important ones in comparison to all other higher modes. This results into a simple yet accurate and robust model of discrete masses and springs for the sloshing behavior. The methodology is validated through comparison studies involving vertical cylindrical tanks. Additionally, the application of the proposed methodology to conical tanks and to the seismic analysis of spherical tanks on a rigid or flexible supporting system is demonstrated and the results are compared to those obtained by rigorous FEM analyses.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Typical free-surface shapes η, for the first three eigenmodes, of liquid motion in vertically axisymmetric storage tanks under horizontal seismic excitation in the x direction. D is the tank diameter at the free surface when the liquid is at rest.

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Figure 2

Model for the representation of fluid motion in liquid storage tanks by discrete masses and spring

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Figure 3

Coordinate system for axisymmetric (with respect to z) storage tanks

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Figure 4

Convective and impulsive mass variations versus the dimensionless fill height for vertical cylindrical tanks

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Figure 5

First sloshing mode of spherical tanks: the free surface and mode shape of half-full case (left) and the variation of the dimensionless frequency versus the dimensionless fill height (right)

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Figure 6

Second sloshing mode of spherical tanks: the free surface and the mode shape of the half-full case (left) and the variation of the dimensionless frequency versus the dimensionless fill height (right)

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Figure 7

Convective and impulsive mass variations versus the dimensionless fill height for spherical tanks

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Figure 8

Convective pressure profile variation with the azimuthal angle for several fill heights in spherical tanks

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Figure 9

Impulsive pressure profile variation with the azimuthal angle for several fill heights in spherical tanks

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Figure 10

Impulsive pressure profile variation with the normalized azimuthal angle for several fill heights in spherical tanks

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Figure 11

Geometry and nomenclature of conical tanks

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Figure 12

First sloshing mode of conical tanks: the typical free surface and the mode shape (left) and the frequency variation with the dimensionless fill height and the tank wall angle Φ (right)

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Figure 13

Second sloshing mode of conical tanks: the typical free surface and the mode shape (left) and the frequency variation with the dimensionless fill height and the tank wall angle Φ (right)

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Figure 14

Convective and impulsive mass variations with the dimensionless fill height and the tank wall angle Φ for conical tanks

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Figure 15

Time histories of convective, impulsive, and total hydrodynamic forces on a spherical tank subject to the Kozani seismic excitation

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Figure 16

(a) Full FEM and (b) hybrid models of a spherical tank supported by a series of columns

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Figure 17

Time histories of the horizontal displacement at the north-pole of the spherical tank subject to an artificial accelerogram compatible to EC8 for several fill ratios and comparison of results obtained by the full FEM and the hybrid models in Fig. 1

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Figure 18

Spherical tank supported by a series of columns and tension-only diagonal braces

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Figure 19

(a) Full FEM and (b) hybrid models of the spherical tank in Fig. 1

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Figure 20

Shape and frequency of the first eigenmode obtained by the full FEM and the hybrid models in Fig. 1

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Figure 21

Time histories of the horizontal displacement at the north-pole of a half-full spherical tank subject to an artificial accelerogram compatible to EC8 and comparison of results obtained by the full FEM and the hybrid models in Fig. 1

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Figure 22

Time histories of the base shear force of a half-full spherical tank subject to an artificial accelerogram compatible to EC8 and comparison of results obtained by the full FEM and the hybrid models in Fig. 1

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