.. _FSIFluidBoundaryElement2D: FSIFluidBoundaryElement2D Element ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Description ########### This command is used to construct an FSIFluidBoundaryElement2D element object. The FSIFluidBoundaryElement2D element is a 2-node linear acoustic boundary element object 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 2 integration points Gauss quadrature. #. Depending on the input variables, it enables the implementation of radiation boundary, reservoir bottom absorption or free surface effects. Input Parameters ################ .. function:: element FSIFluidBoundaryElement2D $eleTag $n1 $n2 $cc $alpha $g <-thickness $thickness> .. csv-table:: :header: "Argument", "Type", "Description" :widths: 10, 10, 40 $eleTag, integer, unique integer tag identifying element object $n1 $n2, 2 integers, the two nodes defining the element (-ndm 2 -ndf 1) $cc, float, speed of pressure waves in water $alpha, float, reservoir bottom reflection coefficient ([LøkkeEtAl2017]_) $g, float, acceleration due to gravity Optional: $thickness, float, the thickness in 2D problems (default 1.0). .. figure:: figures/FSI_FE/FSIFluidBoundaryElement2D_geometry.png :align: center :figclass: align-center :width: 50% **Figure 1. Nodes, Gauss points and parent coordinate system** 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 `_) Example ####### .. admonition:: Three cases of valid inputs are shown below: 1. Radiation boundary, 2. Reservoir bottom absorption and 3. Surface waves effects. 1. **Tcl Code** .. code-block:: tcl # set up a 2D-1DOF model: Radiation Boundary Side model Basic -ndm 2 -ndf 1 node 11 0.0 0.0 node 22 1.0 1.0 # create the acoustic boundary element at radiation boundary side with speed of pressure waves in water, cc = 1.440000e+03 (set alpha = 0, g = 0 to exclude bottom absorption and mass terms for water surface, respectively) set cc 1.440000e+03 element FSIFluidBoundaryElement2D 3 11 22 $cc 0.0 0.0 -thickness 1.0 # set up a 2D-1DOF model: Reservoir Bottom Absorption Boundary model Basic -ndm 2 -ndf 1 node 11 0.0 0.0 node 22 1.0 1.0 # create the acoustic boundary element at the bottom boundary of a reservoir given speed of pressure waves in water, cc = 1.440000e+03 and reservoir bottom reflection coefficient, alpha = 9.990000e-01 (set g = 0 to exclude mass terms for water surface) set cc 1.440000e+03 set alpha 9.990000e-01 element FSIFluidBoundaryElement2D 4 11 22 $cc $alpha 0.0 -thickness 1.0 # set up a 2D-1DOF model: Free Surface Boundary model Basic -ndm 2 -ndf 1 node 11 0.0 0.0 node 22 1.0 1.0 # create the acoustic boundary element at the free surface boundary of the reservoir given g = 9.807 (set alpha = 0, cc = 0 to exclude damping terms) set cc 1.440000e+03 set alpha 9.990000e-01 set g 9.807 element FSIFluidBoundaryElement2D 5 11 22 0.0 0.0 $g -thickness 1.0 2. **Python Code** .. code-block:: python # set up a 2D-1DOF model: Radiation Boundary Side model('Basic', '-ndm', 2, '-ndf', 1) node(11, 0.0, 0.0) node(22, 1.0, 1.0) # create the acoustic boundary element at radiation boundary side cc = 1.440000e+03 element('FSIFluidBoundaryElement2D', 3, 11, 22, cc, 0.0, 0.0, thickness=1.0) # set up a 2D-1DOF model: Reservoir Bottom Absorption Boundary model('Basic', '-ndm', 2, '-ndf', 1) node(11, 0.0, 0.0) node(22, 1.0, 1.0) # create the acoustic boundary element at the bottom boundary of a reservoir cc = 1.440000e+03 alpha = 9.990000e-01 element('FSIFluidBoundaryElement2D', 4, 11, 22, cc, alpha, 0.0, thickness=1.0) # set up a 2D-1DOF model: Free Surface Boundary model('Basic', '-ndm', 2, '-ndf', 1) node(11, 0.0, 0.0) node(22, 1.0, 1.0) # create the acoustic boundary element at the free surface boundary of the reservoir g = 9.807 element('FSIFluidBoundaryElement2D', 5, 11, 22, 0.0, 0.0, g, thickness=1.0) Code Developed, implemented and tested by: | `Massimo Petracca `_ (ASDEA Software), | `Enrique Simbort `_ (UC San Diego), | `Joel Conte `_ (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 `_) .. [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 `_)