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 :
Topology
Formal definitions of :

U : DOF
N : shape functions
L : gradients and
combinations of DOF
D : matrix of physical
coefficients
   d  e  sources
e
    L N U 
T
T
   U  N   L 
    D  
 .d e   wi .i 
e
i  ptsGauss
General examples
Bimorph. Beam – harmonic response – Voltage field and shape.
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
Acoustic. Cavity – pressure field – harmonic response
Porous Materials
Construction of libraries of various u-p Biot-Allard elements
PoroGen2D.py
PoroWeakVariational2D.py
T3RefEle.py
T6RefEle.py
Q4RefEle.py
Q8RefEle.py
Poro2DSet.cao
Main Script File
Variational Form Definitions
Topology Definitions
Cavok Library File
PoroGen3D.py
PoroWeakVariational3D.py
T4RefEle.py
T10RefEle.py
H8RefEle.py
P6RefEle.py
Poro3DSet.cao
3D Plates
RefElePlaq3DMidlin_harm_rot.py
RefElePlaq3DMidlin_harm_rot_Q8.py
Reissner-Mindlin formulation
Selective integration
(Batoz&Dhatt, Tome2, pp 303)
Q4 or Q8
Generalized rotations, third rotation
fictious
Harmonic response of an assembly of 2 thin plates
Others
RefEleAcou3DH8.py
RefEleCoupUPS_Z.py
H8 Acoustics element and a corresponding
fluid-structure coupling element
See section models for examples of use
StrucRaid.py
Example of use of plates elements
From *.cao library
T Beam harmonic response with a plate model
Torsional load
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
2D Poisson problem with an in-plane
triangular mesh
gmshtest3.py
3D Poisson problem with a tetrahedron mesh
Tube_kundt_gmsh.py
gmshtest4.py
2D Poisson problem over a 3D triangular mesh
3D Poroelastic primatic and hexahedric elements
Frequency analysis
From ANSYS
Car_*
1 : mesh importation and saving in a *.cao (cavok) file
2 : analysis definition (CL, etc …)
3 : calculus and post-processing
Conceptual Car-model inluding air (green) and porous (red) domains
Pressure 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
CasimirTest.py
2 plates : 0.5x0.5x0.002 Steel
Free conditions, load on a corner in verical direction
Comparison with ANSYS (FE) and
ETAPE (continuous elements)
-60
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)
-70
-80
Uz in dB
-90
-100
-110
-120
-130
-140
400
410
420
430
440
450
460
Frequency
470
480
490
500
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 Cavok
A 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
Porous 0.1 m
Plate 0.5x0.4m2
+ coupling elements
Air 0.3 m
Response at 500 Hz
Real displacement for plate
Modulus of pressure in Air and Porous
That’All Folks