3.1.9.36. FSIInterfaceElement2D Element

3.1.9.36.1. Description

This command is used to construct an FSIInterfaceElement2D element object. The FSIInterfaceElement2D element is a 2-node linear acoustic-structure interface element object with the following features:

1. It is based on the Eulerian pressure formulation ([ZienkiewiczEtAl1978] , [ZienkiewiczEtAl2000] , [LøkkeEtAl2017] ) for (Class I) fluid-structure interaction problems.

2. It couples the structure and fluid domains.

3. It uses a 2 integration points Gauss quadrature.

4. It has three DOFs per node: two displacements and one pressure DOF. The nodes on the fluid side of the interface between the acoustic/fluid and the solid domains share the same coordinates.

3.1.9.36.2. Input Parameters

element FSIInterfaceElement2D $eleTag $n1 $n2 $rho <-thickness $thickness>

Argument	Type	Description
$eleTag	integer	unique integer tag identifying element object
$n1 $n2	2 integers	the two nodes defining the element (-ndm 2 -ndf 3)
$rho	float	the mass density of the fluid domain (acoustic medium)
Optional:
$thickness	float	the thickness in 2D problems (default 1.0).

Fig. 3.1.9.44 Figure 1. Nodes and local coordinate system

3.1.9.36.3. Theory

For additional documentation regarding the derivation of the implemented finite elements (FSIFluidElement2D, FSIFluidBoundaryElement2D, FSIInterfaceElement2D) based on the Eulerian pressure formulation, please refer to the attached PDF document (Link to PDF)

3.1.9.36.4. Example on how to define a single interface element

1. Tcl Code

# set up a 2D-3DOF model
model Basic -ndm 2 -ndf 3
node 11  0.0  0.0
node 22  1.0  1.0

# create the acoustic-structure interface element with input variable rhoW
set rhoW 1.000000e+03;  # mass density of water
element FSIInterfaceElement2D 2   11 22   $rhoW -thickness 1.0

2. Python Code

# set up a 2D-3DOF model
model('Basic', '-ndm', 2, '-ndf', 3)
node(11, 0.0, 0.0)
node(22, 1.0, 1.0)

# create the acoustic-structure interface element with input variable rhoW
rhoW = 1.000000e+03  # mass density of water
element('FSIInterfaceElement2D', 2, 11, 22, rhoW, thickness=1.0)

Code Developed, implemented and tested by:

Massimo Petracca (ASDEA Software),

Enrique Simbort (UC San Diego),

Joel Conte (UC San Diego).

3.1.9.36.5. References

[ZienkiewiczEtAl1978]

Zienkiewicz O.C., Bettess P. (1978) “Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment”, Inter. J. Numer. Meth. Eng.., 13(1): 1–16. (Link to article)

[ZienkiewiczEtAl2000]

Zienkiewicz O.C., Taylor R.L. (2000) “The Finite Element Method”, Butterworth-Heinemann, Vol.1, 5th Ed., Ch.19.

[LøkkeEtAl2017]

Løkke A., Chopra A.K. (2017) “Direct finite element method for nonlinear analysis of semi-unbounded dam–water–foundation rock systems”, Earthquake Engineering and Structural Dynamics 46(8): 1267–1285. (Link to article)