These
are examples simulated on LAMINA
Ex
#1 : Silicon diaphragm only(filenames
Si_12.datandSi_23.dat)
Si_12.dat
containsvarious input information
and
a
graphic representation of the LAMINA
Si_23.dat
Contains the simulation results U and w at each
grid
point (in the 1st quadrant, assuming all
4
quadrants are symmetric).
Observe
that U's are zero (no inplane stresses)
The
deflection is maximum at the origin.
Standard
result is 0.126E-2 (see Table below)
Table
6.1Deflection at center `w ' for
lateral loads `q'
(Reference
for known results is Timoshenko [6.9])
-----------------------------------------------------------
serial
Boundary conditions
known results
LAMINA
No.
-----------------------------------------------------------
1
X-edges fixed
0.260E-2
0.261E-2
Y-edges free
(TIM pp 202)
2
X-edges simply supp.
0.130E-1
0.130E-1
Y-edges free
(TIM pp 120)
3
All edges fixed
0.126E-2
0.126E-2
(TIM pp 202)
4
All edges simply
10.406E-2
10.406E-2
supported
(TIM pp 120)
-----------------------------------------------------------
************************************************************
File
Si_12.dat
==============
*FILENAME
/WT11/ , VERSION OF WT11 25/10/88 PRAKASH
SOLVE
FOR UW
SI=1,
SIO2=2, SI3N4=3, POLY=4, Al=5
6
UM, 0.4 UM, 0.13 UM,4 UM , 1 UM
N+SUB,
P+SUB, SILICA,QUARTZ, SAPPHIRE
200UM,
200UM,200UM,200UM,200UM
TUNGSTEN,
1UM,
LAMID(
1)= 1( DI-SILICON)THIK(
1)=6.00 MICRON
--------------------------------------------------
ISOTROPIC,
ISO=1
TRANSVERSE
LOAD MULT=1.00000000
MESH
NX=10NY=10
SUMNT=0.000000E+00
DS(1,1),XNMULT=-0.30695E+020.00000E+00
DS(1,1),SUMMT=-0.30695E+020.00000E+00
OLPHA,BETA,GAMMA=0.000000E+000.000000E+000.000000E+00
X-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IX=
1
Y-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IY=
1
4-POINT
APPROX. TO W,X AND W,XX
I,J
AND ID1=11013
I,J
AND ID1=21015
I,J
AND ID1=31019
I,J
AND ID1=41019
I,J
AND ID1=51019
I,J
AND ID1=61019
I,J
AND ID1=71019
I,J
AND ID1=81019
I,J
AND ID1=91023
I,J
AND ID1=101021
=============================
file
Si_23.dat
==============
SOLVE
FOR W AND U BOTH
UPPER
U-MATRIX
LOWER
L-MATRIX
WU-MATRIX
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00
-0.5611E-04
-0.5524E-04 -0.5264E-04 -0.4835E-04 -0.4246E-04 -0.3513E-04 -0.2668E-04
-0.1764E-04 -0.9001E-05 -0.2371E-05
-0.1922E-03
-0.1891E-03 -0.1800E-03 -0.1649E-03 -0.1444E-03 -0.1191E-03 -0.9025E-04
-0.5988E-04 -0.3118E-04 -0.9001E-05
-0.3713E-03
-0.3653E-03 -0.3472E-03 -0.3177E-03 -0.2775E-03 -0.2283E-03 -0.1727E-03
-0.1145E-03 -0.5988E-04 -0.1764E-04
-0.5660E-03
-0.5566E-03 -0.5287E-03 -0.4830E-03 -0.4212E-03 -0.3458E-03 -0.2609E-03
-0.1727E-03 -0.9025E-04 -0.2668E-04
-0.7560E-03
-0.7433E-03 -0.7055E-03 -0.6439E-03 -0.5606E-03 -0.4593E-03 -0.3458E-03
-0.2283E-03 -0.1191E-03 -0.3513E-04
-0.9268E-03
-0.9111E-03 -0.8643E-03 -0.7880E-03 -0.6852E-03 -0.5606E-03 -0.4212E-03
-0.2775E-03 -0.1444E-03 -0.4246E-04
-0.1068E-02
-0.1050E-02 -0.9956E-03 -0.9071E-03 -0.7880E-03 -0.6439E-03 -0.4830E-03
-0.3177E-03 -0.1649E-03 -0.4835E-04
-0.1174E-02
-0.1153E-02 -0.1093E-02 -0.9956E-03 -0.8643E-03 -0.7055E-03 -0.5287E-03
-0.3472E-03 -0.1800E-03 -0.5264E-04
-0.1238E-02
-0.1217E-02 -0.1153E-02 -0.1050E-02 -0.9111E-03 -0.7433E-03 -0.5566E-03
-0.3653E-03 -0.1891E-03 -0.5524E-04
-0.1260E-02
-0.1238E-02 -0.1174E-02 -0.1068E-02 -0.9268E-03 -0.7560E-03 -0.5660E-03
-0.3713E-03 -0.1922E-03 -0.5611E-04
^^^^^^^^
-0.1260E-02
is the deflection at the origin of the first quadrant and hence at the
centre of the diaphragm
****************************************************************************************
Ex
#2 : Silicon-Nitride on Silicon diaphragm without
any transverse load
(filenames
Ni_Si_12.datandNi_Si_23.dat)
Ni_Si_NL12.dat
containsvarious input information
and
a
graphic representation of the LAMINA
Ni_Si_NL23.dat
Contains the simulation results U and w at each
grid
point (in the 1st quadrant, assuming all
4
quadrants are symmetric).
Observe
that U's are non-zero
(inplane
stresses are generated due to thermal mismatch)
The
deflection is large at the origin eventhough
there
is no transverse load applied.
There
is no standard result to compare !!!!!
Ni_Si_NL12.dat
==============
*FILENAME
/WT11/ , VERSION OF WT11 25/10/88 PRAKASH
SOLVE
FOR UW
SI=1,
SIO2=2, SI3N4=3, POLY=4, Al=5
6
UM, 0.4 UM, 0.13 UM,4 UM , 1 UM
N+SUB,
P+SUB, SILICA,QUARTZ, SAPPHIRE
200UM,
200UM,200UM,200UM,200UM
TUNGSTEN,
1UM,
LAMID(
2)= 3( SI3N4)THIK(
2)=0.20 MICRON
--------------------------------------------------
LAMID(
1)= 1( DI-SILICON)THIK(
1)=1.00 MICRON
--------------------------------------------------
ISOTROPIC,
ISO=1
TRANSVERSE
LOAD MULT=0.00000000
MESH
NX=10NY=10
SUMNT=0.101455E+06
DS(1,1),XNMULT=-0.24556E+000.41316E+02
DS(1,1),SUMMT=-0.24556E+000.20658E+00
OLPHA,BETA,GAMMA=0.413158E+020.413158E+020.000000E+00
X-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IX=
2
Y-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IY=
2
4-POINT
APPROX. TO W,X AND W,XX
I,J
AND ID1=11013
I,J
AND ID1=21015
I,J
AND ID1=31019
I,J
AND ID1=41019
I,J
AND ID1=51019
I,J
AND ID1=61019
I,J
AND ID1=71019
I,J
AND ID1=81019
I,J
AND ID1=91023
I,J
AND ID1=101021
=============================
Ni_Si_NL23.dat
==============
SOLVE
FOR W AND U BOTH
UPPER
U-MATRIX
LOWER
L-MATRIX
WU-MATRIX
0.8487E-020.8020E-020.7968E-020.8198E-020.8380E-020.8146E-020.7035E-020.4383E-02
-0.8384E-03 -0.1000E-01
0.1845E-010.1855E-010.1913E-010.1993E-010.2041E-010.1995E-010.1780E-010.1307E-010.4828E-02
-0.7258E-02
0.2717E-010.2730E-010.2766E-010.2794E-010.2756E-010.2584E-010.2204E-010.1543E-010.5667E-02
-0.6573E-02
0.3385E-010.3382E-010.3366E-010.3304E-010.3146E-010.2834E-010.2311E-010.1538E-010.5289E-02
-0.5974E-02
0.3852E-010.3830E-010.3757E-010.3606E-010.3338E-010.2911E-010.2291E-010.1470E-010.4948E-02
-0.5053E-02
0.4155E-010.4117E-010.3995E-010.3771E-010.3418E-010.2912E-010.2238E-010.1414E-010.5003E-02
-0.3790E-02
0.4339E-010.4288E-010.4130E-010.3854E-010.3444E-010.2890E-010.2196E-010.1393E-010.5488E-02
-0.2247E-02
0.4441E-010.4382E-010.4201E-010.3891E-010.3447E-010.2870E-010.2176E-010.1406E-010.6301E-02
-0.5151E-03
0.4491E-010.4427E-010.4233E-010.3906E-010.3446E-010.2860E-010.2174E-010.1437E-010.7216E-020.1241E-02
0.4506E-010.4440E-010.4242E-010.3910E-010.3445E-010.2858E-010.2177E-010.1456E-010.7773E-020.2514E-02
-0.1559E-02
-0.1509E-02 -0.1361E-02 -0.1130E-02 -0.8390E-03 -0.5165E-03 -0.1988E-030.7222E-040.2468E-030.2592E-03
-0.3576E-02
-0.3475E-02 -0.3181E-02 -0.2721E-02 -0.2139E-02 -0.1491E-02 -0.8469E-03
-0.2831E-030.1139E-030.2468E-03
-0.5941E-02
-0.5791E-02 -0.5354E-02 -0.4670E-02 -0.3800E-02 -0.2826E-02 -0.1843E-02
-0.9588E-03 -0.2831E-030.7222E-04
-0.8509E-02
-0.8313E-02 -0.7739E-02 -0.6839E-02 -0.5689E-02 -0.4393E-02 -0.3068E-02
-0.1843E-02 -0.8469E-03 -0.1988E-03
-0.1111E-01
-0.1087E-01 -0.1017E-01 -0.9067E-02 -0.7654E-02 -0.6051E-02 -0.4393E-02
-0.2826E-02 -0.1491E-02 -0.5165E-03
-0.1356E-01
-0.1328E-01 -0.1247E-01 -0.1119E-01 -0.9537E-02 -0.7654E-02 -0.5689E-02
-0.3800E-02 -0.2139E-02 -0.8390E-03
-0.1568E-01
-0.1537E-01 -0.1446E-01 -0.1303E-01 -0.1119E-01 -0.9067E-02 -0.6839E-02
-0.4670E-02 -0.2721E-02 -0.1130E-02
-0.1732E-01
-0.1698E-01 -0.1601E-01 -0.1446E-01 -0.1247E-01 -0.1017E-01 -0.7739E-02
-0.5354E-02 -0.3181E-02 -0.1361E-02
-0.1835E-01
-0.1800E-01 -0.1698E-01 -0.1537E-01 -0.1328E-01 -0.1087E-01 -0.8313E-02
-0.5791E-02 -0.3475E-02 -0.1509E-02
-0.1871E-01
-0.1835E-01 -0.1732E-01 -0.1568E-01 -0.1356E-01 -0.1111E-01 -0.8509E-02
-0.5941E-02 -0.3576E-02 -0.1559E-02
^^^^^^^^^^
There
is a LARGE deflection (-0.1871E-01) even without any transverse
load
**************************************************************
Ex
#3 : Silicon on Silicon-Nitride diaphragm without any transverse load
(filenames
Si_Ni_12.datandSi_Ni_23.dat)
Si_Ni_NL12.dat
containsvarious input information
and
a
graphic representation of the LAMINA
Si_Ni_NL23.dat
Contains the simulation results U and w at each
grid
point (in the 1st quadrant, assuming all
4
quadrants are symmetric).
Observe
that U's are non-zero
(inplane
stresses are generated due to thermal mismatch)
The
deflection is large at the origin eventhough
there
is no transverse load applied.
There
is no standard result to compare !!!!!
However,
compare with ex #2, deflection has changed sign
but
magnitude is still same.
The
U's have not changed values or sign!
Si_Ni_NL12.dat
==============
*FILENAME
/WT11/ , VERSION OF WT11 25/10/88 PRAKASH
SOLVE
FOR UW
SI=1,
SIO2=2, SI3N4=3, POLY=4, Al=5
6
UM, 0.4 UM, 0.13 UM,4 UM , 1 UM
N+SUB,
P+SUB, SILICA,QUARTZ, SAPPHIRE
200UM,
200UM,200UM,200UM,200UM
TUNGSTEN,
1UM,
LAMID(
2)= 1( DI-SILICON)THIK(
2)=1.00 MICRON
--------------------------------------------------
LAMID(
1)= 3( SI3N4)THIK(
1)=0.20 MICRON
--------------------------------------------------
ISOTROPIC,
ISO=1
TRANSVERSE
LOAD MULT=0.00000000
MESH
NX=10NY=10
SUMNT=0.101455E+06
DS(1,1),XNMULT=-0.24556E+000.41316E+02
DS(1,1),SUMMT=-0.24556E+00-0.20658E+00
OLPHA,BETA,GAMMA=0.413158E+020.413158E+020.000000E+00
X-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IX=
2
Y-EDGES
FIXED/SUPPORTED/FREE, GIVE 1/2/3,IY=
2
4-POINT
APPROX. TO W,X AND W,XX
I,J
AND ID1=11013
I,J
AND ID1=21015
I,J
AND ID1=31019
I,J
AND ID1=41019
I,J
AND ID1=51019
I,J
AND ID1=61019
I,J
AND ID1=71019
I,J
AND ID1=81019
I,J
AND ID1=91023
I,J
AND ID1=101021
============================
Si_Ni_NL23.dat
==============
SOLVE
FOR W AND U BOTH
UPPER
U-MATRIX
LOWER
L-MATRIX
WU-MATRIX
0.8486E-020.8020E-020.7967E-020.8197E-020.8380E-020.8145E-020.7035E-020.4383E-02
-0.8384E-03 -0.1000E-01
0.1844E-010.1854E-010.1913E-010.1992E-010.2041E-010.1995E-010.1780E-010.1307E-010.4827E-02
-0.7258E-02
0.2716E-010.2729E-010.2766E-010.2794E-010.2756E-010.2584E-010.2203E-010.1543E-010.5666E-02
-0.6574E-02
0.3384E-010.3381E-010.3365E-010.3303E-010.3146E-010.2834E-010.2310E-010.1538E-010.5289E-02
-0.5974E-02
0.3851E-010.3829E-010.3756E-010.3605E-010.3337E-010.2910E-010.2290E-010.1470E-010.4946E-02
-0.5054E-02
0.4154E-010.4116E-010.3994E-010.3770E-010.3418E-010.2911E-010.2238E-010.1414E-010.5001E-02
-0.3790E-02
0.4337E-010.4287E-010.4129E-010.3853E-010.3443E-010.2889E-010.2195E-010.1393E-010.5486E-02
-0.2248E-02
0.4440E-010.4380E-010.4199E-010.3890E-010.3446E-010.2869E-010.2175E-010.1405E-010.6299E-02
-0.5160E-03
0.4490E-010.4426E-010.4232E-010.3905E-010.3444E-010.2859E-010.2174E-010.1436E-010.7213E-020.1240E-02
0.4505E-010.4439E-010.4241E-010.3909E-010.3443E-010.2857E-010.2177E-010.1456E-010.7771E-020.2513E-02
0.1560E-020.1509E-020.1362E-020.1131E-020.8397E-030.5171E-030.1993E-03
-0.7182E-04 -0.2466E-03 -0.2591E-03
0.3577E-020.3476E-020.3182E-020.2723E-020.2140E-020.1493E-020.8479E-030.2839E-03
-0.1134E-03 -0.2466E-03
0.5943E-020.5793E-020.5357E-020.4672E-020.3802E-020.2827E-020.1845E-020.9600E-030.2839E-03
-0.7182E-04
0.8513E-020.8316E-020.7742E-020.6842E-020.5692E-020.4395E-020.3070E-020.1845E-020.8479E-030.1993E-03
0.1111E-010.1087E-010.1017E-010.9070E-020.7657E-020.6053E-020.4395E-020.2827E-020.1493E-020.5171E-03
0.1356E-010.1328E-010.1247E-010.1119E-010.9540E-020.7657E-020.5692E-020.3802E-020.2140E-020.8397E-03
0.1568E-010.1537E-010.1447E-010.1304E-010.1119E-010.9070E-020.6842E-020.4672E-020.2723E-020.1131E-02
0.1732E-010.1699E-010.1601E-010.1447E-010.1247E-010.1017E-010.7742E-020.5357E-020.3182E-020.1362E-02
0.1836E-010.1801E-010.1699E-010.1537E-010.1328E-010.1087E-010.8316E-020.5794E-020.3476E-020.1509E-02
0.1871E-010.1836E-010.1732E-010.1568E-010.1356E-010.1111E-010.8513E-020.5944E-020.3577E-020.1560E-02
^^^^^^^^^^
A
large deflection(0.1871E-01)without
transverse load.
Note
that the sign has reversed wrt Ex #2.
Also
note that the U at the center has remained same (0.4505E-01)
in
both Ex #2 and Ex #3
Apte
28/1/2001