3.11. Complex Transient Analysis

Problem Description

A complex transient analysis is performed for a rectangular top plate fixed at two ends with a hole in the center. A voltage is applied to the bottom surface of the top plate for a specified time and the voltage is then set to a release value. The top plate does not make contact with the bottom plate. SOLID185 elements model the top plate. TRANS126 transducer elements are created between the plates. FLUID136 elements model the thin film surface and a FLUID138 element models the hole region. The applied voltage is shown in Figure 3.8: Applied Voltage. Displacement and pressure results at the bottom of the top plate on the circumference of the hole are shown in Figure 3.9: Displacement Time History and Figure 3.10: Pressure Time History.

Results

Figure 3.8: Applied Voltage

Applied Voltage

Figure 3.9: Displacement Time History

Displacement Time History

Figure 3.10: Pressure Time History

Pressure Time History

Command Listing

The input file for this example is shown below.

/batch,list
/title, Complex Transient Analysis
!/nerr,,,-1

/PREP7
/title, Complex Transient Analysis
/com    uMKS units

ET, 1,136,1                       ! 4-node option, High Knudsen Number
keyop,1,3,2                       !implicit
keyop,1,4,0                       !compressible
keyop,1,5,2                       !fluid gap option
keyop,1,6,1                       !mech  gap option
et,2,185
ET,3,185                          ! Structural element

s_l=100                           ! Half Plate length (um)
s_w=20                            ! Plate width
s_t=1                             ! Plate thickness
d_el=2                            ! Gap
pamb=.1                           ! ambient pressure (MPa)
visc=18.3e-12                     ! viscosity kg/(um)(s)
pref=.1                           ! Reference pressure (MPa)
mfp=64e-3                         ! mean free path (um)
Knud=mfp/d_el                     ! Knudsen number
mingapf=1e-2                      ! Minimum gap for real constanst on element 136
mech_mingapf=1e-2                 ! Mechanical minumum gap for real constant on element 136
app_volt=23.281                   ! Applied voltage
app_pres=0                        ! Applied pressure at boundaries

mp,visc,1,visc                    ! Dynamic viscosity gap
mp,ex,3,79e+3                     ! Gold
mp,dens,3,19300e-18
mp,nuxy,3,.1

r,1,d_el,,,pamb                   ! Real constants - gap
rmore,pref,mfp,0,0,1,mech_mingapf
rmore,mingapf,1.e+18,0.e-2,-4.e+0,-0.e-2,1.e-0
!     mingapf,penpar,deadpres,deadspr,deaddam,deadeps

!top plate
block,-s_l,s_l,-s_w,s_w,0,s_t     !INSTALL TOP PLATE
lsel,s,line,,4,5,1                !Set element depth
lsel,a,line,,2,7,5 
lesize,all,,,19,-.1 
lsel,s,line,,1,8,7 
lsel,a,line,,3,6,3 
lesize,all,,,11,-.1
lsel,s,line,,9,12,1
lesize,all,,,2
type,3                            !Mesh top plate with Gold material
mat,3
real,3
!mshape,1,3d
mshape,1,3d
cyl4,0,0,s_w/50,,,,s_t+1          !Create a hole in top plate 
vsbv,1,2
numcmp,volu
vmesh,1

!hole
n,10000,0,0,0                     !Specify nodes for hole element (138)
n,10001,0,0,s_t
et,6,138,1,,0                     !Define hole shape
r,10,s_w/200,,,pamb,              !Define hole diameter and pressures
rmore,pref,mfp
type,6
real,10
mat,1
e,10000,10001
lsel,s,line,,13,16
nsll,s,1                          !Tie top plate hole edge to hole element.
nsel,a,node,,10000
cp,next,pres,all
d,10001,pres,0
allsel

!else emtgen computes INCORRECT areas 
nsel,s,loc,z,0
cm,trun,node
allsel
emtgen,'TRUN',,,'uz',-d_el,mingapf*d_el,1.e-18
!Create transducer elements 126 using emtgen
!apply gap information
!fluid
nsel,s,loc,z,0                   !Define Fluid region
esln,s
TYPE, 1
MAT, 1
real,1
esurf                            !Surface the solid top plate with 136 squeeze film elements

nsel,s,loc,x,-s_l
nsel,a,loc,x,s_l
nsel,a,loc,y,-s_w
nsel,a,loc,y,s_w
nsel,r,loc,z,-1e-9,1e-9
d,all,pres                       !Fix pressure at outer plate boundary
nsel,all

nsel,s,loc,x,-s_l
nsel,a,loc,x,s_l
d,all,ux
d,all,uy
d,all,uz
allsel

nsel,s,loc,z,s_t                 !Apply pressure at boundary
sf,all,pres,app_pres
allsel

!fix bottom node voltage/disp
nsel,s,loc,z,-d_el               !Set voltage/displacement at bottom plate
d,all,ux                         !V(bottom)=0V
d,all,uy                         !displacement(bottom)=(0,0,0)
d,all,uz
d,all,volt
allsel

!fix top node voltage
cmsel,s,trun                     !Set voltage on top side to applied voltage value
d,all,volt,app_volt              !for pulldown
allsel

fini

/solu
antype,trans                     !Pulldown stage
kbc,1
time,11.e-5
!autots,on                       !enforce regular timesteps
deltim,1.e-5,
nsubst,10,1000,2
outres,all,none
outres,nsol,2
outres,rsol,2
outres,esol,2
cnvtol,pres,,5.e-6 
cnvtol,u   ,,5.e-6 
nropt,full
neqit,500
save
solve
time,20e-5
nropt,full                       !Reduce number of equilibrium iterations to save time.
neqit,100
outres,all,none
outres,nsol,2
outres,rsol,2
outres,esol,2
cnvtol,pres,,5.e-6 
cnvtol,u   ,,5.e-6 
solve
cmsel,s,trun                     !Setup release time
d,all,volt,1.5                   !Set release voltage across
allsel
time,20.4e-5                     !only limited time here
outres,all,none
outres,nsol,20                   !Long grinding period here, reduce result steps so we don't go
outres,rsol,20                   !over 1000 results.
outres,esol,20
cnvtol,pres,,5.e-6 
cnvtol,u   ,,5.e-6 
cnvtol,pres,,1.e-4 
cnvtol,u   ,,1.e-4 
autots,on                        !Let Autotimestep run here
deltim,.005e-5,0.001e-5,1e-5     !to better capture the overshoot movement on release
solve
time,30e-5                       !After initial snapback, 
autots,on                        !increase timestep as overshoot decays.
deltim,.5e-5,0.02e-5,1e-5
solve
fini

/POST1  
allsel 
GG=node(0,-0.4,0)
SET,LIST,999
SET,,, ,,, ,30  
!*  
!*  
PLESOL, NMISC,13, 0,1.0 
presol,nmisc,13 
/out,
fini
!*list,closes,lis1
!*list,closes,lis2
/post26
NUMVAR,200  
SOLU,191,NCMIT  
STORE,MERGE 
FILLDATA,191,,,,1,1 
REALVAR,191,191 
NSOL,2,GG,U,Z,UZ_2
NSOL,3,GG,PRES,,PRES_3
NSOL,4,GG,VOLT,,VOLT_4
plvar,2
plvar,3
plvar,4

fini