Fluid/structure coupling

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4.6 Fluid/structure coupling

This section illustrates the use of fevisco Fluid commands.

4.6.1 Summary of theory

One considers fluid structure interaction problems of the form []

(4.11)

with q the displacements of the structure, p the pressure variations in the fluid and F^ext the external load applied to the structure, where

(4.12)

Full order equations for the coupled problem are impractical. One thus considers model reduction for both the solid and fluid parts of the model. Given a reduction basis T_s for the structure, one builds a reduction basis containing fluid modes within the bandwidth of interest and static corrections for the effects of vectors in T_s. Thus the resulting basis for the fluid model is

(4.13)

Similar equations can of course be developed for applications where the fluid is represented using boundary elements [].

4.6.2 Acoustic stiffness on a loudspeaker

The procedure is divided in the following steps:

declare the fluid as a superelement in the structure model. A typical call would take the form
```
[modelS,modelF]=fevisco('fluidtest'); % this generates demo models
cf=feplot(fevisco('fluidmerge',modelS,modelF));
fecom('curtabStack','SE:fluid')
cf.sel(1)={'innode {y>=0}& eltname~=SE','colordatamat'}
```
Note that the solid model modelF will often be read from NASTRAN as modeshapes (PARAM,POST,-2) or upcom superelement (PARAM,POST,-4). If node numbers in the fluid and solid are coincident, the call automatically shifts fluid node numbers.
assembly of the fluid/structure coupling and fluid matrices with the FluidMatrix command
```
fevisco('fluidmatrix',cf, ...
  'SelElt selface', ...    % Fluid interface (in fluid SE)
  'SelElt EltName quad4'); % Solid interface (in structure)
cf.Stack{'fsc'} % see the coupling superelement
```
Arguments of the command are
- a pointer to the feplot figure containing the solid model and fluid as a superelement
- a series of femesh commands that allows the selection of the fluid interface for which a fluid structure property is defined. In the example, one selects the fluid (eltname flui) and keeps its exterior boundary (SelFace).
  If the generation of this interface cannot be performed using a single feutil command, then the element matrix should be provided instead of a selection command.
- a selection for the solid interface. In the example, one retains all elements but in practical applications, one will often eliminate parts of the model (weld points, stiffeners, ...). You can again provide the selection as an element matrix.
The result is stored as a fsc superelement. It is obtained by estimating translations at the fluid interface nodes trough MPCs (see ConnectionSurface) and standard integration of the fluid/structure coupling elements. Its DOFs combine DOFs of the solid model and pressure DOFs on the fluid superelement (the MPCs are eliminated).

The final step is to generate a reduced coupled model. This requires defining, applied loads, required sensors, and a modal model structure in vacuum (defined trough its modes def as done here, or a parametric reduced model MVR. You can start by adding additional pressure sensors then use the call

 cf.Stack{'fluid'}=stack_set(cf.Stack{'fluid'},'Info','EigOpt',[6 10 -1e3]);
 cf.mdl=fe_case(cf.mdl,'SensDof','Sensors',[65.01;1.19], ...
  'DofLoad','Point load',[65.01]);
 dsol=fe_eig(modelS,[6 20 1e3]);
 cf.Stack{'info','FluidEta'}=.1;      % Fluid loss set to 10 %
 cf.Stack{'info','DefaultZeta'}=.01;  % Structure loss set to 2 %
 fevisco('fluidMakeReduced',cf.mdl,dsol);

Acoustic loads are not yet considered in this procedure.

Reduced basis computations are then performed using low level fe2xf calls

 [ci,XF]=iiplot
 cf.Stack{'info','Freq'}=linspace(10,250,1024)';
 ci.Stack={'curve','coupled',fe2xf('frfzr',cf)};
 cf.Stack{'zCoef'}(4:6,4)={'-w.^2*1e-3';1e-3;1e-3};
 ci.Stack{'curve','no fluid'}=fe2xf('frfzr',cf); 
 iicom('iixonly',{'coupled','no fluid'})