1. Application of Fluid-Structure Interaction Algorithms to Seismic Analysis
Zuhal OZDEMIR, Mhamed SOULI
Université des Sciences et Technologies de Lille
Laboratoire de Mécanique de Lille
University of Bosphor, Istanbul
GDR IFS
3 - 4 Juin 2010
UTC Compiegne

2. 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

3. 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)

4. Difficulties in the Analysis of Tanks
- Three different domains
* Structure
* Fluid
* Soil
- Material and geometric nonlinearities
- Complex support condition
* Anchored
* Unanchored

5. 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

6. Tank Shell Buckling Elephant-Foot Buckling (Elasto-Plastic Buckling)
Diamond Shape Buckling (Elastic Buckling)

7. Analysis Methods for Tanks
- Simplified Analytical Methods
Fluid : Laplace equation
Irrotational flow, incompressible and inviscid fluid (potantiaql flow theory)
Structure : rigid tank
Spring-Mass Equivalent Analogue
Base Shear and Overturning Moment
Ordinary Beam Theory
Shell Stresses (Axial Compressive and Hoop)
Most of the provisions recommended in the current tank design codes employ a modified version of Housner’s method

8. Fluid-Structure Interaction for Tank Problems
Lagrangian Formulation
Dynamic Structure equation
Navier Stokes equations in ALE Formulation

9. 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)
o = rad/s

10. 2D Tank Problem
Lagrangian

12. 2D Tank Problem non-resonance case amplitude = 0.005 m  = 0.583 o

13. 3D Tank Problem Cylindrical tank size: - radius of 1.83 m
- a total height of 1.83 m
- filled up to height of m
Maximum ground acceleration = 0.5 g in horizontal direction
(El Centro Earthquake record scaled with )

14. Large mesh Deformation

15. Large mesh Deformation
Lagrangian Method

16. Coupling Method

17. Fluid Structure Coupling
2) Euler Lagrange Coupling
Structure
Fluid

18. Up Lift for sloshing Tank

19. 3D Tank Problem
Comparisons of the time histories of pressure for the numerical method and experimental data

20. 3D Tank Problem
Comparisons of the time histories of pressure for the numerical method and experimental data

21. 3D Tank Problem
Comparisons of the time histories of surface elevation for the numerical method and experimental data

22. 3D Tank Problem
Comparisons of the time histories of tank base uplift for the numerical method and experimental data

23. 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

24. Merci

25. 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

26. Pressure distribution inside the tank
3D Tank Problem
Pressure distribution inside the tank

27. 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

28. Change of free surface in time
3D Tank Problem
Change of free surface in time

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

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

31. 2D Tank Problem
ALE

32. 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)
o = rad/s