Ansys Contact
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Penalty vs. Lagrange
ANSYS contact- Penalty vs. Lagrange- How to make it converge
Erke Wang
CAD-FEM Gm!. Germany
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Penalty vs. Lagrange
Variety of algorithmsVariety of algorithms
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Penalty vs. Lagrange
Pena"ty mean# t$at any %io"ation o& t$e contact con'ition (i"" e p)ni#$e' yincrea#in* t$e tota" %irt)a" (or+
Pre !enalty metho"
( ) ( )[ ]dA g g T T T T N N N N ∫ Γ +++ gg δ ε λ δ ε λ A)*mente' a*ran*e met$o'
dA g g dV T T T N N N V
T
∫ ∫ Γ ++=Ψ )( gg δ ε δ ε δε σ δ
$e e/)ation can a"#o e (ritten in FE &orm
F uGG K T =+ )( ε
$i# i# t$e e/)ation )#e' in FEA &or t$e p)re pena"ty met$o' ($ere i# t$e contact
#ti&&ne##
ε
N ε
#
T ε N g
T g
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Penalty vs. Lagrange
Pre !enalty metho"
$e contact #prin* (i"" 'e&"ect an amo)nt ∆,
#)c$ t$at e/)i"iri)m i# #ati#&ie'
F uGG K T =+ )( ε
Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintain
e/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.
F =∆ε
$ere i# no o%ercon#trainin* pro"em
Iterati%e #o"%er# are app"ica"e 3 "ar*e mo'e"# are 'oa"e
$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.
GG K K T ε +=
−
$ere i# no a''itiona" D6F. F uGG K T =+ )( ε
N
N ε
#
T ε N g
T g
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Penalty vs. Lagrange
Pre !enalty metho"
Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintaine/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.
$ifference in d:
0.281e-3/ 0.284e-7
=1e4
$ifference in stress:
(3525-3501)/ 3525
=0.7%
#%N&'
PENE
Stress
#%N&'e(
PENE
Stress
∆ i# t$e 7e#)"t &rom F8N an' t$e e/)i"iri)m ana"y#i#. Pre##)re1 ∆ 9 1: Stre## ε
;00-time# Di&&erence in F8N "ea'# to ;00-time# Di&&erence in ∆
)t "ea'# to on"y ao)t ;< Di&&erence in Contact pre##)re an' t$e re"ate' #tre##.
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Penalty vs. Lagrange
Pre !enalty metho"
Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintain
e/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.
)i!*
As long as the !enetration "oes not lea"s to the change of the contact
region+
)he !enetration will not inflence the contact !ressre an" Stress
n"erneath the contact element
,ation*
#or !re-tension !rolem+ se large #%N'+ /ecase the small !enetration
will strongly inflence the !re-tension force.
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Penalty vs. Lagrange
Pre !enalty metho"
$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.
Iteration n
#
Iteration n+1
#
F,ontact
#
Iteration n+2
I& t$e contact #ti&&ne## i# too "ar*e, it (i"" ca)#e con%er*ence 'i&&ic)"tie#.
$e mo'e" can o#ci""ate, (it$ contactin* #)r&ace# o)ncin* o&& o& eac$ ot$er.
#%N&'
#%N&0.0'
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Penalty vs. Lagrange
Pre !enalty metho"
$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.
$i# pro"em i# a"mo#t #o"%e' #ince =.;, (it$
a)tomatic contact #ti&&ne## a'>)#tment.
8EY6P;012
%EY1P)2'03&0 %EY1P)2'03&4
405
iterations
6(
iterations
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Penalty vs. Lagrange
Pre !enalty metho"
$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.
For en'in* 'ominant pro"em, yo) #$o)"' #ti"" )#e
t$e 0.0; &or t$e #tartin* F8N an' comine (it$
8EY6P;012
#%N&0.0'+ %EY2'03&0
#%N&'* %EY2'03&0 $ivergence
#%N&0.0'+ %EY2'03&4
407 iterations (7 iterations
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Penalty vs. Lagrange
Pre !enalty metho"
$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.
)i!*
Always se %EY1P)2'03&4#or en"ing !rolem se #%N&0.0' an" %EY1P)2'03&4
#or lky !rolem se #%N&' an" %EY1P)2'03&4
,ation*
#or !re-tension !rolem+ se large #%N'. /ecase the small !enetration
will strongly inflence the !re-tension force.
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Penalty vs. Lagrange
Pre !enalty metho"
$ere i# no a''itiona" D6F.
$ere i# no o%ercon#trainin* pro"em
Iterati%e #o"%er# are app"ica"e 3 "ar*e mo'e"# are 'oa"e
)i!*
Always se Penalty if*
? Symmetric contact or self-contact is se".
? 8lti!le !arts share the same contact 9one
? 7$ large mo"el2 700.000 $1#s3+ se P,: solver.
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Penalty vs. Lagrange
? Any %io"ation o& t$e contact con'ition (i"" e &)rni#$e' (it$ a a*ran*e m)"tip"ier.
Pre Lagrange mlti!liers metho"
dA g dV T N N V
T
∫ ∫ Γ ++=Ψ )( gλ Tδ δ λ δε σ δ
Contact con#traint con'ition
0
0
0
=
≤
≥
N N
N
N
g
g
λ
λ
En#)re no penetration
En#)re compre##i%e contact &orce@pre##)re
No contact , *ap i# non ero
Contact , contact &orce i# non ero0= N λ
0= N g
0
=0 g
F
λ
u
G
G K T
$e e/)ation i# "inear, in ca#e o& "inear e"a#tic an' No'e-to-No'e contact. 6t$er(i#e,
t$e e/)ation i# non"inear an' an iterati%e met$o' i# )#e' to #o"%e t$e e/)ation. B#)a""yt$e Ne(ton-Met$o' i# )#e'.
For "inear e"a#tic pro"em#
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
0
=0 g
F
λ
u
G
G K T
a*ran*e m)"tip"ier# are a''itiona" D6F# t$e FE mo'e" i# *ettin* "ar*e.
NG
ero main 'ia*ona"# in #y#tem matri5No iterati%e #o"%er i# app"ica"e.
For #ymmetric contact or a''itiona" CP@CE, an' o)n'ary con'ition#, t$e e/)ation
#y#tem mi*$t e o%er-con#traine'
Sen#iti%e to c$atterin* o& t$e %ariation o& contact #tat)#
No nee' to 'e&ine contact #ti&&ne##
Acc)racy - con#traint i# #ati#&ie' e5act"y, t$ere are no matri5 con'itionin* pro"em#
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
a*ran*e m)"tip"ier# are a''itiona" D6F# t$e FE mo'e" i# *ettin* "ar*e.
)i!*
Always se Lagrange mlti!lier metho" if*? )he mo"el is 4$.
? 7$ nonlinear material !rolem with ; '00.000 $ofs
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
)i!*
<f the Lagrange mlti!lier metho" is se"*
? Always se asymmetric contact.
? $o not se ,P=,E in on contact srfaces
? $o not "efine the mlti!le contacts+ which share the common
interfaces.
For #ymmetric contact or a''itiona" CP@CE, an' o)n'ary con'ition#, t$e e/)ation#y#tem i# o%er-con#traine'
Contact pair-;
Contact pair-;
Sin*"e contact pair
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
Penalty symmetric
Penetration
<terations* '>(
,P?* '00
Pressre
Lagrange symmetric
Penetration
<terations* @4
,P?* 50
Pressre
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
)i!*
?se Penalty is chattering occrs or
,hattering ,ontrol Parameters*
#)1LN an" )N1P
Sen#iti%e to c$atterin* o& t$e %ariation o& contact #tat)#
'&4-$elta
' 4#
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
Penalty
#%N&'
$EL)&0.'
=!re!>
et+'+'67
et+4+'B@
et+7+'>4++(++4
m!+eC+'+4e5
!cir+'@0+400-$EL)+-@0+@0
w!of+0+-"elt!cir+400+4'0+-@0+@0
w!of+0+"elt
esi9+5
Esha+4
ames+all
lsel+s+++'
nsll+s+'
eal+4
ty!e+7
esrf
lsel+s+++>
nsll+s+'
ty!e+4Esrf
=sol
Nsel+s+loc+C+0
$+all+C
lsel+s+++5
nsll+s+'
"+all+all
lsel+s+++7
nsll+s+'Dget+nn+no"e++cont
f+all+fy+400=nn
alls
Solv
?se Penalty is chattering occrs
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
Sy Pene
Pre Lagrange
<ter&'7
Sy Pene
Pre Penalty2#%N&'3
<ter&6
Pre Penalty2#%N&'e(3
<ter&7@
Sy Pene
No nee' to 'e&ine contact #ti&&ne##
Acc)racy - con#traint i# #ati#&ie' e5act"y, t$ere are no matri5 con'itionin* pro"em#
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
Sy Pene
Pre Lagrange
<ter&'7
Sy Pene
Pre Penalty2#%N&'e(3
<ter&7@
Sy Pene
Agmente" Lagrange
#%N&'+ )1L&-7e->
<ter&'74>
No nee' to 'e&ine contact #ti&&ne##
Acc)racy - con#traint i# #ati#&ie' e5act"y, t$ere are no matri5 con'itionin* pro"em#
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
eCam!le-'eCam!le-'Element* Plane'67Element* Plane'67
8aterial* Neo-Hookean8aterial* Neo-Hookean
,ontact*,ontact* Pre LagrangePre Lagrange
Loa"* $is!lacementLoa"* $is!lacement
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
=!re!> =!re!>
et+'+'67et+'+'67
et+4+'B@et+4+'B@
et+7+'>4++7++4et+7+'>4++7++4
t+hy!er+'+++neot+hy!er+'+++neo
t"ata+'+.7+0.00't"ata+'+.7+0.00'
m!+eC+4+4e5m!+eC+4+4e5
m!+"ens+4+>.6e-@m!+"ens+4+>.6e-@
r+4++++++5r+4++++++5r+7++++++5r+7++++++5
!cir+4+5!cir+4+5
agen+5+'+'++44agen+5+'+'++44
agen+4+'+'++''+-70agen+4+'+'++''+-70
agen+(+B+B++44agen+(+B+B++44
rect+-B+-5+-60+0rect+-B+-5+-60+0
rect+5+B+-70+0rect+5+B+-70+0
agen+@+''+''++''agen+@+''+''++''
!cir+5+B+0+'60!cir+5+B+0+'60
agen+5+40+40++44agen+5+40+40++44
w!of+''+-70w!of+''+-70
!cir+5+B+'60+7B0!cir+5+B+'60+7B0
agen+(+45+45++44agen+(+45+45++44
w!cs+-'w!cs+-'rect+-'B+-B+-'00+-60rect+-'B+-B+-'00+-60
rect+-B+-5+-'00+-60rect+-B+-5+-'00+-60
rect+-5+5+-'00+-60rect+-5+5+-'00+-60
asel+s+++'0+7'+'+'asel+s+++'0+7'+'+'
nmm+k!nmm+k!
esha+4esha+4
esi9+4esi9+4
ames+'+46ames+'+46eshaesha
allsalls
mat+4mat+4
ames+allames+all
lsel+s+++>(+'0B+6lsel+s+++>(+'0B+6
lsel+a+++60+''4+6lsel+a+++60+''4+6
lsel+a+++''5+'7'+(lsel+a+++''5+'7'+(
lsel+a+++'77+'(5+(lsel+a+++'77+'(5+(
nsll+s+'nsll+s+'
ty!e+4ty!e+4
real+4real+4
mat+7mat+7
esrf esrf
lsel+s+++'+(lsel+s+++'+(
lsel+a+++@+'4lsel+a+++@+'4
lsel+a+++'>+40lsel+a+++'>+40
lsel+a+++45+46lsel+a+++45+46
lsel+a+++77+7Blsel+a+++77+7B
cm+l'+linecm+l'+line
nsll+s+'nsll+s+'
ty!e+7ty!e+7
esrf esrf lsel+s+++>B+'06+6lsel+s+++>B+'06+6
lsel+a+++>6+'04+6lsel+a+++>6+'04+6
lsel+a+++''7+'4@+(lsel+a+++''7+'4@+(
lsel+a+++'75+'(>+(lsel+a+++'75+'(>+(
nsll+s+'nsll+s+'
ty!e+4ty!e+4
real+7real+7
esrf esrf
lsel+s+++('+((lsel+s+++('+((
lsel+a+++(@+54lsel+a+++(@+54
lsel+a+++5>+B0lsel+a+++5>+B0
lsel+a+++B5+B6lsel+a+++B5+B6
cm+l4+linecm+l4+line
nsll+s+'nsll+s+'
ty!e+7ty!e+7esrf esrf
=sol =sol
nlgeo+onnlgeo+on
acel++@6'0acel++@6'0
asel+s+++'+@+'+'asel+s+++'+@+'+'
cmsel++l'cmsel++l'
cmsel++l4cmsel++l4
nsll+s+'nsll+s+'
"+all+all"+all+all
asel+s+++4@+7'+'asel+s+++4@+7'+'nsla+s+'nsla+s+'
"+all+C"+all+C
ns+5+'5+'ns+5+'5+'
lsel+s+++'0@+++'lsel+s+++'0@+++'
"+all+C"+all+C
"+all+y+0"+all+y+0
allsalls
cnvt+f++.0'cnvt+f++.0'ns+'00+'0000+'ns+'00+'0000+'
solvsolv
lsel+s+++'0@+++'lsel+s+++'0@+++'
"+all+y+-50"+all+y+-50
ns+'00+'0000+'ns+'00+'0000+'
otres+all+allotres+all+all
allsallssolvsolv
)i!*)i!*
#or large sli"ing#or large sli"ing
!rolem+!rolem+
?se Lagrange metho"+?se Lagrange metho"+
the convergencethe convergenceehavior is very goo"ehavior is very goo"
an" stalean" stale
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
Lagrange*Lagrange*
''0 <terations''0 <terations
,P?*,P?*
'( Sec.'( Sec.
Penalty*Penalty*
4'6 <terations4'6 <terations
,P?*,P?*
4( Sec.4( Sec.
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
/en"ing stress/en"ing stress
,ontact !enetration,ontact !enetration
/en"ing eCam!le/en"ing eCam!le Lagrange*
'0 <terations
4 Sec.
Penalty %ey2'03&'*5( <terations
'4 Sec.
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Penalty vs. Lagrange
Pre Lagrange mlti!liers metho"
=!re!>
et+'+'67+++'et+4+'67+++'+++'
et+7+'B@
et+(+'>4++(++4
m!+eC+'+4e5
t+hy!er+4+'+4+moon
t"ata+'+'+.4+4e-7
8!+m+4+0.7
rect+'+5+0+7
rect+4+5+'.5+(
asa+'+4
rect+4.'+5+4.5+7.5
w!of+7+4
!cir+.50'
esi9+.7
ames+'+7+4
esi9+.'
ty!e+4mat+4
ames+4
lsel+s+++4
nsll+s+'ty!e+7
real+7
esrf
lsel+s+++6+'4+(
nsll+s+'
ty!e+(
esrf
lsel+s+++5
nsll+s+'ty!e+7
real+(
esrf
lsel+s+++'7+'(+'
nsll+s+'
ty!e+(
esrf
=sol
nlgeo+on
solcon++++'e-4
nsel+s+loc+y+0
"+all+y
nsel+s+loc+y+7.5
sf+all+!res+4
alls
ns+'0+'00+'
solv
er eCam!leer eCam!le
Element* Plane'67Element* Plane'67
8aterial* 8ooney8aterial* 8ooney
,ontact*,ontact* Pre Lagrange#rictionPre Lagrange#riction
Loa"* PressreLoa"* Pressre
Lagrange*
74 <terations
'7 Sec.
Penalty %ey2'03&4*
B7 <terations40 Sec.
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Penalty vs. Lagrange
Let s talk aot convergence
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Penalty vs. Lagrange
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
? #E 8o"el is not mo"ele" correctly in a !hysical sense
; I& yo) )#e a point "oa' to 'o a p"a#tic ana"y#i#, yo) (i"" ne%er *et t$e con%er*e' #o")tion.
eca)#e o& t$e #in*)"arity at t$e no'e, on ($ic$ t$e concentrate' &orce i# app"ie', t$e
#tre## i# in&inite. $e "oca" #in*)"arity can 'e#troy t$e ($o"e #y#tem con%er*ence
e$a%ior. $e #ame t$in* $o"'# &or t$e contact ana"y#i#. I& yo) #imp"i&y t$e *eometry or)#e a too coar#e me#$ (it$ t$e con#e/)ence t$at t$e contact re*ion i# >)#t a point contact
in#tea' o& an area contact yo) mo#t "i+e"y (i"" en' )p (it$ #ome pro"em# in
con%er*ence.point "oa'
ε
σ
p"a#tic ana"y#i# contact ana"y#i#
Geometry Me#$
Sggestion
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Penalty vs. Lagrange
Sggestion
%EY1P)253&'
%EY1P)253&0
? #E 8o"el is not mo"ele" correctly in a nmerical sense
2 A po##i"e ri*i' o'y motion i# /)ite o&ten t$e rea#on ($ic$ ca)#e# 'i%er*ence in a
contact ana"y#i#. $i# co)"' e t$e re#)"t o& t$e &o""o(in* e a"(ay# e"ie%e, t$at i& (e
mo'e" t$e *ap #ie a# ero &rom *eometry, it #$o)"' a"#o e ero in t$e FE mo'e". )t ')e
to t$e mat$ematica" appro5imation an' 'i#cretiation, it 'oe# not $a%e nece##ari"y to e
ero anymore. E5act"y, t$i# can +i"" t$e con%er*ence. I& po##i"e, )#e 8EY6P to c"o#et$e *ap. Yo) can a"#o )#e 8EY6PH1; to i*nore ;< penetration, i& it i# mo'e"e'.
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
,ation*? <f the ga! !hysically eCists+ yo shol" not se %EY1P253&' to close it+instea"+ yo
shol" se" the weak s!ring metho". $EL)&0.'
=!re!>
et+'+'67
et+4+'B@
et+7+'>4
m!+eC+'+4e5
!cir+'+4-$EL)+-@0+@0
!cir+4+7+-@0+@0
rect+0+'+->+-4.5
aa""+4+7
esi9+.7
ames+all
Ps!rng+(6+tran+'+0+0.5
lsel+s+++'
nsll+s+'
eal+4
ty!e+7
esrf
lsel+s+++>
nsll+s+'ty!e+4
Esrf
+4++++++-'
=sol
Nsel+s+loc+C+0
$+all+Cnsel+s+loc+y+->
"+all+all
Alls
#+(4+fy+0.''
Solv
#+(4+fy+4000
Solv#"el+all+all
#+(6+fy+-.''
Solv
#+(6+fy+-7000
solv
81;, DE10.;
F189B
o c"o#e t$e *ap
F;1;90.;0.;10.;;
LS'* #'&0.''
LS4* #'&7000
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Penalty vs. Lagrange
Sggestion
? N)merica""y a" con"itione" #E 8o"el
4 ANSYS )#e# t$e pena"ty met$o' a# a a#i# to #o"%e t$e contact pro"em an' t$e
con%er*ence e$a%ior "ar*e"y 'epen'# on t$e pena"ty #ti&&ne## it#e"&. A #emi-'e&a)"t
%a")e
&or t$e pena"ty #ti&&ne## i# )#e', ($ic$ )#)a""y (or+# &ine &or a )"+y mo'e", )t mi*$t not e
#)ita"e &or a en'in* 'ominate' pro"em or a #"i'in* pro"em. A #i*n &or a' con'itionin*i# t$at t$e con%er*ence c)r%e r)n# para""e" to t$e t$e con%er*ence norm. C$oo#in* a #ma""er
%a")e &or F8N a"(ay# ma+e# t$e pro"em ea#ier to con%er*e. I& t$e ana"y#i# i# not
con%er*in*, eca)#e o& t$e too m)c$ penetration, t)rn o&& t$e a*ran*e m)"tip"ier.
$e re#)"t i# )#)a""y not a# a' a# yo) (o)"' e"ie%e.
#%N&' #%N&0.0'
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
#%N&0.0'+ %EY2'03&0
#%N&'* %EY2'03&0 $ivergence
#%N&0.0'+ %EY2'03&'
#%N&'* %EY2'03&'
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Penalty vs. Lagrange
Sggestion
? )a'# in#tea' o& tria'# Error in e"ement &orm)"ation or e"ement i# t)rne' in#i'e o)t
J I& #ome e"ement# are "oca""y 'i#torte' yo) mi*$t *et an error in t$e e"ement &orm)"ation or
t$e e"ement i# e%en t)rne' in#i'e o)t. ry to )#e a coar#er me#$ in t$i# re*ion to a%oi'
t$o#e pro"em#. Yo) can a"#o )#e NCNK,0 to contin)e t$e ana"y#i# an' i*nore t$o#e "oca"
pro"em# i& t$ey 'o not e&&ect t$e *"oa" e/)i"iri)m. In *enera", try to )#e trian*)"ar,
tetra$e'ra" or $e5a$e'ra" e"ement# "inear. Do not )#e /)a'ratic $e5a$e'ra" e"ement#.
inear /)a'# Mi'-#i'e tria'#
Error in e"ement &orm)"ation
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
? $e part# $a%e no )ni/)e minim)m potentia" ener*y po#ition.
L I& t$e ma5. D6F increment i# not *ettin* #ma""er an' t$e &orce con%er*ence norm +eep#
a"mo#t con#tant, proa"y #ome part# in t$e mo'e" are o#ci""atin*. !ere, intro')cin* a #ma""
&riction coe&&icient i# )#)a""y etter t$an )#in* a (ea+ #prin*, not +no(in* e5act"y ($ere to
p"ace it. Friction can e app"ie' to a"" contact e"ement# try MB10.0; or 0.;
8?&0.'8?&0
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
)arget
)arget
,ontact
,ontact
Some time#, i& yo) 'e&ine t$e contact an' tar*et proper"y, t$e ana"y#i# con%er*ence#
m)c$ &a#ter, an' t$e re#)"t i# a"#o etter.
,ontact
)arget ,ontact
)arget
##
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Penalty vs. Lagrange
Sggestion
? Bnrea#ona"e 'e&ine' p"a#tic materia"
;; It i# not a"(ay# a *oo' i'ea to 'e&ine t$e tan*entia" #ti&&ne## to e ero )#in* a p"a#tic
materia" "a(. I& t$e yie"' #tre## i# reac$e' a"" o%er t$e ($o"e cro## #ection, t$ere i# no
materia" re#i#tance anymore to carry t$e "oa'. $ere (i"" e a p"a#tic $in*e an' #o t$e
#o")tion (i"" ne%er con%er*e. In t$i# ca#e, inp)t t$e correct tan*entia" #ti&&ne##.
P"a#tic #train Stre## #train c)r%e (it$
tan*entia" #"ope ero
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
? Bnrea#ona"e 'e&ine' p"a#tic materia"
P"a#tic #train
Stre## #train c)r%e (it$
tan*entia" #"ope ;0000
Stre## 'i#tri)tion
Contact re*ion
6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*
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Penalty vs. Lagrange
Sggestion
? $e &ine me#$ an' #imi"ar me#$ are a"(ay# *oo' &or t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.
:eometry:eometry S!here inflenceS!here inflence 8esh8esh
Normal stressNormal stress
,ontact Pressre,ontact Pressre
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Penalty vs. Lagrange
Sggestion
? $e &ine me#$ an' #imi"ar are a"(ay# *oo' t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.
:eometry:eometry
,ontact mesh,ontact mesh
,ontact region,ontact region
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Penalty vs. Lagrange
Sggestion
? $e &ine me#$ an' #imi"ar are a"(ay# *oo' t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.
Normal stressNormal stress
,ontact !ressre,ontact !ressre
Penalty vs Lagrange
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Penalty vs. Lagrange
How can < make the !rolem convergeF
? )rst yorself* <Gm ale to make it converge? ,onsi"er the !rolem as i"eali9e" real worl" !rolem*
40I- 8echanics eC!ertise+ 40I- Engineer eC!ertise
70I- #EA eC!ertise+ 70I- Software eC!ertise
? ?se the magic %EY1P)<1NS
%EY1P)253&'* )o eliminate the rigi" o"y motion
%EY1P)2@3&'* )o eliminate the geometric noise
%EY1P)2'03&4* )o make ANSYS think
Penalty vs Lagrange