Application of Fluid-Structure Interaction Algorithms to Seismic

AnalysisZuhal OZDEMIR, Mhamed SOULI

Université des Sciences et Technologies de LilleLaboratoire de Mécanique de Lille

University of Bosphor, Istanbul

GDR IFS 3 - 4 Juin 2010

UTC Compiegne

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

- 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)

General Objective of the Studies Carried out on Tanks

Difficulties in the Analysis of Tanks

- Three different domains * Structure

* Fluid

* Soil

- Material and geometric nonlinearities

- Complex support condition * Anchored

* Unanchored

- Large amplitude wall deformations (Buckling)

- Violent sloshing which causes damage at the tank wall and shell

General Performance of Tanks during Earthquakes

- High plastic deformation at the tank base

Sloshing damage

Diamond Shape Buckling (Elastic Buckling)

Elephant-Foot Buckling (Elasto-Plastic Buckling)

Tank Shell Buckling

Analysis Methods for Tanks

Irrotational flow, incompressible and inviscid fluid (potantiaql flow theory)

- Simplified Analytical Methods

02 Fluid : Laplace equation

Spring-Mass Equivalent Analogue

Most of the provisions recommended in the current tank design codes employ a modified version of Housner’s method

Structure : rigid tank

Base Shear and

Overturning Moment

Ordinary Beam Theory

Shell Stresses (Axial

Compressive and Hoop)

Structure FluidLagrangian Formulation

Dynamic Structure equation Navier Stokes equations in

ALE Formulation

Fluid-Structure Interaction for Tank Problems

fdivtd

vd )(

2D Tank Problem

width = 57 cm

height = 30 cm

Hwater= 15 cm

Sinusoidal harmonic motion non-resonance caseresonance case

h

a2

)1n2(tanh

a2

)1n2(g2

n

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

o = 6.0578 rad/s

2D Tank ProblemLagrangian

2D Tank Problem

= 0.583 o

= 1 o

non-resonance case

resonance case

amplitude = 0.005 m

amplitude = 0.005 m

3

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

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

Large mesh Deformation

Large mesh Deformation

Lagrangian Method

Coupling Method

Structure

Fluid

Fluid Structure Coupling

2) Euler Lagrange Coupling

Up Lift for sloshing Tank

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

MerciMerci

Analysis Methods for Tanks (cond)

- Numerical Methods

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

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

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

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)

ALE

2D Tank Problem

2D Tank Problem

width = 57 cm

height = 30 cm

Hwater= 15 cm

Sinusoidal harmonic motion non-resonance caseresonance case

h

a2

)1n2(tanh

a2

)1n2(g2

n

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

o = 6.0578 rad/s