object oriented programming for finite element analysis
DESCRIPTION
pTRANSCRIPT
-
"!#%$'&()* +&+,
)* .-/$(021435$(768+)*9:11 1)? !@)?%)?
AB$( CDE+&
FG
HIKJML%NPORQ2S2T%UWVJMQ2XNZY[ZL%LJ
\]_^`].abSIcORL%Oed Ggf UMhRhi[PjW[+kEl F hROiL
-
S2T[=s%OiQcQ[PId5JdOiUWLUMHIKJML%NPORQS2T%UWVJMQXNrY+[ZL%LJ OiQJ%%IcUW[rs
L%Oe[ZIcQqO|d
G
UM
f
JhROiUMIcL%ORJm\?[ZIW[Zhi[
G
HJMhihvZwMw
-
"!#%$'&()* +&+,
)* .-/$(021435$(768+)*9:11 1)? !@)?%)?
AB$( CDE+&
! "#$
&%
('&)
#*
-
6 1)**+(+B"/8,-1C%D,E),-
F6(
-
i uZbz5r.(hJr_5+KrbLJe5{(PJK_P_.J+PJbz
Pz
I
J_5*_ KTUcYJ M5(_ *_rz(K_5U_
-
KKbLJ
mPz5?z_ pzr LK z`J r5zzbJULJ
JvuZzzr.zbuPJoRYJKzz K e5_vK bpW VUuYJ
K
-
z_
(/"? G1,E)8
-
_
!"#
$&%('*) +
,.-/10 23)4 56 78 0 9 +4!
: ;
0
= fZ_LK K_bK_5
-
>=r
ZTUrz5{z5_ K5555555555555555555 ?KU
>=r
\
5c5 z555555555555555555555555 ?
>=r>= {_Pbzp:J bu5555555555555555555555 ?KT
>=rV? _f `Ub{55555555555555555555555
X
>=r
X
ji i%z{b55555555555555555555555
X
>=r 5rbzWd.Jrz z 5555555555555555555
X
?
>=r T _f g UhMb{b5555555555555555555555
X^X
>=r PP^f.liE[PEJEZ55 zb2555555555555555
X
V? ijur(_
b55 55555555555555555555555555 P
V?P_ _vuZTMrzz q555555555555555555555555555 P
V?P
i uPoMz__ K55555555555555555555555555
X
ijuPbz5:(LKu5VcXf
I
P{._P_
PYJU 55
X
X
_ i uP_5= g{LKfMObQf_LJ{bp5Kz25(_z5:5555 BU U
=>=r_
b__5LJ5zb{5555555555555555555 BUr
=>=r
5_
zbE5555555555555555555 BU
=>=r
r
z=r>= UM J_:b555555555555555555555555 BU^=
=>=rV? 5_5r.PzK 55555555555555555 BU
=>=r
X
5_5r.z?zW555555555555555555 BU5
=>=r 5_Z55b 5555555555555555555555 BU5
=V? JroRK_5zb
-
Z
?Z
ijuZ_b_'.rpr=r_
\
bJUz555555555555555555555555555 q
X
>=r
-
Pz
Z>= ijuPbz5:(LKu5Vce=r_ PJ RKz5
Kb_5YJ5Kz2zg555555555 BT5
Z>=r
i uP_5:UM J5_Ez55555555555555 BT5
Z>=r
i uP_5:5z
_z5rb:5555555555 BT5
Z>=r>= `J K b5555555555555555555555 r
ZV? i%KoUKz5Kr ijs{K.P(z5`J
K_5
be5bry5555555555555555555555
ZV?P_
\
bJUz555555555555555555555555555
ZV?P
-
P_z
_
\
b| r "5 ) J6)#5
z
-
u
_
LUJ Q Je5?Jr(K{
QO49 - 9$&9% 0 =r
LUJ Q Je5
0
%(
"5%A)
K ! " #$%' ')+*!,-*.0/'J T ?
>=
LUJ Q J%e51
2EB
032
% *\*
0
"5%A)
b ! " #$%' ')+*!,-*.0/
PJ+55555555555555555555555555555555 T
X
=_ 5z___
I
KUM J5z%K55555555555555555 ^U
=
K e59i uZzzr_55b__52KvK50c 255 5
=
K e59g LK5_255b__52KvK50c5555 BUr
=>=
\
b|e5
%(B9M94
0
5*Q.78%A
0
b555555555555 BU
=V?
LUJ Q Je5
%(B9M9
0
5*Q.78%A
0
zb/0' * * -'PJ BU
=
X
\
b|e5
Q. 7%A
0
%(B9M94
0
K555555555555 BU
=
\
b|e5
9% *\
%(B94B
0
K5555555555555 BU^=
= T
\
b|e5
"' 5 7%A
0
z55555555555555555 BU ?
=
VULJ Q Je5 ZzLJ+:rJ
16' 578%A
0
b555 BU
=_
-
u=_
LUJ Q Je5Z_YJ PJe5.
Q. 7%A 0 Q. - 7 ,.0 %A) I
[
-
ur
Z
I
% !4 K$ 4 \B
\G' K
z5555555555555
*
\
b| r %
-
uZz
*
X
_
I
Ku__5M(i uK_ 55555555555555555
X
=
X
I
bz(bz5KMK_i ur(z55555555555555555
X
=
X
d.KVJK i%Pz=
be5bK
-
uZ_z
.
-
uZ_
*
\
KuNUoJ_TcKc.be5zWzWqNUr5KJ5rNU
z5
\
KuNUTJ_zocc
beb5u5b?5oe5%_%_J(`UTJK
-
I
AR_((Jz{U(_bZYJUrhUbYJ_Er5zbzZbz
e5UZzr*rquZzK.bbPb:K
-
K
-
:< !#%$'&%)* +&
fMObQ 5bz YJ 5((z:e5(?xM_'e+5 b5Kb' 2b 0Q
KK1J5z5(_JU5rbzYUrb__.*5Ur5_JK`Mb
5Kz_|(J 5czrbPb J5_5( fMObQ 5bz YJ R2_vQ
ecc5Kb_YUz K
-
Kz J_5YJNMObQ 5bz YJb55K(zbP4`M_b55(buzQ
JJ J_5J K_TJKvK4PJo=Kzp_ J Z_vuZ_b_=PJ
J aM`Mz zbJU:LK Jr_ y;ur_bz=5("Z5b_aJbz5LJ
bPb K
-
bjK
-
I
AJ_bbK_5:5TUJr9K
-
*
\
rz
-
!
%%$D%$(
UAMuNMPObQ 5bzYJXR_ z -Jr_5J_rz(K_53M
YJ_:z_KWUbq
-
.bpW5
X
I
K_PbJZrzMvuZ_zbKzpNMPObue5p
PJ%z z5`J`J MNUrJy5Jzyz ^R__(?(PJi
I
5oo`Mz Pz {5(z_u5@ep?vK NMrz:
0J5{i35^=urPTJ._ bYJ:Pzb5(
\
?KVcrPbK%?_Ur#Rz-K
-
! #"%$&(')*,+.-0/ $1(')* 243
5
6-0798! #":243
5
6-07;*=@? "
5
(2BADC3
E
3
"%' GFIHKJ(LDM +*.' N *O "5 ) J6)#5
$
ioKp "56 ) J*)56
NMOb
-
PlaneFrame
ModelBuilder
exactly one
many
Class 1 Class 2
Class Name
Domain
MP_Constraint SP_Constraint Node Element
Beam Truss
Analysis
creates
populates is analysed by
Element
BeamPtLoad
ElementalLoadNodalLoadNode
LoadCase
Load
ContinuumElement
KEY
Super class
more subclassesexist
Association:
Class:
Aggregation:Multiplicity of Association:
Inheritance(Generalization):
Assembly Class
Part 1 Class Part 2 Class
Subclass 1 Subclass 2
_NUb
ob 5e5__i%z {:rJ
K=zbb?YJ M Ez_3MK}b
I
b'*? P
Kz5bzrzNMPObQ 5bzYJ:5(_
5
/"0
2 ZI %
I
]c K
-
b K
-
$&(' * ('
(*7*
-
NMPOb.Pb oR
{PJ bZoJYJ'bbz5PJWZVJ_K
-
c59R_z Pz
-
J Kzz K
NP)4 78 0 B%A) %A5
NMPObu JJ _?z5`J 5TMUr_5
oJUi K=
? ')*
-
F6(
-
PTJr%(rJ NMZp_*5zLJPJ`p %UhMKUhMJr5bvQ
QebLJ5 K_u5KzLJWrKJ{KoU{KMr.b_ oe5uboRYJz(
yUbo(rJ'zbZoJYJ(zJzKK
-
"
(*
-
%A5
NMPOb.XM*`JJLJE
%(5 %AH
NMPOb5?`MPOb{eb54
%A5 %AH
NMOb JNMrzK5(NMPOb
I
'zb|'zb:r Q
PTJur //
PJWbK ' *- =27
#
7
"
-4 243
5
6-071=271- - + -. 277"
5
(243
5
6-07@? ')*Tr5bZoJ%(PJNMrpKzPJUhM
o_bZKYJ
156
NMPObJK__`Jc RYJz(}
// 0
(rJz._5NcKYJ}5
"5%A)# %A5
`MPObW K
-
5
6-4 =27
27
=27 " *
-
(
-
5 uKK
-
$&(')*G
$&(' *":243
$&(' *" *
"
(*
-
6 +)?9:11 AB)?111
I
,.0 %A)M[
-
, ,-1 (+ F !,E888
\
(5buhKu5VcEKKM=YJW hUp U'_ J % B4+
J
-
-
e5r %
-
YJz?r __cWUb JJ_5PeKVU%5 M'PTJrYJ(z?r
-
p
z
"!
#$%&'
$)(
)*
,+
-
%.
$
/$0
/
/
0
1
2
/$)3
$
1/4$
5
_*
$%
#
76(
'
0
"+98
3
7
)
%
:;7+?8@A
%&7B
CD)
"E2
_pF
%./
G'(
1H6KH0
%&'
$
% 0$
/"+M
%&
$
% 0$
/,E
R
/$04
>
&/*'0
/
/0
5
0
3/&
%.
E
$
%.
_1
$%>+ -
$0
/
O
p?
E 8HE
)
F
1
%
)
$
%&'
%&'#"
C
+%$
3/1
/$0
/
C
(
C
^
E,
C
"
C
0
p
C
&('
C
T
C
&('
C
T
C
K
"
C
+
)
/0
B
%
$
z
#
_
'
5
/
bp
%.
&
C
&('
C
&
C
K
#
8
"Y8
,
"
:
#
8
"Y8
%
C
:
#
(
8
&
C
)
+
#?
@
z
5
bp
%.
E
>
$0
/
0
5
&$
Q!
$)%.* *'0
/,E;/*0
/
)
+
(
+9-
*
(
_
$)$)(2/ 0
3/
0
E
+ +
%
;C
(
$
_
/M
C
&('
C
E
BA6CD
C
&('
C
*'0
;
r
0
3
p
%&
E
0
p3g
7I/76
/"E %&
)!
g
7I/"E
*'0
-
C
&('
C
0
(
5 6
(
98
K
"Y8
: ;
(
&
A6EXD
(
VXWY[V
=
:
0
(
;
(
+
,
5
(
V3WZY[V
:
AJEFD
(
VXWY[V
=
:
0
,
5 DGFBH 5
&
AJEFD
,
VXWY[V
=
K
D"M H 5
%
A6EXD
,
VXWY[V
P
A6EXD
,
VXWY[V
=
:
6
,
I8
K
"Y8
=
:
0
,
;
,
+
,
K R
,
+
3
K
,
5
,
VXWY[V
:
AJEFD
,
V3WZY[V
=
)
+
# (
;
,
M
DGF
S
M
&
N
P QTSJU
H
V3WZY[V
)
+
# )
R
,
M
D"M
S
M
%
N
P
QS6U
H
VXWZY[V
)
+
#
+
,
M
D"M
S
M
N
P
QTSJU
H
VXWY[V
)
+
# ,
-
3
$)0
+
3
+
,
M/
z
5
p
%.+ "K
7
))%
'
%&%.
%
7
$ +PE
#
>[>
(
+
-9
:%
$ /$
K
(
z
"E
/%.:4
$
'
%.
)!
/%.;N
%.
4
+*>
(
'
%.%.
%
,E
#
>[>
)
+*-
)
$
$
9I
$)(
$
%G
0
"E
.
J5
!
0
)
+
#
E
,-!#E/.10&&32/E5467 E98:;7"@2&
X
=32A + -
B,-!
{
$
.
!
$%&'
%.4$
Q
%
$)(
/
)
%.$ E
%./
/$)$J
%
5
%
'
$ 0
C# $
D'
%&%.
%
#
>[>
)
~
E5FGIHKJ L7"@2& /'WlE 9h
lnhsl]jD R (
Dtu=3>
-
Domain
Node Element
TimeStep LinearSystem
Pidaperti and Hudl
Archer
Miller and Rucki
Analysis
Map
Domain
ConstraintHandler ReorderHandler
MatrixHandler
EigenSolution
Wilson NewmarkJacobi Subspace
DirectIntegration
DynamicAnalysis
AlgorithmicAgent
Algorithm
AlgorithmManager
DOF
Partition
PartitionManager
Element
GeneralElement
Zimmermann and co-workers
"
0i
)
+
#
1B$ j
$
j
iSj% i5LN
)
i
j.
O i2$
Wj i
XiSj
j
3Yj$)0 jj$P(
i
i/$)%
Xh h/%.
0
$H
l
SiXj
'
+ Xh
)
B i
C
E:B j
XiSj l
03l$ j
,->7;- >
0
9
i
!
3/ l$ j
1j$$)J i
nj;
lNj; (j%
l;E$
4
]jYi/j;&/4$
Wj ijj;$)(
)
+N- h
l$ j
j i#-0U>
-
o 0'E
;
A j;
;
v260U+NOSh
Bi
C
j -
-
l/Xi
0
/
iQXh -7"];"1iWl
3
Sh% j;
.ShKjj$P(
4
;Nhj 3/ l/
@i5l/
SiXj
+:="0
Sh#9j$P(.%&7Xh& i
-
GaussElimination
GaussSeidel
ContainerAlgorithm
Newton Newmark
CentralDifference
Algorithm
Jacobi ConjugateGradient
"
0)i
)
+
(
1B$ j
$
j
iXj% iI82$
i
Sh%
l
WiSj iSlnh(
*
$)$Wi5j 6 0)l
C
#
>[>
,
WiSj;
/
E"Sh -0U2"
;
$$j
C
Sh
R
!" 2 ;!2
%.4
(MXh
ilQ3/@l i+B- h -0! 2" /@l5
$)$,Xh
Wi i% Xh
/$)0
/M Xh
(
%A: *'0j
E 0
j>$)%.='(=$%& i.$ "9(7$ " j
i j lnh"+ -9
i%&J3 Ui/%@Sh ,
D
/'Wl
Sh
C
j('Xh
j; /04QXh
/$0
/
j$
i
Xh%RE'+
+:XhQ
@iXj;i
9Xh
iXj;
/
lnh%.
E -0U2" v!2 "
j i
iJ3
"+ - h -0U2" v!2(jYl
j
j
@i%.
j i( Xh
-0! 2" j;RSh,
D
/Wl7
j
vl
j;R
Xh,+ Lj lnh -0! 2"
04
l$ j
$)$hjJ3 j;2$Wj
/-0Y 2" !&32
iJ3
i
+ - h
Wi j l
i Sh -0U2" v!2
03l$ j
2)
0
*'0Q Sh -0U2" l$ j
+
- h
hi Xl%
/
XhXh
)
jYiSlnh
Wl70iE
i$ j
1j HEvj i ShQ /$$)J
;j
- h h
WiSj iSlnh(
i
> i Xh -0! 2" E9h
lnh
B
hJ5
!
0i
)
+
(
E
%
-
!
(RSh iWi
9h
lnh1Xh,
D
Wl7
j i $
%
j ,E
+ +1j '0% @i
lnh%.+.- h
Q)
i/*0
i ki0l Xh j%./0 # i
C1
]j lnh
# $, !
, %
9h
Wi i%
j
i@l
/$)3RSh $
]j i
(
% *'0j;
/
+
l
1B/
XiSj
l]j1$)(> iSl 0
Xh XiSj
i%pj;
/ %.Sh4,+ - h
)
WlWj0
/$P3/Wi
i
C
Sh>Sh .10U&&32i ,
D
/Wl7
i@l$)(/+I- h
'Si0l7
,/*'0j;
/
jpl4pl
'
EXhj;:j
j$)( i E XhPjj$)(
% 0
Xh@i9i
Ui%
lWiSj;XlnhiKl
(
; l&Ui/% XhWi l$ j
jh
Xh7( i
C
ShWi+
-
Q W 9
Y# * 9 /
- jYl
$
Xj; l4(i7=0
(j
i 3
& i j>
9h
lnh
%&i.67[>
0
+
- h7(j$
i%&J3/Ui/% Sh4676jr.10U&&32 l$ j
'Wi j l
%.Xh4
i i%
nj
j(i
0j$K3/@li
EXhj Nj i20
i% Xh
(
%
-
N *'0j;
/
+
l
- h
0!l$ j
D
. .10&&32/j ,
D
Aj i/i
/
$ ihj4
$
Shl/
XiXj
+ - h
)
i%.J3/
Ui% Xh6i
& ShR/Wl7
.
Xh
jj$)(
)
j
i
j
Xh > ]j$"
XhMXhKl/
XiXj
+
)
+ +@32v2
- h +@32 )2BWl7
)
i
$ i
!
Xhl'Si
0
/
5Xh
D
. .10Uvmv!2
j ,
D
-
LinearNewtonRaphsonLagrangeCH PenaltyCHTransformationCH
ConstraintHandler
RCMMinDegree
CentralDiff Newmark Houbolt
AnalysisModel
ElementFE_Element
LagrangeFE PenaltyFETransformationFELagrangeDOFTransformationDOF
Node
IntegratorSolutionAlgorithm
Domain Solver
StaticAnalysis
Analysis
TransientAnalysis EigenvalueAnalysis
IncrementalIntegratorEquiSolnAlgo
DirectIntegrationAnalysis ModalTransientAnalysis
DOF_NumbererGraphNumberer
SystemOfEqn
LinearSOE LinearSolver
BandSPDLinearSOE BandSPDLinSolver
DirectBandSPDLinSolver
DOF_Group
DirectTransientIntegratorStaticIntegrator
"
0i
)
+
)
1B$ j
$
j
iXj;% i
g
8 j$P(
"iXj;%&7Bi
C
-
0i
i
/
$O i
3/
C
ShDj
i
i
j;R%&7Xh
/ Sh /'Wl
Xh
j
i
j
"+
V
`
F@O$OuH]F
`
OXG OJ
YT
`
G V
uH]F
`
OXG O
dCL
-
Sh
RWl7
+ = Sh
3
C
,0
Xh R !" 2 ;!20O/4
@l E99h
lnh
$)$xlWi]j;.Sh
D
. .10Uvmv!2 jm,
D
Xh ,
D
4 u& /@l olWi]j;j.%(j
i
Ui/% j Xh> *'0j;
/D'0% Wi
+ =.Xh
'3
C
!
/Xh68:; Xh *0#1lWj$$- # Shj$ 5 Sh .&% e= !0-0 Wl> Kl]j/, $0Wj i%,
L Xh2 -0U>
-
!
()PP8:; ?/0$ * (@iXj$ %5 Xhi/0
h' XhR# %&)#/02 $0*0,2M iM XhK8:;< l$ j/#%#
j/4J3 0,A (*)$7l&,3@i
!,l& *0#M= nj/*-,"Ej/#E#ShD?E,S*-,
!
0i
)
+
# )
+
L 2
- h +W32] )2@l! 1*0#7i%)4,#*0$- i )iJ3=**0,
%"> Xh# i i%N*0,
Sh8#(# (%
/*'0j$ (*-,#E i
!
,*-,
Shpl!,A Xi*002 %*0,2#G< Xh2
D
. .0&&32pj/,,
D
A
@l! (#1 (E Xh#(# (% 2 *'0j$ %*0,2#EYj/, i902)j7 (*0,
Sh:i%)P/,#%5j$ L Xh/,
D
A
@l! (#+ - h2 +@32 )2 l$ j/##E*0#9j/,6j/# XiSj l! j/# l$ j/##+
"K i< XhR#/$02 %*0,+ # nj$ %* l1j$, XiXj$,#%*-&,A E)i%/$0%"#M(-j$,'*-,lWi%N&,A nj;$7j/))i j lnh Xh
+W!2! )2]!N@l! ?E*)$$LPBj9#0!l$ j$#%# +@ &&320 +@32v2+ - h +W &&7
20 +W!2! )2]! l$ j$#%#E4?9h#Q*0,A (@ij l! *-#@#Sh2 ?E, *-,
!
0i%
)
+
#
+
EP*-# j/,Dj/# SiXj l> l$ j/##+
)i%J3*2 i Xh2 $$0D?E*-,
-
Z
Q
M
HF O
M
H O
M` a
Z ?TYRUR[Z]H Q
QeZ J
Q@Z H@Q+Z R F Q
M
R
c M
RUE
H]F
`
FYH@VnZ
d;f
G QeZ]R^F@Q+ZTYH QG
`
V
M
H
a
Z]R Z]HWVnZ
G
`
Z
d
Q@ZYGIHWZ F]R
9H
M
RUE
d;f
f
J
Q@Z H@Q+Z R^F@Q
M
R
c M
RUE FYH Z]H@Q
d;f
Q@ZYGIHWZ F]R
O
M` a
Z
d;f
7ZnVXQ
M
R
Q@ZYGIHWZ F]R
ZXQ
d;f
Q@Z H@Q+Z R^F@Q
M
RPTYF@QeZ H@V]R
d
f
Q@Z H@Q+Z R^F@Q
M
R
c M
RUE
H]F
`
FYH@VnZ
d;f
g
g
H "10 &
4 B2! o)A ""W!
/ , !"# 3
#
+5- h
( ('
%"> Xh"ED?9h* lnh *0#L*0,3/
C
(R Xh -7"];"3@l! 1 ( %(j
C
8 Xh +@7
&&320 +W!2! )2]! Wl> j ?NjYi% 8 Sh -7"];"
;
&0j/, 8:; Xh# i i%N*0,
Xh2 $0*-,]j i#(# (% 3 *'0j$ %*0,2#+Q- h!#% %N! Xh2 #j i%
&$2'
, -%
E
&2' , , %
E
&' ' . 0,$
Eqj/,
&2' $, , , %
+
- h!#% %"> Xh#E=?9h*^lnhjYi%#Sh2 ?E, *-,
!
0i
)
+
# ,
E2* (@iXj$ %5J3Wi Sh
D
. .10U&&32D#
( i% Xh2 nj/,
&,A j/, $0%"!,A i%!#%*0j$ E j/, * (@iXj$ % J3@i@ Xh,
D
Xh#S?9h*^lnh
!
, Wj lnh $-%N&,A (#rj/, ,2 !#Dl&/,; Si%*-02 (*-, ( % Xh2 #(#
(%O5/*'0j$ (*-,# j/, hD? Xh2 # (=# (% 5 *'0j7 (*0/,#(jYi% #%> 0),+ "i 7
-
V
`
F@O$O H@V]R^Z]E/Z]H Q$F
`
H@Q+Z R^F@Q
M
R T
`
G V) H QeZ R^F@Q
M
RJ
YT
`
G V
HWV]R[Z]E/Z]H@QeF
`
H@Q+Z R F Q
M
R
d;f
\a
GIR QSTWF
`
HWV]R[Z]E/Z]H@QeF
`
H@Q+Z R F Q
M
R
d;f
\
a
GIR QSTWF
`a]M
G OCZXQYGIHSO
d
HWF
`
OXG O
M
Z
`
/Q@Z
M
Z
`
YG H@Z F]R
/Q WZ
O
xc
(&H
f
\a
GIR QSTWF
`
FYHWF
`
OXG O
M
Z
`
]FYH Z
d a]M
G
f
\
E5ZXQ
M
OuQ
M
OCZXQ/T Q@ZNO
O$Q+Z]E
MWc
Z(&TWF@QG
M
H O
a
GIR QSTWF
`
G H Q
c M
RUE FYH Z]H@Q
d a]M
G
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
H]F
`
FYH@VnZ
d aWM
G
f
\a
GIR QSTWF
`
G H Q
c M
RUE
M
YF
`
H]F
`
FYH@VnZ
d aWM
G
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z]E5Z]H Q ZXOXG T]F
` d aWM
G
f
\
E5ZXQ
M
OuQ
M
Z
H@Z
WF@QqQ WZ
)`
ZPFYH
L &
R
M
T O:F KQ
M
Q@ZNO
O$Q+Z]E
MWc
Z(TWF@QG
M
H@OvF
` `
F]R^Z&TYR[Z
a
G R QSTWF
`
_
a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z FYH Z]H@Q
d$ v`
Z]E/Z]H@Q
Q@Z
)`
Z
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z ZXOXG TWF
`Id )`
Z]E/Z]H Q
Q@Z
)`
Z
f
\a
GIR QSTWF
`
G H Q
c M
RUE
M
FYH Z]H Q
dCL% &
R
M
T
Q@Z
L
-
H@V]R[Z]E5Z]H Q$F
`
H QeZ R^F@Q
M
R
c M
RUE FH Z]H Q J$ )`
Z QeZ]R?Q WZ
v`
ZXO
Q@ZuH]F
`
OXG O
M
YZ
`
ZXQ
O
d;f
Q@ZYG H@Z F]R
Z]R
M
d;f
G
`
Z
d$d c
Z
)`
Z
QR sQ WZ
)`
ZXO
d;f$f
f
Jc
Z
)`
Z
QR
c M
RUE FYH Z]H@Q
d
Q@Z H@Q+Z R^F@Q
M
R
f
Q@ZYGIHWZ F]R
/F
d c
Z
)`
Z
QSR ZXQFYH Z]H Q
d;f
c
Z
)`
Z
QR ZXQ
Lud;f$f
g
g
H@V]R[Z]E5Z]H Q$F
`
H QeZ R^F@Q
M
R
c M
RUE
H WF
`
FYHWVnZWJ
Q@ZYG H@Z F]R
Z]R
M d;f
Q G O
c
R
M
E
)`
Z]E5Z]H Q ZXOXG T]F
` d;f
Q G O
c
R
M
E
M
YF
`
H]F
`
FYH@VnZ
d;f
H@V]R[Z]E5Z]H Q$F
`
H QeZ R^F@Q
M
R
c M
RUE
)`
Z]E/Z]H@Q ZXOXG TWF
`
J
$ )`
Z QeZ]R?Q WZ
v`
ZXO
Q@ZuH]F
`
OXG O
M
YZ
`
ZXQ
O
d;f
G
`
Z
d$d c
Z
)`
Z
QR sQ WZ
)`
ZXO
d;f$f
f
Jc
Z
)`
Z
QR
c M
RUEZXOXG &TWF
` d
Q@Z H@Q+Z R F Q
M
R
f
Q@ZYGIHWZ F]R
/F
7d c
Z
)`
Z
QSR ZXQ )ZXOXG T]F
`Id;f
c
Z
v`
Z
QSR ZXQ
Lud;f$f
g
g
H@V]R[Z]E5Z]H Q$F
`
H QeZ R^F@Q
M
R
c M
RUE
M
F
`
H WF
`
FYHWVnZWJL
QeZ]RQ WZ
L
-
,
- ?
> Xh# %oi% j$ % ShQ#%02 %*0, 8 Xh ## %
3 *'0j$ %*0,# (+ Sh
i%!
Ui%&
j7 XhN,
- h!#%
> Xh#E
# $, %
j/,
# $, $ %%
Ej iN4/ Sh
@l jYi%j/#M)0)i% 3=*^i 0j
- h +@ &&320 +@32v2l j/#%#*0# j/,Dj/2# XiSj l! l j$#%#
-40!l j/#%#jYi%G)i%J3*
?9h* lnhF)i 3* *
)0
!,A nj$ %*0,# Xh )0i% 3* i 0j
> Xh#
- ? Xh# Wl j iN*0, Xh2#0)4WiSl j/##Evj/#8 XhE*-,; %Wi j l&E*0,
0i%
) # 0
#ShD?E#
V
`
F@O$O
Q$F@Q G V H QeZ R^F@Q
M
R T
`
G V) H@V]R^Z]E/Z]H Q$F
`
H@Q+Z R^F@Q
M
RqJ
YT
`
G V
Q$F@Q G V H QeZ R^F@Q
M
R
d;f
\a
GIR QSTWF
`
Q$F@Q G V H QeZ R^F@Q
M
R
d;f
\
E5ZXQ
M
OuQ
M
Z
H@Z
WF@QqQ WZ
)`
ZPFYH
L &
R
M
T O:F KQ
M
Q@ZNO
O$Q+Z]E
MWc
Z(TWF@QG
M
H@O _a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z FYH Z]H@Q
d$ v`
Z]E/Z]H@Q
Q@Z
)`
Z
f
\a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z ZXOXG TWF
`Id )`
Z]E/Z]H Q
Q@Z
)`
Z
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
M
FYH Z]H Q
dCL% &
R
M
T
Q@Z
L
-
Q$F QG V H@Q+Z R F Q
M
R
c M
RUE
)`
Z FYH
d$ )`
Z]E/Z]H@Q
Q WZ
v`
Z
f
J
Q@Z
)`
Z Z]R
M
FYH
d;f
Q@Z
)`
Z/F 3Q
M
FYH
d;f
g
Q$F QG V H@Q+Z R F Q
M
R TYF@QeZ
d
ZnVXQ
M
R
f
JL
QeZ]RQ WZ
L Xh#
&' ' .
,
j/,
&$2' $, , ,
Ui
Xh ,lWi
&,A nj ,A (
iXj$ %i5l j/##E02 Xh"E
?9h*^lnh *-#1#hD?E, *-,
0i%
) #
>E7)P@i i
#B Sh
&$2' ,$ -
! Sh , i Xh
+@ &&320 +@32v2pl j/## j$,F Sh&, 0)#J3@iG Sh ,
D
A @l! %#
-
j2*0,
Xh2&* i l!,A Xi*002 %*0,kj$#E?
L
GIR^ZnVXQ ?R^FYH OXG Z]H Q H QeZ R^F@Q
M
R
c M
RUE FYH Z]H Q9J
GIH
aWM
Z, HWV]R[Z]E/Z]H@QeF
`
H QeZ R^F@Q
M
R O
c M
RE FYH Z]H Q E5ZXQ
M
Q G O H@V]R^Z]E/Z]H Q$F
`
H@Q+Z R^F@Q
M
R
c M
RE FYH Z]H Q
d;f
H
M! s` MYM
MWa
Z]R?Q WZ
L% &
R
M
T OL
QeZ]RQ WZ
L Xh#Pj i%))i%J3* % i%> 0i,l!,,@l! (*P3*- 9*-, i
j$ %*0,,E i P$ Xh Xh*-,*P3=*
0j 2
i&
Ui%!
j/, Xh ,
D
A1#
- hG*0, i
j7 (*0/,(i%> 0i, *0#E*0,
-
V
`
F@O$O
Z
ENF]R YT
`
G V
L
GIR[ZnVXQ?R^FYH OXG Z]H@Q H@Q+Z R F Q
M
RJ
YT
`
G V
Z
ENF]R
d
M
T
`
Z
M
T
`
Z
f
\a
GIR QSTWF
`
Z
ENF]R
d;f
\
a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z FYH Z]H@Q
d$ v`
Z]E/Z]H@Q
Q@Z
)`
Z
f
\a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z ZXOXG TWF
`Id )`
Z]E/Z]H Q
Q@Z
)`
Z
f
\a
GIR QSTWF
`
G H Q
c M
RUE
M
HWF
`
FHWVnZ
dCL% &
R
M
T
Q WZ
L
-
V
`
F@O$OuH]F
`
OXG O
M
YZ
`
J
YT
`
G V
uH]F
`
OXG O
M
YZ
` dCL
-
Xh2 i
9j
A" ;Wl!
- h
i%!
Ui%!
iXj/))h"E ?9h*^lnh *-# j
iXj/))h
iE Xh/#%
i%!
Ui%&
?9h* lnhhjJ3/Q4&&, j$#%#%*
, j/, /*0j$ (*-, ,'0
4WiE6*0#
,! % ! %Wi
*0,2S Xh #*
&
j/, #%)j i%#*- G Sh ## (
G *'0j$ %*0,#
- h2
,
D
A
iXj/))hN*-#:0#% "Q ShP,
D
4 u /Wl> %Kj/#%#*
,: *'0j7 (*0/,
,'0
4Wi#E %N ShR*0,2*)3*0j
i%!
Ui%&
+
* > Xh# j i%)iJ3=*'?9h* lnh Xi*
Wi
! Sh 2#*-, XhK,-! @l! EK, ?9h*^lnh
Xh2 j/,j#%*0# *0#1P!*0,
)P@i i
- h!#%
! Sh 2# *0,)l0
' ' "' , $%
E/?9h*^lnh
*0,3/
C
!#
"' ' -%
, Xh2(,-!#Ej/,
,## 4( , ' , $
E ?9h* lnhC*0,3
C
,$#
# 4(,
, Xh2 ,-!
,
- h
! Xh2
( ('
*-#)i%J3* "E ?9h* lnh *-#1l]j0 Sh -0U>
-
!
V
`
F@O$O
L% &
R
M
TKJ
YT
`
G VL% &
R
M
T
d
GIH@QQ$F
M
YZ
E
?M
Z
f
\L% &
R
M
T
d
GIH@QQ$F GIH@Q:H
L f
\a
GIR QSTWF
` L% &
R
M
T
d;f
\
E5ZXQ
M
OuQ
M
OCZXQ
WM
@QeFGIH E5F GIH GIH
c M
RUE5F@QG
M
Ha
GIR QSTWF
`a]M
G OCZXQ
Lud
G H QGIH@Q
f
\a
GIR QSTWF
`
V
M
H@O$Q1
L
ZXQ
Lud a]M
G
f
V
M
H O$QS\
E5ZXQ
M
O
c M
R
M
@QeFG HGIH
c M
F
M
T@QQ@Z
L%
Oa
GIR QSTWF
`
G H Q ZXQ F
d aWM
G
f
V
M
H@O$Q\a
GIR QSTWF
`
G H Q ZXQ
TE
L%&d aWM
G
f
V
M
H@O$Q\a
GIR QSTWF
`
G H Q ZXQ
TE
R[ZnZ
L%&d aWM
G
f
V
M
H O$QS\a
GIR QSTWF
`
G H Q ZXQ
TE
M
H@O$QR F G H@Z
L%&d aWM
G
f
V
M
H O$QS\
E5ZXQ
M
OuQ
M1c M
RUE Q@Z9QeFYH Z]H@Qa
GIR QSTWF
`
V
M
H@O$Q1F@QSR G & ZXQFYH Z]H Q
d aWM
G
f
\
a
GIR QSTWF
`a]M
G
c M
RE FYH Z]H Q
d
H QeZ R^F@Q
M
R
Q@Z H QeZ R^F@Q
M
R
f
\
a
GIR QSTWF
`a]M
G
Z]R
M
FYH Z]H Q
d aWM
G
f
\a
GIR QSTWF
`a]M
G F $ Q
M
FYH
d
M
T
`
Z
c
FWVXQ
_
f
\
E5ZXQ
M
OuQ
M1c M
RUE Q@Z TH]F
`
FYH@VnZ
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
HWF
`
FHWVnZ
d aWM
G
f
V
M
H@O$Q\a
GIR QSTWF
`a]M
G
c M
RE
HWF
`
FHWVnZ
d
H QeZ R^F@Q
M
R
Q WZ H QeZ R^F@Q
M
R
f
\
a
GIR QSTWF
`a]M
G
Z]R
M
H WF
`
FYH@VnZ
d a]M
G
f
\
a
GIR QSTWF
`a]M
G F
Q
M
H]F
`
FYH@VnZ
d
M
T
`
Z
c
FWVXQ
_
f
\
E5ZXQ
M
OuQ
M
TYF@QeZNQ WZNQRUG F
`
R[ZXO
M
H@OCZXO/F@QQ@ZH
M
YZXO
a
GIR QSTWF
`a]M
G OCZXQ
M
YZ
L
G O
d
V
M
H O$Q 7ZnVXQ
M
R
f
\
a
GIR QSTWF
`a]M
G OCZXQ
M
YZ Z
`Id
V
M
H O$Q 7ZnVXQ
M
R
f
\
a
GIR QSTWF
`a]M
G OCZXQ
M
YZ
-
i%!
Ui&
i%!)i%!#%!,; % Xh2;Wl! Xhj$ 5hj/,2/ *-#-j/##%&l&* j7 ( ?E* Xh j/, .10U&&32 *-, Xh ,-! i
*0#R*0,A Si% l& N % #%
Bl&,# XiSj/*0,A L (6j # %*
2
,# j$,$i - j ( Xh2N# # (
*j$ %*0,2#7# lnh j$#L?9h2&, 2#%*0,
)4&,j- i (Wi
*-,*0,
Xh
j/))*-,
P> ? (#j/##%&l&* j$ ( ?E*- Sh XhN47< /Wl> (#
* > Xh#9j i5)i%*2 ( *-,# Si l> Xh
D
. .10&&32@ ( > (Wi
*-,@ Sh*0#
j/)2)*0,
j/, (Bi! )i%, Xh
j/))*-,
(
! Xh2
,
*-# )i%* ( i%> i, Xh3*2&,A (*Wi#B Xh,
D
-
V
`
F@O$O
)`
Z]E/Z]H@Q5J
YT
`
G V
$ )`
Z]E/Z]H@Q
d)`
Z]E/Z]H Q
Wf
\$
)`
Z]E/Z]H@Q
d
G H QNHTYE
L% &
R
M
T GIH@Q/H
L%f
\a
GIR QSTWF
` $ )`
Z]E5Z]H Q
d;f
\
a
GIR QSTWF
`
V
M
H@O$Q1
L
ZXQ
L%
Q$FO
d a]M
G
f
V
M
H O$QS\a
GIR QSTWF
`a]M
G OCZXQ
Lud a]M
G
f
\a
GIR QSTWF
`
V
M
H@O$Q1
L
ZXQ
Lud a]M
G
f
V
M
H O$QS\
E5ZXQ
M
OuQ
M1c M
RUE Q@Z9QeFYH Z]H@Qa
GIR QSTWF
`
V
M
H@O$Q1F@QSR G & ZXQFYH Z]H Q
d aWM
G
f
\a
GIR QSTWF
`a]M
G
c M
RE FYH Z]H Q
d
H QeZ R^F@Q
M
R
Q@Z H QeZ R^F@Q
M
R
f
\
a
GIR QSTWF
`a]M
G
Z]R
M
FYH Z]H Q
d aWM
G
f
\
a
GIR QSTWF
`a]M
G F 3Q
M
FYH
d
M
T
`
Z
c
FWVXQ
_
f
\a
GIR QSTWF
`a]M
G F (Q
M
FYH
d
M
T
`
Z
c
FWVXQ
_
f
\
a
GIR QSTWF
`a]M
G F $ Q
M
FYH
d
M
T
`
Z
c
FWVXQ
_
f
\
E5ZXQ
M
OuQ
M1c M
RUE Q@Z R[ZXOXG &TWF
`
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ ZXOXG &TWF
` d a]M
G
f
\
a
GIR QSTWF
`a]M
G
c M
REZXOXG &TWF
` d
H@Q+Z R^F@Q
M
R
Q WZ H QeZ R^F@Q
M
R
f
\
a
GIR QSTWF
`a]M
G
Z]R
M
)ZXOXG T]F
`Id aWM
G
f
\a
GIR QSTWF
`a]M
G F )Q
M
ZXOXG TWF
`Id
M
T
`
Z
c
FWVXQ
_
f
\
a
GIR QSTWF
`a]M
G F
]M
R^VnZ
d
V
M
H O$Q 7ZnVXQ
M
R
M
T
`
Z
c
FWVXQ
_
f
\
a
GIR QSTWF
`a]M
G F
L WM
R[VnZ
d
V
M
H O$Q ZnVXQ
M
R
M
T
`
Z
c
F@VXQ
_
f
\
a
GIR QSTWF
`a]M
G F $
]M
R[VnZ
d
V
M
H O$Q 7ZnVXQ
M
R
M
T
`
Z
c
FWVXQ
_
f
\
E5ZXQ
M
OuQ
MKM
Q$F G H
c M
R[VnZXO
c M
R3Z
`
Z
Z
`
ZPO
M`
T QG
M
H@Oa
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQFYH
]M
R[VnZ
d
V
M
H@O$Q 7ZnVXQ
M
R
M
T
`
Z
c
FWVXQ
_
f
\
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
]M
R^VnZ
d
V
M
H O$Q 7ZnVXQ
M
R
M
T
`
Z
c
V F@Q
_
f
\
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
L ]M
R[VnZ
d
V
M
H@O$Q ZnVXQ
M
R
M
T
`
Z
c
V F Q
_
f
\
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
WM
R[VnZ
d
V
M
H O$Q ZnVXQ
M
R
M
T
`
Z
c
V F@Q
_
f
\
g
\
"$ , &
D
. .10U&&32
/ ,
-
i%!
Ui%!
iXj$)h6j/, XhK,
D
A
iXj/)h
)
* > Xh#Bj i )i%* ?9h* lnh.?E* /j - ? j$, +W32] )2'@l! ( *-,# Si l> Xh
D
. .10U&&32N@l! (# hD? ( i
Sh&*^i l!,A Xi*0 2 %*0,2#R % Sh"# # (
M *j
(*-,#B?9h* lnh i5 Xh2N*-,lWi
&,A nj8#% 2 (*-, # SiXj$ %
jYi%
* /&, *j$ %*0,2#
) ( (
j/,
) (
+
h2%Kl&/,; Si%*- 2 (*-,#9j i ! %Wi
*-, ?E*- Sh Xh1h0) 1 Xh +@32 )2
@l! )j/#
D
. .0&&32E;Wl! %#5jYi%E,/ =)4Wl> (" (RPPj ?5j i%?j 2 Sh)P##%*-0
*^i%Wl> E*0,A (
iXj7 (*0/, #Slnh
!# ShKj/,j=#
*
hA lnh#% ( #
+
* > Xh#
, -
j/,
. 0, %
j i%)i=*' (:2 Xj/*0, Sh l!,A Xi%*-
(*-,#
,
* > Xh#+ % 2 Xj/*0, Xh ))i% l! 9 Xh -
&,A (#+ Xj/,
!,A E# %*
2
,#
j/##oj/,
j
)*-,
j$ Si%*^l&?E* Xhmj /Wl> (i j i%N)i* iR-
&,A G 0
!,; G# 2 %*0,
# SiXj$ %
*-
)j
)- "# !l j/#%#
D
. .10U&&32 j i 8:
D
. .10U&&32
6
&0
2 >
D
. .10U&&32/j/,
X
"
)2!
D
. .10U&&32
5Wl> (# 2 Xh!#%5l j/##%!# &, iSl!
Xh l&,2# XiSj/*0,A %#
h
D
. .0&&32G@l! %#1j i%KlWi]j$ % Xh2
R
!"@2];320U
@l!
2 %Pl@i%Wj$ (3 Xh
D
. .10U&&32 j/,6,
D
-
j/,(j/#%#*
,(j/,"*-,*- %* j
j$))*0,
4! ?&!,9 Xh
i%&!#
Ui&2
j/," Shj$ %*0,",
P@i%#
h R 3"@2 3260U-l j$#%#Q*-#j/, j/2# XiSj l! l j$#%#
)j
)0!# E#!l j$#%#%!#
Xh j/,j#
j # %+&, iSl! Xh2 l!,# SiXj/*-,A (#jYi%
6
&0 2 > 8 j/,
X
"
)2 U!
V
`
F@O$O
M
H O$QSR^FGIH Q7FYH
`
Z]R7J
YT
`
G V
M
H O$QSR^FGIH@Q7FYH
`
Z]R
d;f
\a
GIR QSTWF
`
M
H O$QSR^FGIH@Q7FYH
`
Z]R
d;f
\
a]M
G OCZXQYGIHSO
dCLM
E5FGIH&/Q WZ
L (@i
*0, Xh
j$))*0,
6 Xh!* i 0&l]j
i%!
Ui%&
( Sh j$ %*0, ,
P@i%#
h ,
D
4 u& l j$#%#E?9h# *0,A (@ij l! *0#9#hD?E,
*0,
)i%
)i%*2R ? Xh#
( (' %
L?9h* lnhC*0#*0, // Xh -7"];"
@l! @ %+*-, i
XhG@l! 5 Xh -7"];"
;
&08*0, Xh j/,j#%*0#Pj
i%
j$ (*-, j/,
' %
h
' %
> Xh #M Xh2
A"4u @l! E)j$#%#%
*0, ShDl!,# Si l> (i9 %.,
4Wi+ Sh @i %* l&!# *0, Sh ,
D
A
iXj$)h
)j
)0
A "4 u #!l j$#%#%!# Shj$ kl& P # Sh j/,j=# 1j$#'#hD?E, *0,
i
j i%
;
,- j/,
R
;
&?9h2* lnhG*
)0
!,; P Xh
*0,*
i%!
*0,2,
j/,j /@i> 2
j$, i/Wi%# 2 Sh*
*l&$ $R!i
> 2
,
4Wi*0,
#lnh
Nj/# , Xh @i ( ,
P@i%*-,
< Shr,
D
4u & ?E* Sh&,
C Shi%
h Wj lnh
*0,2* * j),
D
-
@l! (#
V
`
F@O$O
L%
TYE Z]R[Z]RJ
YT
`
G VL%
TYE Z]R[Z]R
d;f
\L%
TYE Z]R[Z]R
d&
R^F
TYE Z]R[Z]R /Q WZ
&
R^F
TE Z]R^Z]R
f
\a
GIR QSTWF
` L%
TYE Z]R[Z]R
d;f
\
a
GIR QSTWF
`a]M
G OCZXQYGIHSO
d
HWF
`
OXG O
M
Z
`
/Q@Z
M
Z
` f
\a
GIR QSTWF
`
G H Q5HTE Z]R
L% d aWM
G
f
\
g
\
#"$ , &$
,
D
4 u
/ ,
;1 L
h=?> "*-# #%
% # )2) Xh2*0#G*0, i
j7 (*0/,
h @i (*^l&!#Q Sh
A " @l! Q)j/#%#.*0,
j # Si l> iSj j/,j#%*0#kjYi% j/4- j$#% , Xh iWi*0,
G Xh
i%!
Ui%!
?9h* lnh hj/# 4&!, 2! (@i
*0, Xh ,
D
4 u
h2
8:; i, *0, Xh'i%*
*0,j (* * .E Xh
j$ Si%* *-#Q*
)4i Xj/,A uj/# * Bj0D?E# Shkj/,j# Q %
#)P@l&* S XhQ )4NN8:;
> Xh
!"
5*0#-j0#% )i%* ( j -D? Xh j/,j# + ( lnhj/,
Xh=?!0 !
)i%*0,
Sh l&)i%#%Gqj/,j/,j=#*0#
* > Xh#6j i )i%* (.#% Sh ## %
j$ (*-,#kj/, i! i%, Xh
l!
)2 ( i -
' 0
h*0#*0#j
> XhS?9h*^lnh ?E*
-
V
`
F@O$O YGIHWZ F]R
T
`
G V
O$QeZ]E
xc
(HKJ
YT
`
G V
YGIHWZ F]R
)d
G H@Z F]R
M` a
Z]R /Q WZ
M` a
Z]R
f
\a
GIR QSTWF
`
YGIHWZ F]R
)d;f
\
a
GIR QSTWF
`
G H QqOCZXQ
G
Z
d&
R^F :Q@Z
L &
R^F
f
\a
GIR QSTWF
`
G H Q ZXQ
TE
(H
d a]M
G
f
V
M
H O$Q
\
a
GIR QSTWF
`
G H QuF
d
V
M
H@O$Q11F@QSR G & vV
M
H O$Q1
L
M
T
`
Z
c
FWVXQ
_
f
\a
GIR QSTWF
`
G H QuF
d
V
M
H@O$Q 7ZnVXQ
M
R vV
M
H O$Q1
L
M
T
`
Z
c
FWVXQ
_
f
\
a
GIR QSTWF
`a]M
G
Z]R
M
d aWM
G
f
\
a
GIR QSTWF
`a]M
G
Z]R
M d aWM
G
f
\
a
GIR QSTWF
`a]M
G OCZXQ
d
G H Q
` M
V
M
T
`
Z
a
F
`
TWZ
f
\
a
GIR QSTWF
`
G H QqOCZXQ
M` a
Z]R
d
YG H@Z F]R
M` a
Z]R H@Z
M` a
Z]R
f
\
a
GIR QSTWF
`
G H QqO
M` a
Z
d a]M
G
f
\
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
d a]M
G
f
\
a
GIR QSTWF
`
V
M
H@O$Q 7ZnVXQ
M
R ZXQ
d a]M
G
f
\a
GIR QSTWF
`
M
T
`
Z1H
M
RUE
d a]M
G
f
\
g
\
."$ , &
8:;
h #%!)j iXj7 (*0/, Xh2 ## %
Rj$ %*0, j/, #% @i9*0,A (C ? #% @i9*0,2*- (* j j/, Xh!,
( j$,
*- %WiXj7 (* /#% @i j$ (@i
h* -
;
)2j$, K& 2Q@l! (# l&S4 2#% *-,# %]j Sh =3>[>
l!
*-,*0,
Xh2
j$ Xi* j/, @l! ( i
-
L
GIR^ZnVXQ
FYH
L
YGIH
M` a
Z]R O
M` a
Z
d;f
J
O
M` a
Z
G
cqd c
FWVXQ
M
R[Z
c
F
`
OCZ
f
O
a d
! H! ! HR @O QSR !
`
#
@QR !
`
!PGIH
c Mf
\
Z
`
OCZ
QSR O
d
! H! ! HYR O @QR!
`
#
QSR !
`
!9G H
c Mf
\c
FWVXQ
M
R[Z
QSRUT@Z]\
g
" 0 &5
,6U & 2 tu=
6
,k8:;x= B. =?30!
,
3
j$ XjC*0,A %C,2 ;Wl! (i%!# (#N*0,
i l&*-&,A ol! j/#N Xh')4WiXj7 (*0/,# ,$ (hj /
(
S Xh)i%
hC Xh2
;
)2 j/, & 2 *-,; %Wi j l&!# ( 2 Xj/*0,ml&
)P/,&,A (#
0# i
l&
, # ( iXj
N#Slnh2
*
))i% -(j$,C#)j i#% Xh:?9i%* (WiR j8:; Xh ( &, iSl!
l&,2# XiSj/*0,A %# j i% Wi#% 2 Sh*
*l&
,
4Wi*0,
#Slnh
6 Xh2 >?M (,
j/)h#,
#% 2 (*-, j
i%* Xh
xj$, j j/, #
! Xi* l )4#%* (* ,* ( ## %
j7 (*0/,#
?9h* lnh'*0#M# /'6j 2* i%@l! #% @i*-#9j/# -D?E#
L
-
!
V
`
F@O$O
)`
Z
)`
Z
&
Q$F QG V
M` a
Z]R T
`
G V
v`
Z
)`
Z
M` a
Z]R
YT
`
G V)`
Z
)`
Z
&
M` a
Z]R
d
M
T
`
Z Q
M`
_
Z
$
f
\
G H QqO
M` a
Z
d a]M
G
f
\
]R G
a
F@QeZ
M
T
`
Z
Y\)`
Z
)`
ZYGIHWZ F]R
Q WZYGIH@Z FR
g
)`
Z
v`
Z
&
M` a
Z]R O
M` a
Z
d aWM
G
f
J
7ZnVXQ
M
R
Q@ZYGIHWZ F]R
ZXQ
d;f
7ZnVXQ
M
R PR
Q@ZYGIHWZ F]R
ZXQ
d;f
7ZnVXQ
M
R _Z]R
Md;f
7ZnVXQ
M
R
d
R
f
7ZnVXQ
M
R
d
_
G
Z
d;f$f
M
T
`
Z1R
M
QR
R
R
G
`
Z
d
O(&R Q
d
R
M
QSR
f
f
J
_
Z]R
Md;f
$
Q+Z]R/Q WZ
ZXO
Q WZYGIH@Z FR
ZXQ
O
d;f
G
`
Z
d$d v`
Z]E/Z]H@Q
Q WZ
v`
Z
Q@Z
$
O
d;f$f
f
J
Y_
-
?R^FYH O
c M
RUENF@Q G
M
H Q@Z
M
H O$QSR^FGIH@Q7FYH
`
Z]RU\
Q@Z
&
R^F
TYE Z]R[Z]RU\
L%
TYE Z]R[Z]R?Q WZ
L%$
TE Z]R^Z]R
d
Q WZ
&
R^F
TE Z]R^Z]R
f
\
uH]F
`
OXG O
M
YZ
`
Q WZ
M
YZ
`
\
L
G R[ZnVXQ
FH
L
Q@Z
M` a
Z]R\
FYH
L
Q@ZYGIHWZ F]R
vd
Q@Z
M` a
Z]R
f
\
Q$F@Q G V H QeZ R^F@Q
M
R!Q@Z H QeZ R^F@Q
M
RU\
#
Z
Q
M
HF @O
M
H Q@Z
M`
H
`
M
\
$
Q$F@Q G VuHWF
`
OXG OqQ WZuHWF
`
OXG O
d
Q@Z
LM
E5FGIH Q@Z
M
H O$QSR^FGIH@Q7FYH
`
Z]R
%
Q@Z
L%
TE Z]R[Z]R vQ WZ
M
YZ
`
Q@Z
M`
H
`
M
Q WZ H QeZ R^F@Q
M
R &Q@ZYG H@Z F]R
f
\
Z]R
c M
RUE Q@Z9FYH]F
`
OXG O
Q@Z
L
?
j/,
?
*-, ShRi%*
*0,j4?E* Xh Xh 0D?E*0,
GIH
L
Z R[ZnZ Q@Z
&
R^F
TYE Z]R[Z]RU\
M
H-'TF@QeZ
&
R^F G Z]H Q
WF]R[OCZ
L
Q@Z
M` a
Z]RU\
]F]R OCZ
L
Q@ZYG H@Z F]R
)d
Q WZ
M` a
Z]R
f
\
)4Wi i
j9,,
0*0,2]j i# %&)
# (!) =,j
*^l j/,j#%*-# #*0,
Sh >?
j iS*-,; %
iXj7 (*0/, # XiSj$ (
?E* Xh6l&,# nj/,A %#
8
j/,
7
, Xh
j/*0, 0*-,
?
?
j/,
?
2Q*0,9 ShRi%*
*0,j j i1i%!) j l! ?E*- Sh Sh -D?E*0,
Z
E5F]R PQ WZ H QeZ R^F@Q
M
R
d
f
\
$
L
GIR[ZnVXQ H QeZ R^F@Q G
M
HuH]F
`
OXG OxQ WZuHWF
`
OXG O
d
Q@Z
L
-
V
`
F@O$O
&
YT
`
G V
(&T G
M`
H
`
M
YT
`
G V
&
d
G H Q/E5F
QeZ OG H Q5HTYE H@V]R
M
T
`
ZNQ
M`
M
T
`
Z
&
Q
M`
M
T
`
Z E5F
Z FR[V
f
\
GIH@QO
M` a
Z TRUR^Z]H Q
Q+Z
d aWM
G
f
\
aWM
G V
M
E T@Q+Z
L
G R[ZnVXQG
M
H
d
G H QNHTYE
QeZ
f
\
#
aWM
G
`
GIHWZ
Z F]R[V
d;f
\
$
aWM
G V
M
E T@Q+Z ?R G F
`
H WF
`
FYHWVnZ
d
ZnVXQ
M
R
QSR G F
`
ZnVXQ
M
R /QR G F
`
HWF
`
FHWVnZ
f
\
%
]R G
a
F@QeZ
M
T
`
Z
Y\
GIH@Q/HYTE
M
F $ H@V]R 3E5F
QeZ On\
7ZnVXQ
M
RTYHWF
`
FHWVnZ
M`
H WF
`
FYH@VnZ F
g
#
&
O
M` a
Z TRUR[Z]H@Q
Q+Z J
$
Q@Z H@Q+Z R F Q
M
R
c M
RUE
H]F
`
FYH@VnZ
d;f
%
Q@Z H@Q+Z R F Q
M
R
c M
RUE FYH Z]H@Q
d;f
TYH]F
`
FYH@VnZ
Q@ZYG H@Z F]R
ZXQ
d;f
v_
Z]R
Md;f
HYTE
Q+Z
G
`
Z
d
TYHWF
`
FHWVnZ_ H
M
RUE
d;f
HYTE
Q+Z @OM E5F
Q+Z @O
f
J
Q G O/V
M
ET@Q+Z
L
GIR[ZnVXQG
M
H
d;f
Q G O
`
GIHWZ
Z F]R[V
d;f
Q@Z H QeZ R^F@Q
M
R9T YF@QeZ
d
f
#
Q@Z H QeZ R^F@Q
M
R
c M
RE
HWF
`
FHWVnZ
d;f
$
M`
H WF
`
FYHWVnZ
TH WF
`
FYH@VnZ
%
TH WF
`
FYHWVnZ
Q WZYGIH@Z FR
ZXQ
d;f
HTYE
QeZ
g
g
#
&
V
M
E T QeZ
L
G R[ZnVXQ G
M
H
d
G H QNHTYE
QeZ
f
J
#
G
cqd
HYTE
Q+Z
f
J
#
Q@ZYGIHWZ F]R
:O
M` a
Z
d;f
#
Q WZYGIH@Z FR
ZXQ
d;f
#
g
Z
`
OCZJ
##
TH WF
`
FYH@VnZ
M`
H]F
`
FYH@VnZ
#$
HTE
QeZ
d
Yd
f$f
#%
a
HTE
QeZ
d
UO
O(R Q
d$d
f+Yd
M`
HWF
`
FHWVnZ
f$f$f M `
H WF
`
FYHWVnZCTH]F
`
FYH@VnZ
#
M
T
`
Z
HYTE
Q+Z
TH WF
`
FYH@VnZ
#
TH WF
`
FYH@VnZ
na
HTE
QeZ
$
c M
R
d
G H Q '
HTYE
QeZ !
\ '
\ '
f
J
$
'
$
d a
'
f
$
$
g
$
Q@ZYGIHWZ F]R
:O
M` a
Z
d
f
$#
Q WZYGIH@Z FR
ZXQ
d;f
$$
a
$%
R
$
c M
R
d
G H Q '
\'
-
]
%
d
'
f
%
%
g
%
%
g
%#
g
%$
&
`
GIH@Z
Z F]R[V
d;f
J
H FYHKGIH QeZ]R
a
F
`
O F O?V
M
H@QeFG H GIHKF R
MYM
Q
O F
_
O
_
&
F
TH WF
`
FYHWVnZ
#
QSR G F
`
$
Q G O:V
M
EYT QeZ
H WF
`
FYHWVnZ
d
QSR G F
`
QRUG F
`
H]F
`
FYH@VnZ
f
%
&
QR G F
`
HWF
`
FHWVnZ
G
`
Z
d&
F
&
sOG ENF
Z F]R^V
f
J
O F
O
O
_
O F
&
F
&
QRUG F
`
d
O
f
Q G O/V
M
ET@Q+Z
H]F
`
FYH@VnZ
d
QSR G F
`
QSR G F
`
H WF
`
FYHWVnZ
f
&
QSR G F
`
H WF
`
FYH@VnZ
#
g
$
%
G
cqd&
F
&
f
J
G
c
H
M
G H QeZ]R
a
F
` c M
TH BT@OCZPF R[Z T
`
F]R
Z
Q
M
H O$Q+Z
g
Z
`
OCZJ
T OCZ R[Z T
`
F!
c
F
`
OXGQ
M
YZXQ+Z]RUEPGIHWZ Q WZ1R
M M
Q
HTYE QeZ]R
G
`
Z
d
F O
d&
F
&
f
&
Q
M`
d
HTE Q+Z]R E5F Q+Z]R
f$f
J
#
O$Q+Z
O F
&
F
d
O FUO
f+Yd&
F
&
f
$
QSR G F
`
O$QeZ
%
Q G O:V
M
E T QeZ
HWF
`
FHWVnZ
d
QR G F
`
QSR G F
`
H]F
`
FYH@VnZ
f
&
O$Q+Z
QSR G F
`
H WF
`
FYHWVnZ
G
cxd&
O
&
F
f
J
O F
O$QeZ
&
F
&
O$Q+Z
g
Z
`
OCZJ
O
O$Q+Z
&
&
O$QeZ
#
g
$
g
%
O
g
g
-
lnhj/,
XhSi%*
*0,j))i%
iSj
(.)4Wi i
j/, j/,j#%*0# #%*-,
Xh*-#9#% 2 %*0, j
i*- Xh
?E* Xhmj
j =*
? ?
* (@iXj$ %*0,#7j
j =*
?
j
j0#* # (&)2#j
l&, /Wi
&,l! (-WiXj$,l&
j/, j
j =*
#%]jYiSlnh0!,
Sh
6?
Xh2Nj/,j# #%*
)
i%!) j l! 0*-,
?
*-, XhRi*
*-,j
j/*-, )i%
iXj
?E*- Sh
#
&
Q WZ
M`
H
`
Md
Z
_
f
\
h*0# )j
)0
,# XiXj7 ( Xhj7 ;?E*- Xh 0# Shj/,
? ?
0*-,7l! 2 = Shj$,j# Nl]j$,
*0,A Xi l&pj',2!? l j/## *-,; %' ShN## %
hot
D
= l j/## ))i%*!# j',!? . % e=?30
-0S#3l j/##?9h*^lnhlWj/,'P #S*-,6j/,kj/,j#%*0# ?9h2* lnh6i%*^i%!# j .&% e= !0-0
l j/#%#
h*-#
i%Wj$ G*0,l@i%]j$#% Sh ,
4Wi 4)P##%*-05j/,j=#*0# )2 (*-,#1 Xhj$ uj i%5jYj/* j/0
( Xh2 j$,j#
h UiSj
!?i lWj/, 4 (!, (F*0,l 2'$ Xh@i: )4N1j$,j#*0# )ivl! i
# lnh j/#&*
&, Yj 2j/,j#%*-#
j XiSj/,#*0&,A j$,j#*0#3j/,S# nj7 (* l ) #hWi
iWj lnh
,!? j/,j#%*-#Q)i%&l& i # !l j/#%#:E Xh j/#%*^lol j/#%#:*0, Sh-j
i%
j$ (*-,
# :P
,
h*-#@#%@l! %*0, !#Sl@i%*04?9hj$ 1lnhj/,
%9 Xh UiSj
!?i j i%
j2 ( *-,l
&*
&, Yj 2 j/,j=#*0#9j/,
jP SiXj/,#*0!,; j/,j#%*-#
E
, #%-*
@lnhj/,*^lj$, # Si l> iSj !,
*-,&@i%*0,
4 Sh 2! (@i
*0,j7 (*0/, 8 Sh l 0*0,
0 j j/, Sh ! %Wi
*-,j$ (*-, Xh ,j7 iSj Ui&,)l&*0!#kj/,
2 #Shj$)P!# G# Xil
iE*0#Pj l&
, )4WiSj$ (*-,
,'&*
&, Yj j/,j#%*0#M*-# l&,)l&Wi,'?E*- Sh ,*0,
Sh
j/,A (* (*0!#
h 6j i%R= nj/*-,Ui%
#% *0,
!*- Xh2WiM1 Xh 0D?E*0,
Xj/,j iC!*
!, j )i-
i1l]j/#"
-
DOF_Numberer
EigenvalueSOEEigenvalueAnalysisDomain
ConstraintHandler AnalysisModel
DOF_Group FE_ElementNode Element
EigenvalueAlgo EigenvalueIntegrator
EigenvalueSolver
StandardEigenSolver GeneralizedEigenSolver
RayleighBandDiagEigenSolver
BandDiagEigenSOE
*
i
?
j/## 5* j
iXj
i8*
!, j
,j#*0#
$&,@iXj-* & .&*
&, Yj 29)i%/0
;
i l]j/# @,j$ iSj
Bj/,
Ui% &,l!*0!#@)i0
h@i%jYi%Kj
j/*-,
j/,9?5j =# ("#% XhG)i0
)3Wl> (i
*- %WiSj$ (*-,
! Sh 2#
j 0&*
h $ (*0!,A M*- %WiXj7 (*0/, )j$,
-
,,$ ~
h2*0#5*-# Sh
! Xh2 S?9h2* lnh *0#*0, / %9)4Wi i
Xh &*
&, Yj
j/,j#%*-#
29 Xh*-#* 5*0, //!#
' , , %
, * (# !j/, Xh!,
"
!"#$
/, Sh .1!& )0-0!'@l! j/#E#ShD?E,S*-,
i
l
#$, 3
h*-#5*0# j
> XhS ( 2)j7 ( ShQ,j*0#) jYl&
&,A %#@?E*- Sh
Sh Yj !# Xhi! )i%,# Sh Yj 2 j$, t 70;
h
/2 !"#$%
K Xh t 70; l j$#%#?9h2* lnh *0# #ShD?E,:*0,
i
$?E*
> (Wi
*-, Sh l 0*-,
#Shj/)45j-,-!
h
!"#$%
-
G Z]H
a
F
`
T@ZHWF
`
OXG O FYHWF
`
Z
d aWM
G
f
J
G
cqd
Q@Z
LM
E5FGIH WF@O
L
/ , /2 !"#
3
.1v 0 +@32 )2
h:.1!& )0 +@32v2/Wl> *-#7i%!#%)4,#%*-08))i%
**-,
! Xh2 #8 Shj$ 8 Xh2P.& 0 :l]j/, #%
hP.1& )0 < +W
2 )2 l j/##2?9h2#%R*0,A %WijYl&*0#Nj/#M#ShD?E,'*0,
i%
=)i%*!#
> Xh#< %
i
Xh j/,
j$ Xi* l&!#j/,
> Xh#R (S*-,# Si l> Sh
D
. .10&&32pj/,
,
D
A @l! (# h2 ? % ! %Wi
*0,2" Xh2&* i l&,A Xi*0 = (*0/,C ( Sh
j7 Xi%*^l&!#
-
hBl j/#%#Kj-#% )i=* j
> Xh A G Sh Xi* j *0#) j l!
&,A pj$ Xh4 /Wl> (#NjM ( Sh#% Yj 2:#%)4Wl!* *-, Sh'&*
&, @l! ( i
)j/##% Dj/#M Xh2 jYi
&,A
V
`
F@O$O
G Z]H
a
F
`
TWZ H QeZ R^F@Q
M
R YT
`
G V) H@Q+Z R F Q
M
RJ
YT
`
G V
G Z]H
a
F
`
TWZ H QeZ R^F@Q
M
R
d;f
\a
GIR QSTWF
`
G Z]H
a
F
`
TWZ H QeZ R^F@Q
M
R
d;f
\
a
GIR QSTWF
`a]M
G OCZXQYGIHSO
d
HWF
`
OXG O
M
Z
`
G Z]H
a
F
`
TWZ
f
\a
GIR QSTWF
`a]M
G FYH]F
`
OXG O
M
YZ
`
WFYH Z
d aWM
G
f
\
E5ZXQ
M
OuQ
M1c
R
M
EsQ@Z, FYH mENF@QR G VnZXOa
GIR QSTWF
`
G H Q
c M
RUE
d;f
\a
GIR QSTWF
`
G H Q
c M
RUE
d;f
\
E5ZXQ
M
OuQ
M
GIH O$QSRUTWVXQQ@Z
$ )`
Z]E5Z]H Q+O/FYH
L &
R
M
T M
'+ZnVXQ;O
M
Q
M
ZXQeZ]RUE9G H@Z9Q@ZWG R!V
M
H O$QSR G T QG
M
H@OuQ
M
FH a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z FYH
d )`
Z]E5Z]H Q
Q@Z
Z
)`
Z
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
)`
Z FYH
d$ )`
Z]E/Z]H Q
Q@Z
Z
)`
Z
f
\
a
GIR QSTWF
`
G H Q
c M
RUE
M
FYH
dCL% &
R
M
T
Q@Z
L%
R
f
\a
GIR QSTWF
`
G H Q5TYF@QeZ
d
V
M
H O$Q ZnVXQ
M
R
f
\
g
\
! #"$ , &$
.1v 0 +@32 )2
/ ,
.1v 0= B.
h/.1!& )0= B. /Wl> *0#i%!#%)4,#*0- iL# (i*0,
Xh
;
j/,
j$ Xi* l! i (ij/, i)i%*2*0,
jYlWl&!#%#M ( j/,
hp.& 0 Xh# % j+ (R Xh2 j/,
j$ Xi* l!
,oj2*- (*-,: Xh "*-,l E Xh
! Xh2 #
A?9h* lnh ?E* )i! )i%,pj XhM!*
!,/Wl> (i#
?9h2* lnh:?E* &i%> i,
j #*0,
-!*
!, Wl> (i
=?9h*^lnh+?E* i%! i%,kj Xh@&*
&, Yj !#
?9h*^lnh
?E* 9i%! i%, j #*0,
0S!*
!, j 9j/,
M?9h*^lnh ?E* E*-,//
, Xh
j/##%&l&* j7 (k.1& 0
!l j/#%# .1& 0
.1v 0=?!0 !
h .& 0 -l j/#%#"?E*- Xh ?
! Xh2 #
( (' %
?9h* lnh #! (# 2) -*0, ;#
( Sh Wl> (#:*0,. Sh6j
i
j$ %*0,
%
j/,
!"#
?9h* lnh *0# @l j i% sj/#
) i * i j
)j
)0!## !l j/#%#G
;
70
X
"]U&32-0! j i
-
Z
Q
M
HF O
M
H
M
F
`
O
M` a
Z ?TYRUR[Z]H@Q
QeZ J
T F QeZ5Q WZ1E
M
Z9OWF ZXO
c M
R!Q@Z9V]TYRUR[Z]H QxO$QeZ G
c
V
M
H
a
Z]R Z]HWVnZPO
` M
G
cqd
HYTE Q+Z]R^F@QG
M
H@O!]F@O$Q1 HYTE QeZ]R^F@QG
M
H O ZnV F
`
V
G Z]H
f
J
Q@Z
G Z]H H QeZ R^F@Q
M
R
c M
RUE
d;f
\
Q@Z
G Z]H H QeZ R^F@Q
M
R
c M
RUE
d;f
\
Q@Z
G Z]H
O
M` a
Z
d;f
\
Q@Z
M
YF
`
?R^FYH@OXG Z]H Q H QeZ R^F@Q
M
R9T YF@QeZ
d
Q WZ
G Z]H
ZXQ
d;f$f
\
g
H
M!
Z]R
c M
RE
M
HPQ@Z R[ZTWVnZKO
O$Q+Z]E
Q@Z
L
GIR[ZnVXQ?R^FYH OXG Z]H@Q H@Q+Z R F Q
M
R
c M
RUE
H]F
`
FYH@VnZ
d;f
\
G H Q5HTYE QeZ]R^F@Q G
M
H O!F@O$Q
\
G
`
Z
d
Q@ZYGIHWZ F]R
9H
M
RUE
d;f
f
J
Q@Z
L
G R[ZnVXQ3R FH@OXG Z]H@Q H@Q+Z R^F@Q
M
R
c M
RUE FYH Z]H@Q
d;f
\
Q@ZYGIHWZ F]R
O
M` a
Z
d;f
\
7ZnVXQ
M
R
Q@ZYGIHWZ F]R
ZXQ
d;f
\
Q@Z
L
G R[ZnVXQ3R FH@OXG Z]H@Q H@Q+Z R^F@Q
M
RPTYF@QeZ H@V]R
d
f
\
Q@Z
L
G R[ZnVXQ3R FH@OXG Z]H@Q H@Q+Z R^F@Q
M
R
c M
RUE
H]F
`
FYH@VnZ
d;f
\
HYTE QeZ]R^F@QG
M
H O!F@O$Q3
\
g
g
! " 0 &$
4 B2! oA""W!
;
70
, /2 !"#
3
-
h*0,A (@ij l! i Xh
D
. .10Uvmv!2j/,k,
D
-
5 5
! #"$%
,S '&)(+*-,.&)/1032'4657/18:9=?4@,A2?BC9F)* )*?4@FM(H8_^`8)(a2'4b4@W+4@LO4@8E2c/18`/YW+d>*D(+* )*?(H8)Ge/f&)(H465'/15?,.&Xd[*D(HLO(HWH/15g2'9h2'&`/Y2i035D4@*?4@8E2'46FS(H8
,.&`/1032D4@5 3Qcjk/18EdS91Ig2'&34f,@Wl/Y*D*D46*bF)46^)8)4@F(H8m,.&`/Y032'465 _/15D475?4AB )*D46FNIJ915nF)9
-
!" #%$
&('%) *
7( >(HF)4]/Y8)FM,69F Y/-F)9
-
!" $
12
1,2
(+G=)5D4o)Q
79
-
!" $
-]&)4@5?4
]a{
YY
m
]
p
YY
]aY p] pp
p
] p Y
w
]
H
YY
]aYH ]aHH
p
]aHY
m
]
p
{
YY w
]
H
{
YY
s
o3Q P t
/18)F
o|{
Y
m
o
p
Y
]_Y p7]
p
pp
oqp
w
o
H
Y
]aYH ]
p
HH
o|H
m
o
p
{
Y
w
o
H
{
Y
s
o3Q ot
_
&)(H*O,@92D4@8)F)46F2'9F)9
-
!" $
9F)* =)*D46* (+8U^`83(+2'4c4@W+4@LO4@8E2 /18`/1Wado*?(H*6Q
_
&)4cLO9F, /Y8 ;\4_/S,69FEA
(H*f;\4@(+8)GD=)*D46F 2D9N*D9Fj=),62 , /Y8V;\4K91;32./1(+8)4@F -](+2D&)9=32
44Fo0)W+(H,@(a2'WadMIJ9
-
!" $
]X{
(+*
m
]'(
*
]'nd]
p
d d
s
].d9
*
t
s
o)QLK t
83,@4[,69FO(+*=)*D46FV2'9U4@83IJ915D,@4]2'&34-F)(+*D0)WH/1,@46LM468E2 ,69(H8)Ge4ON =`/Y2D(H9
-
!" $
_
&)(H*b,69*q2'4@L
91I4ON =`/Y2D(H9
-
!" $
h N=)/Y2'(+9LOLM4A2'5?(H,M/18)F 8)918)*D(+8)G=)WH/15U/18)FEA /Y*T0\9F)* 2D&)4@5?4f/15?47*D44?*?2
K*?2@Q
Q -9%- 2D9k0)/15?2D(+2'(+9
-
!" $
/15q2'(+2D(H9F)*@Q /15?2D(+2D(H9
-
!" $
&(' !"#$
: 8 8
&%(')+*,%
7-%/. '0 7-!1%/.
8
%/2 %/
$ 5D45?>(+45-(H*78)9%-LV/YF)4[91Ic5D46*D4@/15D,.& 9F)*_/183F%&)9%-2D&)4SF)9
-
!" $%#
5D460P4@/Y2'46FSG
-
!" $%$
F)46,@9*D(+* A /Y*e9=o2'WH(+8)4@F (H8*D46,62'(+9*?(H* A 2D&)4 -](+WHW
;\4_/1*M14@FIJ915 (+2D* *q2'( P8)46*D* APLV/Y*D*f/183FF`/1LO0)(H83GMLM/Y2'5?(H,64@*@Q
_
&)4[LM/Y2'5?(H,64@*]2'&`/Y2
/15?4T5?462i=35D8)46F /15D4
]#`A
/18)F
`AN-]&)465D4 (H*b2'&34e2'5D/18)*qIJ9
-
!"
F)(+*D, =3*D*D46F_(H8U*D46,62'(+9
-
!"
SymmPosDef_SOE
Band_SPD_SOE
LinearSOESubdomain
FETIAnalysis
AnalysisModelConstraintHandler DOF_Numberer
Domain
PartitionedDomain DomainPartitioner GraphPartitioner
DomainDecompAnalysis
DomainDecompAlgo
DomainSolver
DOF_Group FE_Element
SolverBand_SPD_SOE
Band_SPD_SOESubstrSolver
SolverSubstructuring IterativeSubString
Solver
LinearSOESolver
Analysis
IncrementalIntegrator
Metis
Element
SubstructuringAnalysis
IterativeSubStringAnalysis
(HG2=)5D4 o)Q P
=G
WH/1*D*137(l/YG(HF)46*]*D9F IJ9
-
!"
!"# $%'&
!"# (
)* * +%,-%. 0/12( 435
6
7!98:)* * +%,;35
-
!"
2'&)5?9=)G.*0$&% '*) =?4@,A2T(+*f5D4@*?0P918)*D(+;)WH4_IJ9.750$&% '*) o)Q8:kA (H*/18[/Y;)*?2D5'/1,A2 ,@WH/1*D* -]&)(+,.&[F)46^)8)4@* 2D&)4 *?(H8)G1WH4iLM4A2'&)9>F +1g/1*;P46(H8)GK0j=)5?4
?>(H5?2=`/1W Q +C2 (H*]2'&)4T*=);\,@WH/1*D*?4@*791I
o
2D&`/Y27035D9%?>(HF)4U2'&)4e(HLO0)WH46LM468X2'/Y2'(+9
-
!"
F)(H*?, =)*?*D46FV(H8 *?4@,62D(H9*?2 AY2'9]2./!M14n/YF ?Y/18E2./1G
-
!"
JK!"?%E !": %D
!"# $%E &
!"# (
JK!"??E,IED+Q35
6
7!98 JK!"??E,;35
C C R/172 C 35
6
7!HED >!B
DQH,
6
. 35
!BKCC !,
6
. 35
6
7!HED >!B
DQ),TD CI? /?35
6
7! CI? / Q?C ("!XDQ? ,
6
. 35
6
7!$#$79 $/ Q?C!XDQH,
6
. .35
6
7!$#$79 $/ Q?C KCC !:,
6
. .35
!B(S .(KC?-,
6
. 35
Y
5
Z
[X\*)K]_^ + ) ` a ` *b,
# c
,
-
!"
(H82D&)44$ # o 9=?46,62 A /1*h/m5?4@*=3W+2h91Ic2'&)4 0`/Y5?2'(a2'(+9(+F)(H8)G
2'&3(H*c(H83IJ9
-
!"
JK!"??Ee @9?T !XQH,
6
. .3%&
C!TG72 C Ig-h D- ,;35
Y
D #$T =/ JK!"?%Ee Q?C!KQH,
6
. 3%&
C!TG72 C Ig-h Q?CK- ,;35
Y
Z [X\ ] /0, c !$` a) k b ! .` b, c ,
x 13546),.7013$&9:542+ 0),' *q2U/18)FZ0`/1*?*D4@FZ2'9S2D&)4 $
$
/1*h/15?G=)LO4@8E2'*
(H8 2'&)4,@918)*?2D5=),A2'9*q2K2D9M*?4@W+4@,62K2'&34UF39(HF34@*
KF -]&3(H,.&:(+*-(+8U?=?4@,A2'*K(H8m2'&)4U/1G1G(H9=)*c*D46,62D(H9
-
!" #
0\4@5?IJ915DL 2D&)4h8=3LM465D(H,@/1W$,@91LM0j=o2./Y2D(H9 C ,LJK!"?%E>/ 72(+%
K4?ED W/12
$ SR!G"?)0/172(SR!G"?)
C #=./172 #=.
%EG Q?'/12NJH: Q?
N( J$ /172NJ
Vf)%DVfDICQH I? / 72(VfBCQH4DI?
%EJH
6
W/172NJH
6
435
6
7!98 J* K*D C ,;35
6
7!HED N,
6
. 35
6
7!HED %E 2DQ?,
6
. 35
"BC
6
7!HEDRQ?C7SR! IT(,
6
. .35
6
7!HED >!B(VfBL(KC?D-,
6
. 35
6
7!HEDU@PT!XDQ?,
6
. .35
6
7!HEDU@PT KCC !:,
6
. 35
6
7!HEDU@PT!XDQ C7W).!C, CB+/ @P)D35
6
7!$#$79 $/ Q?C!XDQ?D7,
6
. .35
6
7! CI? / Q?C KCC !:,
6
. .35
6
7! CI? / Q?C!XDQ C7W).!C7,
6
. .35
Y
5
Z
[K\ ]_^ + ) 4` ?a$` *b, $
$
# c
,
_
&)4T/Y,62i=)/1W$8 =)LM465D(+, /1W ,69=?4@,A2'*](H8m2'&34e/YG
-
!" $
%+> C Ne @9?T !KQ?D7,
6
. 3%&
72(VfBCQH4DI?g-h @PT!XDQ?,;35
C!TG72(+%JH
6
eg-h D- ,!FVfD 35
Y
D #$T =/ ?EG C Ne Q?C"!XDQ?,
6
. 3%&
C!TG72(+%JH
6
eg-h Q?CKD- ,;35
Y
%+> C C Ne >!B(VfBL(KC?D-,
6
. 3 &
C!TG72 Q?g-h -
6
!T)IJHB,;35
Y
Z
[X\ H] ,
c
! ` a) k b ! ` b, $
$
#
c
x
13546),.7013$&9:542+ '7/= '*) =?4@,A2S(H* 5?4@*D0\9=?4@,A2'*f(H8k2'&)4
Q
_
&)44$
$
AN-]&)9*D(+*@Q$ * 2D&)4 ,69
-
!"
?EG Q?H !": J* !? JH: Q? &
!"# (
+> Q?,;35
6
7!98:+> Q?,;35
6
7!HEDR-
6
!L)DJI,
6
. .35
6
. -C 7,-+%.> C /172 C
C #=/ 72 #=.
Vf 1DVfBCQH I? /12(VfDICQH B
N J /172NJ
?EJH
6
W/172(J
6
JK!"?%EG/12NJK!"?%(35
Y
5
Z
[X\K]_^ + ) 4` ?a$` b, "+ a
c
,
%EG Q?He -
6
!L)DJI,
6
. .3_&
CI? /% C?- 72NJK!"??ENg-h Q?C (IT J&'KC?-,;35
72(+%JH
6
eg-h -CKG!DIU 7,T C?-D35
72(+%JH
6
eg-h -
6
,;35
72(VfBCQH4DI?g-h!?.DI,972N J g-h Q?C ,;335
Y
Z
[X\ K] ,
c
!d` b, $
$
c
, ,
c
+ )
k b
-
!"
F)9!B XD- #$D C,IED_!GVf
CI? /G!3 .5
6
7!$#$79 $/ Q?CX- ,
6
. 3 .5
6
7! CI? / Q?CX-% JK,
6
. .3 .5
6
7! CI? / Q?CX-#$ C7,
6
. .3.5
6
7!HEDR-C X>!DI+ ,T CI? /_3 .5
6
7!HEDR-
6
D7,
6
. .3 .5
Y
5
Z
[X\ [X]_^ + )4` ?a$` b, $
#% c
,
_
&)4$
%
,@WH/1*D*5A -]&39F)*b/15?4 0)5?9%?o(+F)4@FS2D9TIJ9F (+*e;\4@(+8)G =)*D46FEA 2'&)4
-](+WHW (+8)*?2D4 /1FZIJ9F0-]&3(H,.& (+*J=3*D4@F%;EdZ2'&34&$
$
91;>=?4@,A2 2D9U*?462
*
(H8 2'&34
91;>=?4@,A2 Q +CI$/
&`/Y*c;\4@468
4@LO0)W+9 d14@FEA)2D&)(H*c-](+WHWP*D462
Q
-
!"
P3Q , "+ 0#
_
&)(+*f(H*h/SLO462D&)9oF2D9N*D9-
$
$
=
$$
! ?$
%
oA@ PA@
_B(
-CD$%$/ E
3.F
(,$G%5>
4F
HDI(
()$B(,
?
%>
)&7
@
_B(
5?
$
3.F
AKJ
(
(L$M$%(A
J
LN7,:
=
o@RK *
($O?D %-
()
A/ !2+1@
_B(A$P
()Q--
J
$
*
.R(
(
)X
A
(
>)X
APJ
--9$
M
(
>)X
Y?.0% (
Z
%%>
=
[\(
:
E
A
]&.^%(
$=
#
&
J
- -_$
M
(
#
%`.0%a%($
>
=
%
@
_B($P $B$%(
J
U ]7,:
=
JoA@RK 7@
-
!"
%D_ !": $?EX>?D%&
!"# (
%D7,IRQ35
6
7!98* %D7,;35
6
7!HEDRQ?C7SR! ITS .C,
6
. .3 D .5
6
7!Ve / Q?C ITES0.C,
6
. 3 .5
!BNJHII,
6
. 3 .5
6
7!
6
. 'G IJB,
6
. 3 .5
6
7!$#$79 $/ Q?CJ # ,
6
. .3 .5
6
7!$#$79 $/ Q?CC+>,
6
. .3 .5
6
7!$#$79 $/ Q?C#$,
6
. .3 .5
6
7!
6
. N ?,
6
. 3 .5
6
7!HED %?,T CI? /> ?.3 .5
6
7! CI? / Q?C KCC Q),
6
. .3 .5
6
7!
6
. 'G IJB,
6
. 3 .5
$&%!')()*&+-,/.10203,4%!562*7.1890-:;+%=?$-0-%!8/@BADC2E
Y
5
Z
[X\ iX] ^ + )4` ?a$` b,
c
% O 17e @9?T !XQ?D7,-VfDICQH B MN72(S %VfBCQH I?43&
@R, & GF
H
?3
-. B %D
@U, 7g-h_ *JK!"?%,;3 @T -D3
2(VfDICQH Beg-h @9?T !XDQ?D7,972? 35
-F&
JK!"?% MN2NJK!" ,LJK!"?%E$M3 O 5
2NJK!"Dg-h >!DI!XQH,;35
Y
Y
Z
[X\ JIK] ,
c
!$` *b,
c
_` (*1+,. + $k b
-
!"
'). N2 &%( &'0. -%/. ')
-!1%/. %/2 %/
6$38
(
3,
>- < .1%($O"A"%
( =>,$
"A$
G
w w
":D $
7,%$3`"
$
@
&7
8$O%U(A$G"A%:%
(
' D
%U"
A
J
"A%D2
:D$
J
(
(Y"
.0%
V
B- ,$
":D "
.0$T6%A$%
_- A$
% :U
%()
@
;$
># $;
`
D
(LD.
J
(
(
$
$^Q
%$
G
(A-- 2
&M
/>
:`$
(
`
%(
:
$32 .C2 .0
A /"A%7,-
$%32
:
$
(
=$%
%(
$
>V
ON
8$
@
(
.F
"%>-
J
(A
(
$
$O
$
G
%(- -&2
&M
/>
:$
(
N6>,
5$3%:
$
(
% $%
(
ON
D%A$,$B$-
Q>"?)
2 #=
72NJH Q?
2(VfDICQH B
2EN4J$35
2(%E #.JK!"?%,92NJK!"?%(35
Y
%O"!? W "! $2$1.M
%
.P%%)
% ",D--
- "%:6 :=$O7,%$3/"
$
@.,
J
$ %(
]
.
$%:^
$
(]Y",D- -
- /*: %(
7
-
()%
. )X
2 %
/":D6:P6
-
$
&4>A-
.0 %(
7
T
-
() $ "A
$
J
(
(Y$ ^6A 7
%$ .K(
%G6)
- U"#"
-^"- -
- >)X
2 %
'"A%:%6 : 6)
-
@1,
.0%
J
32
$9"%
U.0P(A$9
J
6
-RN6$
$$% 5.
J
(,D
(:
$M
54
U% (
$:?"
$
\(
"
$
(,"A
%$` $^:
@
(
Y
(,"
-
$
J
&(ID
6"-
D. ",D- -
-V>)X
2 %
UD,-
-
/!4 J?!
! "$#&%('()+* -,.%(/0)1#
.243
765879
3:313
5?9@A56@
;
;30>
BI0@A5
3
@ABH7
;
KEA9
2
9
283LG
@M97
3
54I
3
EAN9
283
@A56@
;
U3
EAFHVWF
3
BDE
FDI
3
BXEANYI0EA5
A3
5?97EZ56@
;
BD754[
;=3\G
FHEJI
3
B]
BDEZF^I0E
>1G
9
3
FHB0_
5`@
GK3
FD7EJOaEAN:@bN
3c
B
2
EAFH9dV
3
@AFHB
G
@AFD@
;=;30;
IUG
9
3
FDB
2
@
A3&eK3
I0E
>U3
@
F
3
@
;
7f9gVh@Bi@
@AFD7
3
9gVaEAN
G
@AFD@
;=;30;
I0E
>UG
9
3
FHB
2
@
Z3XeK3
I13
I0E
>1>13
FDI
EAF
3
7
>1G
EAFH9l@5m9
;
VbNnEZF
G
F@AI97=I1>13
Op@B
G
@AF@
;=;=3
@I
2
7=5
3
B
3
_q[4_
Rr
sts
54O
3
FD@
>
uvZvZwJx
s
54O
3
F@
>y3
9@
;
_ zuvZvA{m|
R ,~} ,Q
s s
Q
@
;
2m7=5
3
9@
;
_ 6uvZvA{m|?
3
F 2
313
BHB@A[
3^G
@ABHBD7=58[
7=5?9
3
FHN@AI
3
BH9l@54O6@AFHO
R
sn
@
;
2
3
FuvZvA{m|_
,
I0EA54BD7O
3
FD@
e4;=3
@
>
E
5?9dEN.F
3
B
3
@FDI
2W2
@AB
e313
FDI
@AI
2
75
3
BA9
243~R
83UG8;
@AFL@A54O-@
@FD7
3
9gV+EAN
c
EZF32mBH9@97EZ55
3
9
c
EZF32mBF
54547=58[
54O
3
F
S
547
,}.Qc:2
7I
2
EA
3
F
Z3
FDBH7=EZ54BNnEZFL9
243UQ
F@V
Q
vZw+@A54O
]
R>
@AI
2
7=5
3
B9
243
s
R
9
283
s4
~
FD7[Z7=5
wZwZw Z9
243~R J3UG4;
@AFT@A54OU@
@AFD7
3
9gViEAN
c
EZF32mBH9@97EZ515
3
9
c
EZF32mB8@A58O
s
Q.
,
s
:} ,
c:2
7=I
2
EA
3
F
Z3
FDBH7=EZ54BNnEZFo9
243bQ
F@V
Q
vZw@A54O
]
R>
@AI
2
7=5
3
B@A54OW9
283bLR J30>1G4;
@AF
>
@I
2
7=5
3
_
.243
F
3
@ABHEZ5NnEZF9
243
B
>
@
;=;
5
4>de3
FEANBHEAN9
c
@F
3G
@I 2@[
3
B.@54O9
283~;
7
>
7f9l@9D7=EZ5dEAN
9
243
B
3
BDEAN9
c
@AF
3G
@AI 2M@A[
3
B:9E1@iN
3
@AI
2
7=5
3
B.I@A5
e3
@9H9FH7
e
9
3
OX9E1@i5
4>oeK3
F:EANzN@AI13
O
BD7=58[
>
@AI
2
7=5
3
B~9
2
@M9Y@AF
3
54E
;
EZ58[
3
F75
B
3
9ECO6@VZ_
.2
7=B(7B
eK3
I@
B
3:>
@A5?VoI
FDF
3
5?9
c
EZF 2mBH9l@M97=EA54BTI@A5iE
9
GK3
FHNnEAF
>
9
243
B
3:G
@AF@
;=;=3
@AI
2
7=5
3
B.EANzV
3
B9
3
FDO6@VZ_
_
.243
@
e
7
;
7f9gV9E
G
EZF9I0ECO
3
NnFHE
>
EZ5
3>
@AI
2
75
3
9DEY@A54EA9
243
F7B
;
7
>
79
3
O_
.2
7B7=B
eK3
I0@
B
3
I0E
>UG
7
;=3
FDB@A54O
;
7
e
FD@AFD7
3
B@
@A7
;
@
e4;=3
EA5&O47
3
F
3
5?9
G
@AF@
;;=3
@AI
2
7=5
3
B@AF
3
EAN9
3
5
A3
54O4EAF
G
FHE
G
FD7
3
9@AFHVNnEAF
3
@
>UG4;3
EA
3
FHB
TS
NnEAF
G
FHEZ[ZFD@
>U>
7=58[iEZ57f9B
s
R
uo@A54O
s
R
>
@AI
2
7=5
3
B
5?9
30;
EA
3
FHB
NnEAF79B~7
R
s
Q
@A54O
R
@AFD@A[ZEZ5
>
@AI
2
75
3
B
.2
7=5 2C754[
@M]
-
I
2
75
3
BEA
3
F
3
O
Q
NnEZF7f9B
Q
@54O
Q
>
@I
2
7=5
3
B@54O5
QS
EA
3
F
3
O
R
s
NnEZF.7f9B.5
QS
ud@A58Ob5
QS
1>
@AI
2
75
3
B
@A58I
3
EAN9
243
I0E
>1G
EZ5
3
5?9DBLEANz9
243
G
@AFD@
;=;30;J>
@AI
2
7=5
3
BC7t_
3
_
G
FDECI
3
BHBDEZFHB
>U3
EZFVi@A58OI0E
>U>
547=I0@97EZ5i7=5?9
3
FDI
754[
c30;=;
EZ51I
3
FH9@A7=5
>
@AI
2
7=5
3
B
e
9
GK3
FNnEZF
>
7=58[
G
ECEZF
;
V
EZ5+EA9
243
F
>
@AI
2
7=5
3
B0_
{4_
.243
I0ECO
3ic
@AB
c
FD79H9
3
575
G
FDECI
3
O
F@
;;
@A58[
@A[
3
B
c:2
7I
2
F
3
B
4;
9$@AB
c
@ABYO47BDI
BDB
3
O
7=5+B
3
I
B
c:2
7=I
2
@AF
3
75
3
7
e4;=3
@A54O\O47!1I
8;
9.9E
3
9
3
54O_
,
B
;
@A58[
@A[
3
B
3
_ [4_
s
G8;
79]
Q
s
Q 8;=;=3
F
3
91@
;
_ uvZv
|d@54O
LR#"
s
~R#"$"
EZF
4>
:uvZv
|
@A54ObBDEAN9
c
@AF
3G
@AI 2M@A[
3
B
3
_ [4_
Rr
K
,%
@A58O
R Q
eK3
I0E
>U3Y>
EZF
3c
7=O
30;
VX@
@A7
;
@
e8;=3
NnEZF@
@AFH7
3
9gVkEN
G
@AFD@
;=;30;(>
@AI
2
75
3
B
G
@F@
;;=30;G
FDEZ[AF@
>
BYI@A5`58E
c e3c
FD7f9D9
3
5
c:2
7I
2
I@5
e3G
EZFH9
3
O 9EO47
3
F
3
5?9
G
@AF@
;;=3
@I
2
7=5
3
B0_
5EZFHO
3
FX9E
>
@ 2
33
!1I07
3
5?9
B
3
EANd9
243
B
3
>
@I
2
7=5
3
B
2
E
c3A3
Fz7f97=B~54EA9
3
54E
[
2
9
2
@99
243iG
@AI 2M@A[
3
B
e3iG
EZF9l@
e4;3
_
.2
7B7=B
eK3
I0@
B
3
9
243dG3
FHNnEZF
>
@A58I
3
EN9
243
@A54@
;
VCBD7B@
;
[ZEZFH79
28>
B
@AFD7
3
BL[ZF
3
@9
;
V
eK3
9
c303
5
G
@AF@
;;=3
@AI
2
75
3
B
s
"
@AF
2
@9 6uvZvZw
e
|_
"
EZF(9
2
7=B(F
3
@ABDEA5U9
283
BHEAN9
c
@F
3G
@AI 2M@A[
3
B9
2
@9@AF
3
O
3Z3
BH9
e3
3
7
e8;=3
K@
;;
E
c
7=58[9
243
@56@
;
VCB9L9DEI
2
ECEZB
3
9
243
@
G4G
FHE
G
FD7=@9
3
@
;
[ZEZFH79
28>
NnEZF&B
G3
I074I
G
FDE
e4;30>
BX@A54O B
G3
I07f6I
>
@AI
2
7=5
3
B0_
.283
BHEAN9
c
@AF
3-G
@I 2@[
3
B
>
B9\@
;
BHE
e3
3
9
3
54BD7
e4;=3
m@
;=;
E
c
7=54[9
243
@A54@
;
VCBH99E7=5?9DFDECO
I
3
5
3
-
G
F
3
B
3
5m9
3
O7=5
c:2
7=I
2
@+F
3
7
3
754[
>
EJO
3U>
7=54[
>U3
9
2
ECO4B7B.[Z7
A3
5_
5+B
3
IU33
7=BH9D7=54[
c
EAF32hEA5
G
@AF@
;=;=313
5?9@A56@
;
VCBD7B0_
.2
7=BoF
3
7
3c
EN
3
7=BH9D7=54[
c
EZF 2h7=B
G
F
3
B
3
5?9
3
O
7=5WEZFHO
3
Fo9DE7O
3
5?9D7NVh9
243
@
G4G
FHE?@AI
243
B19
2
@91@AF
3
9gV
G
7=I0@
;=;
V
B
3
O9E
G
@AFD@
;=;30;
7+*
3
9
243
65879
3
30;30>13
5?9i@A54@
;
VCBD7B0_
5 B
3
I97=EA5J_q{ @ B
;
7[
2
9
;
V
>
ECO47
3
O
G
@AF@
;;=31>
754[
>
ECO
30;
7=B
G
F
3
B
3
5m9
3
OXNnEZFT9
243
E
eCH3
I
ECO47f
3
O
>
EJO
3
7=547
>
7+*
3
BI
2
@A54[
3
B9DE9
2433
7=B97=58[O
3
BD7[Z5&@54O@
;=;
E
c
BNnEZF
>
EZF
3.3
!1I07
3
5?9
G
FDEA[ZF@
>
B0_
5PB
3
I
BH9
eK3
@
c
@F
3
EAN
c:243
5
G
FDEA[ZF@
>1>
7=54[&75k@
G
@AF@
;;=313
5?9_
5B
3
I1G4;=3U3
5m9@97EZ5
O
30>
EZ54B9FD@9
3
B:9
243
5
3U>13
9DFHVA_
-
PP P p21
M M M1 2 m
Interconnection Network
! #"$&%('*),+&+!%-$
Interconnection Network
P P21
M M1 2 M
pPp
/.