Examples Cavok V3 R9

• Part 1 : RefEle construction• Part 2 : Modeling• Part 3 : Mesh import

O. Tanneau & P. Lamary 2006

Copyright © Volage Limited 2001 - 2006

Part 1 : RefEle Construction

Cavok includes a constructor of reference element

Main Entries :

. .

e

e

e

T T

e ii ptsGauss

d sources

L N U

U N L

D

d w i

TopologyFormal definitions of :

U : DOFN : shape functionsL : gradients and combinations of DOFD : matrix of physical coefficients

General examples

RefEleTest2.py : Q4 for 2D Poisson equation

RefEleTest3.py : Q4 for 2D Piezzo-electricity

RefEleTest4.py : Q8 and H8 for Poisson equation (2D and 3D respectively)

RefEleTest5.py : H8 for 3D Acoustic

RefEleTransfo_FM2UY.py and RefEleTransfo_FM2UYCT.py : introduction of rotations in 2D plates elements

Bimorph. Beam – harmonic response – Voltage field and shape.

Acoustic. Cavity – pressure field – harmonic response

Porous Materials

PoroGen2D.py PoroGen3D.py

PoroWeakVariational2D.py PoroWeakVariational3D.py

T3RefEle.pyT6RefEle.pyQ4RefEle.pyQ8RefEle.py

T4RefEle.pyT10RefEle.pyH8RefEle.pyP6RefEle.py

Main Script File

Variational Form Definitions

Topology Definitions

Construction of libraries of various u-p Biot-Allard elements

Poro2DSet.cao Poro3DSet.caoCavok Library File

3D PlatesRefElePlaq3DMidlin_harm_rot.py

RefElePlaq3DMidlin_harm_rot_Q8.py

Reissner-Mindlin formulationSelective integration (Batoz&Dhatt, Tome2, pp 303)Q4 or Q8Generalized rotations, third rotation fictious

Harmonic response of an assembly of 2 thin plates

Others

RefEleAcou3DH8.pyRefEleCoupUPS_Z.py

StrucRaid.py

T Beam harmonic response with a plate modelTorsional load

H8 Acoustics element and a correspondingfluid-structure coupling element

See section models for examples of use

Example of use of plates elementsFrom *.cao library

Part 2 : mesh importation

3 mesh strategies are proposed :

1) Internal use of structured mesh cavok functions (see examples in others sections )

2) Gmsh tool : usefull for unstructured mesh 2D and 3D (triangles and tetrahedrons)

3) From Ansys importation

From GMSH

gmshtest2.py gmshtest3.py

gmshtest4.py

Tube_kundt_gmsh.py

2D Poisson problem with an in-plane triangular mesh

3D Poisson problem with a tetrahedron mesh

2D Poisson problem over a 3D triangular mesh3D Poroelastic primatic and hexahedric elementsFrequency analysis

From ANSYS

Car_*1 : mesh importation and saving in a *.cao (cavok) file2 : analysis definition (CL, etc …)3 : calculus and post-processing

Conceptual Car-model inluding air (green) and porous (red) domainsPressure modulus at 1000 Hz

Part 3 : Modeling

4 examples :

- 3D Plate BenchMark

- Active Control of a double-wall (with porous lining) coupled to an acoustical cavity

- Use of the external Acoustical Boundary Element solver

- Simple Box with one elastic side and a porous layer

3D Plate BenchMark

400 410 420 430 440 450 460 470 480 490 500

-140

-130

-120

-110

-100

-90

-80

-70

-60

Frequency

Uz

in d

B

Bleu : étape Rouge : Ansys Cyan : Cavok Q8 450 éléments (noeuds 31x31 x2, eq : 1800 Q4) Violet : Cavok Q8 800 éléments (noeuds 41x41 x2, eq : 3200 Q4)

2 plates : 0.5x0.5x0.002 SteelFree conditions, load on a corner in verical direction

CasimirTest.py

Comparison with ANSYS (FE) and ETAPE (continuous elements)

Active Control of a double-wall (with porous lining) coupled to an acoustical cavity

Script chain programming in Control_Flat_Panel_Cavity.py :

Loop :For all chosen frequencies :

- Calculus without control- Introduce transfer function between sensor and actuator- Calculus with control activated

Actuator

Sensor

Use of the external Acoustical Boundary Element solver

This examples illustrate how to create BEM analysis from CavokA transfer between Cavok FE results and BEM boundary conditions is also performed

BEM_Cyl_1.py

Radiation from a cylindrical with Un = 1

BEM_Plaq_1.py

Chain FEM for the plate and BEM for radiation

Simple Box with one elastic side and a porous layer

ShoesBox1.py

Plate 0.5x0.4m2+ coupling elements

Air 0.3 m

Porous 0.1 m

Response at 500 HzReal displacement for plateModulus of pressure in Air and Porous

That’All Folks