.. _FSIFluidElement2D:

FSIFluidElement2D Element
^^^^^^^^^^^^^^^^^^^^^^^^^

Description
################
This command is used to construct an FSIFluidElement2D element object. The FSIFluidElement2D element is a 4-node bilinear acoustic element with the following features:

#. It is based on the Eulerian pressure formulation ([ZienkiewiczEtAl1978]_ , [ZienkiewiczEtAl2000]_ , [LøkkeEtAl2017]_) for (Class I) fluid-structure interaction problems.
#. It uses a full 2x2 Gauss quadrature, and therefore has a total of 4 integration points.

Input Parameters
################

.. function:: element FSIFluidElement2D $eleTag $n1 $n2 $n3 $n4 $cc

.. csv-table:: 
   :header: "Argument", "Type", "Description"
   :widths: 10, 10, 40

   $eleTag, integer, unique integer tag identifying element object
   $n1 $n2 $n3 $n4, 4 integers, the four nodes defining the element (-ndm 2 -ndf 1)
   $cc, float, speed of pressure waves in water


.. figure:: figures/FSI_FE/FSIFluidElement2D_geometry.png
	:align: center
	:figclass: align-center
	:width: 50%

	**Figure 1. Nodes, Gauss points and parent coordinate system**

Recorders
#########

This element does not feature specific queries for element recorders. However, you can visualize the following quantities: the **added hydrodynamic pressure**, its **first-time derivative**, and its **second-time derivative** by examining the first component of **displacement**, **velocity**, and **acceleration** at the nodes.

Theory
######

For additional documentation regarding the derivation of the implemented finite elements (FSIFluidElement2D, `FSIFluidBoundaryElement2D <https://github.com/esimbort/OpenSeesDocumentation/blob/master/source/user/manual/model/elements/FSIFluidBoundaryElement2D.rst>`_, `FSIInterfaceElement2D <https://github.com/esimbort/OpenSeesDocumentation/blob/master/source/user/manual/model/elements/FSIInterfaceElement2D.rst>`_) based on the Eulerian pressure formulation, please refer to the attached PDF document (`Link to PDF <https://drive.google.com/drive/folders/1QnWEC6kJrFct5korO89bqL1lcn7zi4yG>`_)

Example of how to define a single 2D acoustic finite element
############################################################

   1. **Tcl Code**

   .. code-block:: tcl

      # set up a 2D-1DOF model
      model Basic -ndm 2 -ndf 1
      node 1  0.0  0.0
      node 2  1.0  0.0
      node 3  1.0  1.0
      node 4  0.0  1.0
      
      # create the acoustic element with speed of pressure waves in water, c = 1.440000e+03
      set cc 1.440000e+03
      element FSIFluidElement2D  1  1 2 3 4  $cc
      
      # record added hydrodynamic pressures at element nodes (4 columns, 1 for each node)
      recorder Element  -xml  pressure_out.xml  -ele  1  pressure
      # record first time derivative of added hydrodynamic pressures at element nodes (4 columns, 1 for each node)
      recorder Element  -xml  dpressure_dt_out.xml  -ele  1  dpressure_dt

   2. **Python Code**

   .. code-block:: python

      # set up a 2D-1DOF model
      model('Basic', '-ndm', 2, '-ndf', 1)
      node(1, 0.0, 0.0)
      node(2, 1.0, 0.0)
      node(3, 1.0, 1.0)
      node(4, 0.0, 1.0)
      
      # create the acoustic element with speed of pressure waves in water, c = 1.440000e+03
      cc = 1.440000e+03
      element('FSIFluidElement2D', 1, 1,2,3,4, cc)
      
      # record added hydrodynamic pressures at element nodes (4 columns, 1 for each node)
      recorder('Element', '-xml', 'pressure_out.xml', '-ele', 1, 'pressure')
      # record first time derivative of added hydrodynamic pressures at element nodes (4 columns, 1 for each node)
      recorder('Element', '-xml', 'dpressure_dt_out.xml', '-ele', 1, 'dpressure_dt')

Code Developed, implemented and tested by:

| `Massimo Petracca <mailto:m.petracca@asdea.net>`_ (ASDEA Software),
| `Enrique Simbort <mailto:egsimbortzeballos@ucsd.edu>`_ (UC San Diego),
| `Joel Conte <mailto:jpconte@ucsd.edu>`_ (UC San Diego).

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 <https://onlinelibrary.wiley.com/doi/10.1002/nme.1620130102>`_)
.. [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 <https://onlinelibrary.wiley.com/doi/abs/10.1002/eqe.2855>`_)