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					  Application of Fluid-Structure
Interaction Algorithms to Seismic
Analysis of Liquid Storage Tanks

         Zuhal OZDEMIR, Mhamed SOULI
   Université des Sciences et Technologies de Lille
          Laboratoire de Mécanique de Lille
            University of Bosphor, Istanbul
         Outline of the Presentation

General Objective of the Studies Carried out on Tanks
Difficulties in the Analysis of Tanks
Analysis Methods for Tanks
Fluid-Structure Interaction for Tank Problems
2D Rigid Tank
3D Flexible Tank
        General Objective of the Studies
            Carried out on Tanks


- Limit the tank damages observed during earthquakes

- Determine the response parameters in order to take
precautions
    - sloshing wave height (freeboard)
    - uplift displacement (flexible attachments for pipes)
    Difficulties in the Analysis of Tanks


- Three different domains
      * Structure
      * Fluid
      * Soil

- Material and geometric nonlinearities
- Complex support condition
      * Anchored
      * Unanchored
       General Performance of Tanks
           during Earthquakes

- Violent sloshing which causes damage at the tank
wall and shell
- Large amplitude wall deformations (Buckling)

- High plastic deformation at the tank base




             Sloshing damage
                         Tank Shell Buckling




Elephant-Foot Buckling (Elasto-Plastic Buckling)



                                                   Diamond Shape Buckling (Elastic Buckling)
                        Analysis Methods for Tanks
      - Simplified Analytical Methods
               Fluid :            Laplace equation                            2  0
               Irrotational flow, incompressible and inviscid fluid (potantiaql flow theory)

               Structure :                            rigid tank

              Spring-Mass Equivalent Analogue
          k5 / 2   M5    k5 / 2

                   M3
          k3 / 2         k3 / 2
                                                                                 Ordinary
          k1 / 2
                   M1    k1 / 2
                                                                   Base Shear     Beam      Shell Stresses
                    M0                           h5
                                                                      and        Theory         (Axial
                                       h1
                                            h3
                                                                   Overturning              Compressive
                                  h0                                Moment                   and Hoop)



Most of the provisions recommended in the current tank design codes employ a modified
version of Housner’s method
           Analysis Methods for Tanks                            (cond)




 - Numerical Methods
      * 2D finite difference method
      * FEM
      * BEM
      * Volume of fluid technique (VOF)


FEM is the best choice, because
 -structure, fluid and soil can be modelled in the same system
 -proper modelling of contact boundary conditions
 -nonlinear formulation for fluid and structure
 -nonlinear formulation for fluid and structure interaction effects
   Fluid-Structure Interaction for Tank
                Problems

       Structure
                                      Fluid
 Lagrangian Formulation
Dynamic Structure equation
                             Navier Stokes equations in
                               ALE Formulation
       dv
          div( )  f
       dt
                                2D Tank Problem

                                                             width = 57 cm
                                                             height = 30 cm
                                                             Hwater= 15 cm
                                                             Sinusoidal harmonic motion
                                                                     non-resonance case
                                                                     resonance case


The sketch of the 2D sloshing experiment (Liu and Lin, 2008)


                                       (2 n  1)        (2 n  1)     
                              2  g
                               n                   tanh 
                                                                       h
                                                                         
                                           2a                2a         

                                         o = 6.0578 rad/s
2D Tank Problem
    Lagrangian
2D Tank Problem
      ALE
                2D Tank Problem


                             non-resonance case

                             amplitude = 0.005 m
                                 = 0.583 o




  resonance case

amplitude = 0.005 m
       = 1 o
                           3D Tank Problem

Cylindrical tank size:
         - radius of 1.83 m
         - a total height of 1.83 m
         - filled up to height of 1.524 m
                                                    3


       Maximum ground acceleration = 0.5 g in horizontal direction
            (El Centro Earthquake record scaled with 3 )
3D Tank Problem




 Change of free surface in time
    3D Tank Problem




Von Mises stresses on the anchored tank shell
       3D Tank Problem




Von Mises stresses on the unanchored tank shell
         (displacements magnified 10 times)
                    3D Tank Problem




Comparisons of the time histories of pressure for the numerical method and
                            experimental data
                   3D Tank Problem




Comparisons of the time histories of pressure for the numerical method and
                            experimental data
                        3D Tank Problem




Comparisons of the time histories of surface elevation for the numerical method and
                                experimental data
                       3D Tank Problem




Comparisons of the time histories of tank base uplift for the numerical method and
                                experimental data
                            Conclusions

(1) ALE algorithm lead highly consisted results with the experimental
   data in terms of peak level timing, shape and amplitude of pressure
   and sloshing.
(2) Method gives reliable results for every frequency range of external
   excitation.
(3) ALE method combined with/without the contact algorithms can be
   utilized as a design tool for the seismic analysis of rigid and flexible
   liquid containment tanks.
(4) As a further study, a real size tank will be analysed
THANK YOU
3D Tank Problem




Pressure distribution inside the tank
          Analysis Methods for Tanks                              (cond)



- Experimental Methods
    * Static tilt tests

    * Shaking table tests




Schematic view of static tilt test   A cylindrical tank mounted on the shaking table

				
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posted:9/19/2012
language:English
pages:25