Select “Aster”

Add study case Select command file Select mesh

Maximum memoryMaximum calculation time

Number of CPUs to use

Code Aster command file (modal-111Wafer.comm)

DEBUT(IGNORE_ALARM='UTILITAI4_2',);

### Read MESH ###Mesh=LIRE_MAILLAGE(UNITE=20, FORMAT='MED',);

### Define Model ###Model=AFFE_MODELE(MAILLAGE=Mesh, AFFE=_F(TOUT='OUI', PHENOMENE='MECANIQUE', MODELISATION='3D',),);

### MATERIAL (Single Crystal Silicon) ###C_Si=DEFI_MATERIAU(ELAS_ORTH=_F(E_L=130800.0, E_T=130800.0, E_N=130800.0, NU_LT=0.28, NU_LN=0.28, NU_TN=0.28, G_LT=79570.0, G_LN=79570.0, G_TN=79570.0, RHO=2.33e-15, ALPHA_L=0.0, ALPHA_T=0.0, ALPHA_N=0.0,),);

Read a mesh (Unit number = 20, defined in ASTK)

3D Mechanical solver apply to the mesh

Define a material (single crystal silicon)

Caution! Unit is not a MKSA, but a uMKSAi.e. Length : umMass : kgTime : sStress : MpaDensity : kg/um3

### Angle of the local Coordinate ###### (111) direction is aligned to Z asix ###CARA_EL=AFFE_CARA_ELEM( MODELE=Model,

MASSIF=_F( GROUP_MA = 'TOUT',ANGL_REP=(30, -35.26438968275467, 45,),)

);

### Set material to the model ###Material=AFFE_MATERIAU(MAILLAGE=Mesh, AFFE=_F(TOUT='OUI', MATER=C_Si,),);

### BOUNDARY CONDITIONS ###### Fixed points ###BLOCAGE=AFFE_CHAR_MECA(MODELE=Model, DDL_IMPO=_F(GROUP_MA='Gfix', DX=0.0, DY=0.0, DZ=0.0,),);

Default orientation of material axis is same as global axis(i.e. same as 100 wafer)When use (111) wafer, local coordinate should be rotatedas follows

Apply a material to the mesh

To apply all meshes

Define a boundary condition (fixed nodes)

Node belonging to the group “Gfix”

X, Y and Z displacement is fixed at “0”

### COMPUTATION OF MASS AND STIFFNESS MATRICESASSEMBLAGE(MODELE=Model, CHAM_MATER=Material,

CARA_ELEM = CARA_EL, CHARGE=BLOCAGE, NUME_DDL=CO('NUMEDDL'), MATR_ASSE=(_F(MATRICE=CO('RIGIDITE'), OPTION='RIGI_MECA',), _F(MATRICE=CO('MASSE'), OPTION='MASS_MECA',),

),);

### MODAL ANALYSIS ###MODES=CALC_MODES( SOLVEUR_MODAL=_F(METHODE='SORENSEN',), MATR_RIGI=RIGIDITE, MATR_MASS=MASSE,

OPTION='CENTRE', CALC_FREQ=_F(FREQ=(200000,),NMAX_FREQ=10,), VERI_MODE=_F(STOP_ERREUR='NON',),);

Create a matrices (Stiffness and Mass)

Define a name of matrices

Material Local coordinate

B.C.

Modal analysis

Matrices

Center frequency Number of modes to calculate

### Calc STRESSESMODES=CALC_CHAMP(reuse =MODES, RESULTAT=MODES, CONTRAINTE=('SIEF_NOEU',),

CRITERES=('SIEQ_NOEU',), );

### PRINT THE RESULTSIMPR_RESU(FORMAT='MED', RESU=( _F(RESULTAT=MODES,),),

);

FIN();

Calculate stress from the result

Nodal stress

Nodal equivalent stress (von Mises, etc)

Write a result to file

Right-click → export to ASTK Check this

Click this to run the solver

ASTK

ASJOB

Progress

Click this to refresh the information

“ASJOB” window

When error occurs, check the message file

For exampleMessage is written in French…. You need to translate it.

When group “TOUT” is missing

If no error occurs

Select “ParaVIS”

Right-click → Open

Result file is opened

Apply color (Displacement)

Select “MODES__DEPL”

Displace a model according to the modal shape

Select warp-by-vector

Magnification of displacement

Model is displaced

Display the original shape with half-transparency

Display the original shape

Change opacity

Select a mode

Eigen frequency

Select a mode

Frequencies of two modes are notperfectly matched.Error was about 19 ppm.(maybe due to numerical error)

Change color to the stress

Color range can be modified