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fsc

Purpose

Fluid structure/coupling with non-linear follower pressure support.

Description

Elasto-acoustic coupling is used to model structures containing a compressible, non-weighing fluid, with or without a free surface.

The FE formulation for this type of problem can be written as [51]

 
    (9.7)

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

 
    (9.8)

To assemble fluid/structure coupling matrix you should declare a set of surface elements (any topology) with property p_solid('dbval 1 fsc'). The C matrix (solid forces induced by pressure field) is assembled with the stiffness (matrix type 1), while the CT matrix (fluid pressure due to normal velocity of solid) is assembled with the mass (matrix type 2).

Some formulations, consider a surface impedance proportional to the pressure. This matrix can be computed by defining a group of surface elements with an acoustic material (see m_elastic 2) and a standard surface integration rule (p_solid('dbval 1 d2 -3')). This results in a mass given by

 
    (9.9)

Follower force

One uses the identity

 
    (9.10)

where (r,s) designate local coordinates of the face (assumed such that the normal is outgoing). Work of the pressure is thus:

 
    (9.11)

On thus must add the non-linear stiffness term:

 
    (9.12)

Using (idem for s), and also

 
    (9.13)

this results in

 
    (9.14)

Base tests : fsc3 testsimple and fsc3 test.

In the RivlinCube test , the pressure on each free face is given by

 
    (9.15)

Implementation

Fluid structure coupling has been renewed in SDT 7.2. In particular flui4 elements and fsc elements are obsolete and are not supported with these commands. One must now use classical volume elements assigned with proper m_elasticproperties for fluid modelling and classical ND-1 elements for the interface, assigned with proper p_solidproperties.

Implementation strategy relies on a solid model to which fluid and coupling superelements are added. This easens solid or fluid coupled models. Reduced solutions are generated by default through the generation of a pre-assembled reduced model using free solid modes and free fluid modes.

A coupled fluid structure model is thus composed of three sub-models

To help keeping track of performed modelling operations and main options associated to fluid structure models, a running option structure is stored in the base model stack as info,fscOpt. This structure can be a priori defined by the user to store options once for all. It will be completed on the fly during the procedure execution. This structure will contain in particular

Commands

AddFluid

AddFluid generates one or several fluid superlements in a model. The base model either already contains the elements modelling the fluid in which case an element selection can be provided, or an external model to be added. By default the fluid model is considered as an independent mesh i.e. not compatible with the solid structure. If that is the case, command option -combine does not renumber the fluid superlement to keep mesh compatibility.

Syntax is model=fsc('AddFluid',model,mof,RO); with

Output model contains a fluid superelement and stack entry info,fscOpt keeping track of the fluid superlement name and other options.

Command options can be defined in three ways. It can either be specifed in the AddFluid command string with a - prefix, or provided as an additional argument RO or as a structure stored in model.Stack{'info','fscOpt'}. Potential multiple definitions are handed by the following priority rule. Options are taken in input argument RO if provided, it is then completed by the string command option parsing. Additional fields specified in info,fscOpt will eventually be added.

Fluid parameters are directly propagated to the global model if mof is provided as an assembled model, see fe_case par and matdes -1.1 in mattyp. In such case parameters declared in mof are translated as superelement parameters associated to the fluid superelement matrices in the base model.

The following options are available

% Generate a demonstration model containing a structure and a fluid (no interfaces)
mo1=fsc('TestModel');
% Declare the fluid and generate the superlement, based on the material
mo1=fsc('AddFluid',mo1,'matid1');

AddCoupling

AddCoupling generates fluid interface coupling elements between the solid structure and the fluid model. The fluid model must have already been declared with command fsc AddFluid. These elements must be defined as compatible interfaces to the fluid model. The base model either already contains the fluid interface elements or an externally defined fluid coupling model is provided, or it can be eventually defined on the fly by specifying a selection with FindElt providing the interface topology. In the latter case, one must keep in mind that the fluid coupling interface must be compatible with the fluid model, two cases exist depending on the provided selection.

Syntax is model=fsc('AddCoupling',model,moc,RO); with

Output model contains a coupling superelement and stack entry info,fscOpt keeping track of the fluid and fluild interface superlements names and other options. In particular stack entry info,fscOpt contains the fields

Command options can be defined in two ways. It can either be specifed in the AddCoupling command string with a - prefix, or provided as an additional argument RO. Potential multiple definitions are handed by the following priority rule. Options are taken in input argument RO if provided, it is then completed by the string command option parsing.

The following options are available

% Now declare coupling
% by default fluid surface is taken
mo1=fsc('AddCoupling',mo1);

SolveMVR[,-direct]

SolveMVR generates and assembles the reduced fluid structure coupled model. The solid and fluid are respectively projected onto their reduction basis and the fluid interface model is then projected. Reduced matrices are then assembled maintaining solid, fluid and coupling contributions apart. The global assembly rule is provided in a zCoef stack entry, see section 6.5.1.

Syntax is model=fsc('SolveMVR',model,RO); with

Output model is the base model, with additional stack entry SE,MVR containing the reduced assembled fluid coupled model. This model itself is assembled and contains in its stack entry info,zCoef the assembly rule, see section 6.5.1. The MVR entry contains the following fields

If command option -direct was used the following fields are also present

Command options should be defined with the RO input with supported fields

% Generate the reduced coupled fluid structure model
mo1=fsc('SolveMVR-keepT',mo1);  
% Recover the assembled model
MVR=stack_get(mo1,'SE','MVR','get');

SolveEig

SolveEig computes complex eigenmodes of the reduced fluid structure coupled model generated by fsc SolveMVR.

Syntax is def=fsc('SolveEig',model);.

The following command options are available

% Compute coupled modes
def=fsc('SolveEig',mo1);
% Restitue modes on full DOF
dfull=fesuper('sedef',MVR.TR,def);

Obsolete Non-conform conforming match

SDT supports non conforming element for fluid/structure coupling terms corresponding to the structure are computed using the classical elements of the SDT, and terms corresponding to the fluid are computed using the fluid elements (see flui4).

The coupling term C is computed using fluid/structure coupling elements (fsc elements).

Only one integration point on each element (the center of gravity) is used to evaluate C.

When structural and fluid meshes do not match at boundaries, pairing of elements needs to be done. The pairing procedure can be described for each element. For each fluid element Fi, one takes the center of gravity Gf,i (see figure), and searches the solid element Si which is in front of the center of gravity, in the direction of the normal to the fluid element Fi. The projection of Gf,i on the solid element, Pi, belongs to Si, and one computes the reference coordinate r and s of Pi in Si (if Si is a quad4, −1<r<1 and −1<s<1). Thus one knows the weights that have to be associated to each node of Si. The coupling term will associate the DOFs of Fi to the DOFs of Si, with the corresponding weights.

See also

p_solid, m_elastic


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