3 7' 5//q o - nasa2.1 control program (figure 1) routine "intrfc" controls the...
TRANSCRIPT
NASA Contractor Report 187225
///- 3 7'
5//q o
Slave Finite Element for Non-Linear
Analysis of Engine StructuresVolume II Programmer's Manual and User's Manual
D.L. Witkop, B.J. Dale, and S. GellinBell Aerospace- Textron
Buffalo, New York
October 1991
(NASA-CR-187225) SLAVE FINITE ELEMENT FOR
NON-LINEAR ANALYSIS OF ENGINE STRUCTURES.
VOLUME 2: PROGRAMMER'S MANUAL AND USER'S
MANUAL (Textron Re]] Aerospace Co.) i24 p
CSCL 20K
Prepared forLewis Research Center
Under Contract NAS3-23279
G3/39
N92-I1388
Unclas
00511_0
NASANational Aeronautics and
Space Administration
https://ntrs.nasa.gov/search.jsp?R=19920002170 2020-02-25T04:51:27+00:00Z
4
SLAVE FINITE ELEMENT FOR
NON-LINEAR ANALYSIS OF ENGINE STRUCTURES
PROGRAMMER'S MANUAL
1.0 INTRODUCTION
The programming aspects of SFENES are described in the User's Manual. The
information presented here is provided for the installation programmer. It is
sufficient to fully describe the general program logic and required peripheral
storage. All element generated data is stored externally to reduce required
memory allocation. A separate section is devoted to the description of these
files thereby permitting the optimization of I/0 time through efficient buffer
description. Individual subroutine descriptions are presented along with the
complete Fortran source listings. A short description of the major control,
computation, and I/0 phases is included to aid in obtaining an overall
familiarity with the program's components. Finally, a discussion of the
suggested overlay structure which allows the program to execute with a
reasonable amount of memory allocation is presented.
2.0 GENERAL PROGRAM LOGIC
The general organization of the SFENES program is illustrated in Figures
I thru 6. The element routines consists of a control program and four
principal computation phases; namely,
I. Input interpretation phase
2. Spatial integrations and computations
3. Matrix computations and time assembly
4. Stress recovery and element output phase
2.1 Control Program (Figure 1)
Routine "INTRFC" controls the element computation flow. Initially, the
"Input Phase" and "Spatial Computational Phase" are executed. These two
phases are outside of the iteratlve phases and need only be executed once.
Routine "INTRFC' then executes the "Matrix Computation and Temporal Assembly
Phases". Control is referred to the "MAIN" program for all spatial assembly
and displacement computations, [KF]{U}={FD}. The "INTRFC" portion is re-
entered for convergence checking and the stress recovery phase is then exe-
cuted. The iterative process is repeated until convergence or the maximum
number of iterations is achieved. The Control program is the interface be-
tween the element routines and the MAIN program unit.
2.2 Input Interpretation Phase (Figure 2)
The purpose of this phase is to read the formatted element input data and
control data from the input file "lOIN". The data, in some cases (element
loads and local grid coordinates), is used in additional computations and is
finally output to binary files "IOEL", "IOLD", and "IOUS" for use by the
remaining phases. This phase is only entered prior to the first Iteration of
the problem. Routine "INPUT' reads the formatted data, provides an echo print
for the user and outputs all data to the output files. "GRIDG" computes all
of the remaining grid point coordinates from local grid points 13-16 and the
corner thicknesses. Routine "LOADIN" reads the input element load data and
computes the resulting grid point forces at the user input time increments.
2.3 Spatial Integrations and Computations (Figure 3 & 3A)
The "Spatial Computation Phase" is executed once prior to the first iter-
ation. The function of this phase is to perform all spatial computations and
any other "one" time computations which required spatial integrations. The
primary tasks of this phase are outlined briefly below.
a) The volume, area, and surface definite integrals are computed for the
polynomial terms xnymz I and DkxiyJzl; O<_n_9, 0<_9, 0<_i_7, 0__k_3, 0<_I_7,
O<j<7. These integrals are computed by routines VOLCOF, COLXYZ, CEAXYZ,
CNLXYZ, CURCOF, CURPSI, CNRPSI, CURXYZ, CNRXYZ, TRLCOF, VOL-, VL-, REA-,
RA-, SUR-, and SUP-.
b) Routine LOADD computes the element force vector {F} by combining the
input element loads as a function of time, (file IOLD) the appropriate
spatial integrals from (a) above, the Hermltlan time functions, and Inte-
grations over the local time ranges. The resulting combination of ele-
ment body force, pressure and traction forces are output to file "IOFO"
for intersolutlon of [KF]{U}={F} equation.
c) The final function of this phase is to compute and store the spatial
matrix partitions of [M], [K], [X], [A], [B], [Ce], [B28], [P28 ], [C],
[P28]'[B28]-I. These matrices are stored on file "IOCF",[Nx ], and
"ICPR", and "IOTF' for use by the third phase. The matrices computed in
this task are reused in subsequent iterations since the shape functions
are constant.
2.4 Matrix Computation and Time Assembly Phase (Figure 4)
The function of this phase is to compute the element stiffness and stress
matrices for each local time range. This involves the computation of the [E6]
matrices as a function of time, (routine EPQP19)and integrating over the
local time intervals. The result of the time integrations is multiplied by
the spatial matrices as computed in the spatial computation phase and assembled
into the element [Ke], [Se], [A e] and [Be ] matrices for each local time in-
terval. These computations may be made for either the linear elastic quad
plate or the non-llnear elastlc-plastlc quad plate elements (routines LEQP and
EPQPB respectfveiy). Spatial matrices are input from files "IOPR" and "IOTF'
and prior iterative values of {w} and {c) are input from file "IOUS". The
"IOA{Y' and "lOAf" are used alternately to read the previous and store the cur-
rent coefficients of polynomials in (t) used to compute the [E7] matrices.
File "IOKE", "IOAE", "lOBE", and "IOLD" are output files for storing element
[Ke] [Ae], [Be] and [Se] matrices respectively.
Routines "TBASEM" and "TABSEM" perform the temporal assembly of the
element [Ke] matrices for the "LEQ_' anbd "EPQ_' elements respectively. Files
"IOKE", "IOCE", "lOBE", "IOAE" control the input to these routines and the
final element [Kf] matrices are output to file "IOKF". For the "EPQ_' element
[Be]'[Ce ]-I is stored on file "IOLD" for element stressthe computation
computations.
2.5 Stress Recovery and Element Output (Figure 5)
The "CNVR_' routine checks for convergence of all displacement/velocity
values and stores the latest value of {u} on file "IOUL" for the next
iteration. Element stress is recovered in routines "CSIGO" or "CSIGL" for
element types "EPQF' and "LEQF' respectively. The input to these routines is
contained in files "IOTF", the current displacement/veloclty values {u}, and
"lOLl', the stress matrices [S] or [Ce]-! [Be]. The displacement/velocity {u)
and stress {a} vectors are output to file "IOUS" to be used in the computation
of [E 7] for the next estimate of [Ke]. Printed output of selected grids
displacement and/or stress values for each iteration is provided for by
routine "WRITO". This output is at the major time intervals only.
Convergence of the problem initiates the extrapolation and output of
displacement/velocity values at user specified time intervals within the major
time increments.
2.6 Displacement Computation (Figure 6)
Control is returned to the "MAIN' program after the stiffness [KF] and
[Ce-I]'[B e] matrices have been time assembled in the matrixstress [s] or
computation phase. The "MAIN' program calls routine "COMPS' which performs
the following functions:
a) Read the partitions of the [Kf] matrix (see Figure 7 tb Figure 9 for
description of [Kf] matrix)
b) Applies the user input boundary conditions to the individual partition
(eliminates rows and columns) and forms the reduced [KF] matrix.
c) Eliminates all rows containing displacement related data at times T=0 and
T=t N (rows 1-84 and rows IN*168+I to N*168+84 of the [KF] matrix).
Reads the {FF} vector partition s and time assembles the local partitions
(see Figure 14 for a description of the assembled {F} vector).
e) Applies user input boundary conditions as in step b) and c) above to the
{FF} vector rows.
f) Computes {u} = [KF -l] {F} and stores data or file "IOTP" for stress
recovery and output phase.
The newly computed displacement vector {u} is then read by the stress
recovery phase and the next iteration is entered if required.
d)
INTRFC
MAIN
L D m _ ..... _ ....
SPATIAL
ASSEMBLY
& COMPUTE
{u}
INPUT
INTERPRETATION
PHASE
SPATIAL INTE-
GRATIONS ANDCOMPUTATIONS
fdv,fds , I4A
_}, ICe-_]
IMATRIX CC_4PU-
TATION & TIME
ASSEMBLY.
[KF], [S],
[Ca-l] •[Be],
[%1
{c},
RECOVERY
& OUTPUT
FIGURE 1
6
INTRFC
READ,
INTERPRET
AND STORE
EL_ENT
INPUT DATA
INPUT
GRIDG
LOADIN
ICHK
WRITD
PRINI
IPRIN
ERROR
.-f_
FIGURE 2
SPATIALCOMPUTATIONS
[B28]-l,[P28],
[D]'[_xl],
[P28]'[B28] -I
MINV
CDNXR
PARTAL
BTC
UTILITY
ROUTINES:
WRITD
PRINI
IPRIN
ERROR
IN_fRFC
ELEMENT DATA
LOAD DATA
EPQPA
/vxnymzedv
VOL ((nH,mH,eH)
fAxnymz edA -
REA (n+l ,mH, IH)
GMPRD
VOLCOF
COLXYZ
(FIG 3A)
CEAXYZ
(FIG 3A)
CNLXYZ
(FIG 3A)
CTLXYZ
ds
f xnymz ld ssu
CURCOF
CURPSI
SURPSI
SURPS3
SURPS5
CNRPSI
(FIG 3A)
CURXYZ
(FIG 3A)
CNRXYZ
(FIG 3A)
TRLCOF
ofl[NI]"fi(t)dt
" IF]
LOADD
RDOTDT
PTPLDI
PTPMULI
MINV
CALCBF
BTCTD
BTC
CALCAL
CLOAD
{F}
SPATIAL
COMPUTATIONS
[m],[k],[X],
[Ac],[Be],
[Ce-I ]
BTCTD
VOLPTP
PTPMUL
SURPTP
PTPMUL
SPTPIO
BTC
FIGURE 3
8
COLXYZ
ivxnymz idV
VOLIII
VOL211
VOL311
VOL411
VOLSII
VOL611
VOL711
VOLII3
VOL213
VOL313
VL313
VL363
VOL413
VL413
VL453
VOL513
VLSI3
VL543
VL553
VOL613
VOL713
VL713
VL733
VOLII5
VOL215
VOL315
CEAXYZ
n m ifA x Y Z dA
REAIII
REA211
REA311
REA411
REA511
REA611
REATII
REAII3
REA213
REA313
REA413
KA413
RA433
REA513
RA513
RA553
REA613
REA713
CNLXYZ
IvxnymzldV
VOLI81
thru
VOLOII
(13 Rout)
VOLI83
thru
VLI043
(32 Rout)
VOLI45
thru
VOL845
(29 Rout)
VOLII7
thru
VOL447
(4 Rout)
CNRPSI
_s pkzldS
SURPIX
SURPYI
SUP53X
SUP63X
SUP73X
SUPYI3
SUPY23
SUPY33
SUPY43
SUP55X
SUP65X
SUP75X
SUP155
SUP165
SUP175
SUP255
SUP265
SUP275
SUP355
SUP365
SUP375
SUP455
SUP465
SUP475
SURPS7
CURXYZ
_s xnymzldS
SURXYI
SURXY3
SURXI3
SURX23
SURX33
SURX43
SURX53
SURX63
SURX73
SURXY5
SURXI5
SURX25
SURX35
SURX45
SURX55
SURX65
SURX75
CNRXYZ
IdsnnymzldS
SURXSI
SURX91
SURXOI
SUR8YI
SUR9YI
SUROYI
SURX83
SURX93
SURX03
SUR8Y3
SUR9Y3
SUROY3
SURX85
SUR8Y5
SURXI7
SURX27
SURX37
SURX47
FIGURE 3A
9
ELEMENT
OUTPUT
CONTROL
INTRFC
ISLAVE
LEQP
COMPUTE:
IS] AND lEe]
FOR ALL TIME
POINTS
LEQP
BTCTD
ERROR
121NT
131NT
LEQPKS
WRITD
PRINI
IPRIN
IOPR
s]
IOTP
SPATIAL MATRI,
EPQP
IOKE
%
lOBE
{u
IOUS
IOAO
fOAl
COMPUTE:
[Ke],[Ae],[Be],
[E7] FOR ALL
TIME POINTS
EPQPB
EPQPI9
QCOEF
EPQP26
BTC
EPQP28
BTC
EPQPI_
EPQPI5
EPQP22
EPQP21
EPQPEP
BTC
BTCTD
EPQP8
EPQP9
EPQPI0
EPQPII
FIGURE 4
I0
PERFORMTHETIME ASSEMBLY
OF
[Ke](t) [KF]
FOR ELEMENT
TBASEM
WRITD
PRINI
IPRIN
:Ke ]
[Ae][Ce-l][Be
ICe] -I
[Be]
[Ae]
[Ce]-l[Be] @
PERFORM THE
TIME ASSEMBLY
[Kelt +
[Ae]-[Ce-l] •
[Be](t) [KF]
CGMPUTE AND
STORE
[Ce-l][Be]
TASSEM
ATEMP
WRITD
PRINI
IPRIN
FIGURE 4 (Continued)
II
INTRFC
COMPUTE:{o}:[Ce-l][Be]
u
FOR ALL TIMES,
PRINT u
A_ FOR
REQUESTED TIME
CSIGO
CDISP
WRITO
EPQP
NO
IOTP
IOLD
YES
CHECK
FOR CONVERG.
LEQP
CNVRG
COMPUTJ:
{o]--[slwFOR ALL TIMES,
PRINT u
AND FOR
REQUESTED TDIE
[SCSIGL
CDISP
WRITO r. ÷
\ IOUS
FIGURE 5
i2
MAIN i
READ [_F] AND{F) MATRICES.APPLY BOUND &
INITIAL COND.
COMPUTE:
[Kf].<u) = {F)
AND SAVE {u}
CCMPU
REDUCK
CONDK
REDUCF
CONDF
DGELC
BTC
EXPAND
FIGURE 6
13
3.0 MATRIXDESCRIPTION AND LABELING
The basic matrices generated by the element computations consists of the
[KF], [S], and {FF} matrices. The matrices are stored on files "IOKF",
"IOLD", and "IOFO" respectively. The basic matrices are illustrated in
Figures 7 to 14 and are described as follows.
3.1 Stiffness [KF] Matrices
Figure 7 depicts the time assembled [KF] matrix for the EPQP element.
Each numbered box represents a 168 by 168 partition and each partition is
labeled from T O to T N (global time, were TO-0.O ). The numbering of the
partitions signifies the order in which they are_ored on the sequential file
"IOKF". Similarly, Figure 8 depicts the tlme assembled [KF] matrix for the
LEQP element. It should be noted that rows 1-84 of partition rows TO and TN
are to be reduced from the matrix before using to solve for {u}. Finally,
Figure 9 illustrates the labeling of each KF partition.
14
3.1.1 [KF] MATRIX LABELING
The [KF] matrix partitions are computed and time assembled (K F = K e +
[Ae][Ce-l][Be]). The non-zero 168 by 168 KF partitions are stored on File
IOKE. Figure 7 shows the KF matrix-partltion labeling and order of storing on
file IOKF for the EPQP element. Similarly, Figure 8 represent the K F matrix
for the LEQP element. Figure 9 is a sketch of the labeling of each partition
for both the EPQP and LEQP elements.
FIGURE 7: EPQP [KF] MATRIX PARTITIONS
TI T2 T3
TO ! 1
' "---1T1 2 N+2 i 0
T2 3 N+3
T3 4 N+& 2(N+I+i
TN_ 1 TN
0 0 0 0 0 0
0 0 0 0
o 0 0
0 0 0
0 0
__i N 2(_i 3(N+I_4
TN N+I !2(3+| 3(N+I_3
• 0
IC
_+IR- Z (I-l)I-I
IC"COL. NO./IR=RO__ NO.N -NTIME-I
where:
Note:
T(L ) = input global times
T O
i)
2)
3)
= 0.0
Matrix partition col. no. 1 contains time T 1 partitions
Partitions are output to file IOKF in the order they are
numbered in diagram
Each partition is a 168 by 168 matrix, see Figure 9 for
labeling of partitions.
15
FIGURE8. LEQP[KF] MATRIXPARTITIONS
TO
TI
T2
T3
T1 T2 T3 TN_ 1 TNi
i 0 0 0 0 0 0
2 4 I o
°i['0 9
0 0 0
0 0 0
0 0 0
0 0 - 0 0
0 O 0 0
10 0
0 I -'
0 o
0 0
0 0
• 0
-3 (IC-1)+IR-IC+IIC=COL. NO.
(1 to (N))IR-ROW NO.
(I to N+I)
Where:T(i ) = Input global times
T O = 0.0
Note : 1)
2)
3)
Partition matrix col. no. 1 contains time T 1 partitions
Partitions are output to file IOKF in the order they are
numbered in diagram above
Each partition is a 168 by 168 matrix. See Figure 3 for
labeling of partitions.
16
T(i)
G 1
R
FU I
D _ 28
G 1
R" FV I
D 28
G 1
R
"_ FW I 4
D 28
G 1
R•= FO I
D 28
G 1
R
D 28
G I
R
D 28
xU
GRID
1-28
xV
GRID
1-28
xW
GRID
1-28
GRID
1-28
GRID
1-28
[KF] PARTITION
168 BY 168
GRID
1-28
NOTE: GRID NOD ARE LOCAL
FIGURE 9
I?
3.2 Stress [S] Matrices (EPQP Element)
The equation to compute the six (6) stress components at the 28 element
grid points for time interval J is:
{o}j = [co-l][Bol]{u o} +
J ([co-l]'([Bo I] + [BT(I-I)])'{u(I_I)}) +l
1--2
[C -I][BTJ ]{u(J)} -
JT. ([Co-1]{q(I)}) + {go }
I-i
(i)
The time assembled resulting matrix equation, collecting llke terms,
could be represented as follows:
a( ) =
a( )
:( )
[sl] • u0
U I
bU2
UN
- [$2] •
(Nx28x6) (N'I68)x(N+I) (N'168
(N+I) -168 x
•168 (N'168)
qT 2
ib
0 o
0 o
(n'168) (N" 168)
Figure I0 illustrates the [SI] matrix which is computed in routine
"TASSEM" and stored on file "IOLD" in 168 by 168 partitions. The number of
each partition represents its location on the sequential output file "lOLl' as
well as the terms of equation (I) above as listed below•
PARTITION TYPE
1
2, 4, 6 .... (Nx2)
3, 5, 7, ... (Nx2)-i
CONTAINS
[Co-1]'[BoI]
[Co-I]'[BTIR]; IR=I,N
[CjI]'([Bo(IC+I)]+[BTIC]); IC=I,(N-I)
18
Figure 11 illustrates the [$2] matrix. Matrix [$2] is simply the time
assembled -[CI] -I matrix where [CI]=-[C e] with the first column removed; i.e.,
[c° ] [co ] o o o
o - [co] [Co] , 0 0
[C ] =e
[c I] =
o o o -[c o] [co]
[co ] o o o o o
[co ] [co ] o o o o
o -[c o] [co] o o o
o o -[c o] [co] o o
(N x (N+I))
(N x N)
o o o o -[c o] [co]
File "IOCE" contains a 168 x 168 partition, [Co-I]. The remaining
variables namely, {w}, {q}, and {Uo/Oo} are stored on files "IOTP", "IOQT",
and "IOUS" respectively.
Figure 12 contains a sketch of the partition labeling for both the IS1]
and [$2] matrix partitions.
19
FIGURE 10. STI:LF.SS [S1] MATRIX
T 1
T o
1
T1 T2 T3 • TN_ 1i
2 0 0 . • 0
T N
6
0
T 2
T 3
T(i ) •
TN- 1
TN
o
L_
I
1
1
i 3 4 0
1 3 5 6
3 5 7
3 5 7
"k
0 0
0 0
N'2-2
0
N*2
/
= (IC-I):2+I
(N)x(N+I)
PARTITIONS
IC
(IR+I)
IC - Column Number
IR = Row Number
T( ) _ Input Global Times
T O - 0.0
NOTE:
I) Matrix partition row number I contains time T I partitions
2) Partitions are output to file "fOLD" in the order they are numbered in
diaKram
3) Each partition is a 168 x 168 matrix, see Figure 12 for labeling of
partitions
20
FIGUREII. STRESS[S2] MATRIX
T 1
T2
T3
-[s2] ,, •
T1
-[ca-Z]
-[co-1]
-[ca "z ]
-[co-I]
T 2 T 3
o
-[co-1]
-[co-1]
0
o
-[co-l]
• -[c_-I]
• -[co -1]
NOTE:
1) Each partition is identical and the 168 x 168 matrix [Co-l] is stored on
file "IOCE" by routine "EPQPA".
21
FIGURE 12. EPQP STRESS MATRIX PARTITION LABELING
r(i)
XX
YY
zz
xy
XZ
yx
G
R
I
D
G
R
I
D
G
R
I
D
G
R
I
D
xU
GRID
1-28
1
2_
1
2@
1
2_
1
2_
1
2_
1
28
xV
GRID
1-28
xW
GRID
1-28
xU xV
GRID GRID
1-28 1-28
[SI]/[$2] PARTITION
168 X 168
xW
GRID
1-28
Note: Grid Numbers are Local
OGRID,6,t ) " IS I] • {ut} - [$2] {qt } +
t-l-N Nx t=0-N NxN t-l-N
(N+]) Partl-
Partitions tions
oo
°o
°o
°!
22
3.3 Stress [S] Matrices (LEQP Element)
The 6 x 84 x 28 stress matrices for the LEQP element are generated in
routine LEQP and stored on file "fOLD". The equation used to obtain [S] is
[S]f[E6][Nxl](GRID), where [Nxl ] is evaluated at each of the 28 grid points of
the quadrilateral plate. Figure 13 illustrates the labeling of [S]. Since
[S] for the LEQP element is time independent, the same matrix is used for each
time increment in the problem solution and the velocity terms of the {u}
vector are not used in this solution.
FIGURE 13. LEQP STRESS MATRIX LABELING
FOR ALL TIME INCREMENTS
"Jxx (GRID)
_-Oyy (GRID)
=Ozz (GRID-)
=OxY(GRID )
=Oxz (GRID)
=°YZ (GRID)
xU
GRID
1-28
xV xW
GRID GRID
1-28 1-28
[S] MATRIX
(6 X 84)
GRID i
GRID 2
I GRID 3
[i
°(6,GRID) t = [ S6X84
@
I GRID 28
](GRID) I! l84XI
i
m
m
!
IS] = [E6][N x ](GRID)
6 x 84 x 28
23
3.4 Element Force Vector {F F}
Figure 14 illustrates the force vector labeling and the time assembly of
the element load vectors. The equations to adjust the force vectors for known
initial conditions are as follows:
{FF(o)} = {Fol} - [Koo I] {u o} - [Aol] {Oo} (I)
i [Ao2][Co 1][Boi]) {uo} (2){FF(1)} = {Fo2 + FTI} - ([KTo ] + - _
([Ao2] + [ATI]) {qo } + [Ao2][Co-I ] {ql)
If N=I {FF(1)} = {FF(1)} - [AT1] [Co-I] [Boll {uo}
-([Ao(J+l) ] + [ATJ]) [Co'l ] [Bol ] {uo} -{FF(j)} _ {Fo(J+I)+FT J}
J=2,N
([Ao(J+l) ] + [ATJ]) {Oo} +
J-1 (J+1) J) [Co-I ] {qL} +(([A 0 ] + [AT( ])
L=I
[Ao(J+1) ] [Co-1 ]{qj }
The first force vector is written to file IOFF (I) for solution of the
problem [KF] {u} = {FF}.
NOTE:
(I) The above computations are not currently performed in the program. It is
assumed that {Uo} = {oo} = {q} = {0} and therefore file "IOFO" contains
the {FoIT L} vectors (unassembled). Routine "COMPS' currently preferring
the time assembled.
24
FIGURE14. {F} VECTORTIMEASSEMBLYANDLABELINGN=NTIME,TO-0.O
_LOCAL
F GRID {FTo,I)+{FTI,2}+{FT2,3)+{FT3,4}+ ... +{FT )+{F T } , {F}
Fu 1-28
rv 1-28
r_ 1-28_u 1-28
tv 1-28
Fw 1-28
Fu 1-28
Fv 1-28
Fw 1-28
_u 1-28
_v 1-28
Tw 1-28
F u 1-28
Fv 1-28
Fv 1-28
_'u 1-28
1_v 1-28
1-28%-
Fu 1-28
T v 1-28
Fw 1-28
_u 1-28
}'v 1-28
#w i-28
F u 1-28
Tv 1-28
Fw 1-28
_u 1-28
_'v 1-28
Jt
t0
../.
N-2 N-1
N-I N
j ....
tO
u m
tO
tO -
I+. -+m
_T
.
_Q
m
+
i
I
fw 1-28 ----
Fu 1-28
Fv 1-28
Fw 1-28.........................
#u 1-28
f 1-28V
#_, 1-28 "
.......... =N
25
4.0 EXTERNAL DATA SET STRUCTURE
The SFENES program uses 18 data sets during execution. The dataset
variable unit names are stored in labeled common "I_' and are initialized to
the integer unit number in routine "INTRFC". Table 1 contains the dataset
names, default unit number, routines using the dataset and a brief description
of the contents of each dataset. Table 2 lists the record descriptions and
record formats contained in each dataset. All datasets contain binary output
except "lOIN" and "16". The binary datasets in several instances contain
variable length records.
26
4J
o'o _J8) :1
°_ _
u
_ _ 0
n_ _ u
•_ 0,_
• 4J
o ,-.I E
.i.i .i.i _
II _ _li
I _ 0"_ ,--.I _ =:_
0_--, _ _J _ _•_ _ _-_._l 0 _' _
o _. ,-_ _ _ o_
-MI.-, -,-I8J ._
0
0
c_
W
w _IJo
oo
4_o
o
o
o
_M
DO
B_
0
Z0_-_
[._O0
= =_ o=zzz Z:Zb4 _=4
o
z_
00_
c_
I-I
V
,.'-',. 4-.I
0_._
Z0
_/_ Z_ _-_
0 0 0 _0
27
I"4
0
%..
,-4'
#a
<
u
o
z_-4
4-J
,-4
;..4
I=0
-,-4.iJ
O0_J
I=""4
"0l=
I=0
",-i
.&.;
I
_ Z _
,-I IN
•, Z _ 4-,
"0 eO
D
Z Z _ Z _o_ Z _
I Z Z
•, ,--, N [-' "-" ['-'Z ,"-'
Z
0
0o
.,4
-,4
o
,-4
o
o
_0E_
E_
[-__ZZ
0
m.o
4-1
00
0
0
<
Z
o •
,z: u
-,4
1.1 _-i
u t_
,,,,.4 ,-4
_ 0
I
o
_m
1,40
• N
° ?m
o _
ZZ _ _Z
Z__Z
0"" CY O"_._ 1_;-d f..d ,-]
O" O' O"
,.4[._<
Z
v
t_
v
=-,-4_n
I-4
_Z0i-4
0 0
28
,--%
Z
Z0
[.-,
0
Z
u u o .,_E (U
o
_o
o 0
• o __ U E * 0
,-_ I= ,-_ _ 0 ,.t= _: _[._.] -,..4 [.._ .,-f r._ .u .,-I o
Z0_-_
0
r_
m
o
0
4J,-_
o
_ZO_
1.1
E
,-4m
0
&J
X:
=
=0
•,4 _ 0
_-_ u oi _1 &.l _J
0
•._ _ 0._:
.c: _ m 0U
0 ,-I",'40
o .I-I _, _
_ _ _ o _m _ _a:u_ M
E-_ o b_u_ m _
[-_
=o§ "-
I-4
0cy
o%[._ ,-4rm_o cY
<mE.)
dZ
I-4
v v
-,-4
v
u_,-4
-,4
v
=
v
_ Z
_2<0 0
F-4
<oo<0
0i.-4
0i-4
En0 0
29
FILE NAME
IOLD
(Load Data)
(LEQP
Stress
Matrix)
(EPQPStress
Matrices
[Ce]-l'[Be]
IOEL
(E!ement
Input Data)
RECORD DESCRIPTION RECORD FORMAT
I
Element Load Code
((LCODE (I _J), I=I, 7) _J=l_ 6)_
42 integers/record
2
Element forces at NGRID
affected grids for this
load type and for D.O.F.
U,V_W
((FVO(I,J),J=I,NGRID),I=I,3)I
NGRID = I0, 12, or 28
.'. 30, 36 or 84 real data/record
.
If ID=2 Only element rateof force at NGRID affected
grids for this lead type
and D.O.F. u,v,w -
.((FVT(I,J),J=I,NGRID),I=I,3)I
NGRID = 10, 12 or 28
:30, 36, or 84 real data/record
NOTE: Records (2) or (2 and 3) are repeated for each input
load type and for each time point.
The data is overwritten by:
1
Element stress matrix
6 components, computed
from 84 displacement
D.O.F. for all 28 grids
i(((STRM (I, J ,K), I=l, 6) ,J=l, 84) ,Ii
K=I,28)
14112 real data/record
or by:
I
Element stress matrix
partition [C ]-I([Bo]N+
[BT]N-I)
2
Element stress matrix
partition [C ]-I.[BT]N
((DOT(I,J),I=l,168)_J=I_I68) '28224 real data/record
,((DT(I,J),I:I,168),J=I,168) _28284 real data/record
NOTE: Records i and 2 are repeated (NTIME-I) times (N=I,
(NTIME-I))
I
Element name and code
2
Element local coord.,
material prop., and
load codes
ANAM I NEL_M
21 real and 1 integer/record
(X (I), Z (I)=l, 28), (H(J),J:l, 4),
RHO, AMU, ALPHA, NU, E, YSTR, AJ,
(ILOAD(T),I:I_7)_ NONLIN94 real and 9 integer data items/
record
TABLE 2
SO
FILE NAME RECORD DESCRIPTION RECORD FORMAT
IOUS
(Element
Input Data)
lOIN
(Element Input
Formatted)
IOPR
(Spatial
Computation
Data)
i
Element stress components
(6 each) for 28 grid poin
points
2
Element disp-vel, compo-
nents (u,v,w,6,_,_) for
28 grid points
((SIG(I,J),I=I,28),J=I,6)168 real data/record
'((Ul(l,J),I-l,28),J=l,6hl
168 real data/record
NOTE: Records i and 2 are repeated NTIME times
Several See User Input Description
I
The [B28] -I matrix
((B28(I,J),I=I,28)_J=I,28) !784 real data/record
2
The [D]'[Nx'] computation
for all 28 grid points
_(((DNXPP(I,J,K),I-I,7),J=I,84),i
,K=I,28)16414 real data/record
3
The {P28}'[B28] -I computa-
tion for 28 grids
((SIGNX(I,J),I=I,28),J=I,28)
784 real data/record
I=polynomial terms 1-28
J=grids 1-28
4
The evaluation of {P28 }
for 28 grids
((P28(l,J),l=l,28), J+I,28)
784 real data/record
l=polynomial terms 1-28
J=grlds 1-28
5
The mass computation
[B28-1]T.[/v P28T.P28dV] •
[B28 -I ]
((CUUM(I,J),I=I,28),J=I,28)784 real data/record
6
The [K]_computation
[B28-1]T'[/v P28(e)"
PIT.pjdV]'[B28 -I]
(((CIJK(M,N,K,),M=I,28),N=I,28),
K=I,9)7056 real data/record
NOTE: Record 6 is repeated NLIN TIMES
for LEQP NLIN=I
for EPQP NLIN=28
and L=I, NLIN:
Table 2 (Continued)
31
FILE NAME
IOPR
(toni,)
RECORD DESCRIPTION RECORD FORMAT
Record: NLIN + 6
The [X] computation-
(J!l (([BI0-1(j)]T "
[_P28(L)'Plo T(J)'PIds] -
[B28 -lIT" [_P28 (L) .P28T(J) •
PidS] ) "ANG (K,J)) ). [B28-I ]
NOTE:
!(((CIJXE (M, N, K),M=I, 28), N=I, 28), I
{K=,I,6)4704 real data/record
K_ I 2 3 4 5 6
I= x y z x y zANG(K,J) - SIN SIN SIN COS COS COS
Record is repeated NLIN Times and L=I, NLIN;
For LEQP, NLIN=I
For EPQP, NLIN=28
Record: 2*NLIN+6
The [Ae] spatial computa-
tions - EPQP only
( ([B28-1]T'[_PIT'P28dV] +
I(((ClJA_,N,K),M=I,28),N=l,28),K=I,3) '2352 real data/record
K- 1 2
I - x y
((BI0-1 ]T. [suf T ANG(K,J) - SIN COSJ=l (J) PIO(J)
P28(j)dS]- [B28-1]T.
[£P28(j)T'P28(j)dS]) "
ANG(K,J)))" [B28 -l]
3
z
0.0
Record: 2*NLIN+7
The [Be] spatial computa-
tions - EPQP only
"{ [B28-1]T'[/P28(L)'P28T"}-I"PIdV]'[B28
Note:
( ( (CUA (M,N,K) ,M=I, 2S), N=I, 28, K=l, 3)
K= 1 2 3
l=x y z
Record is repeated NLIN times and L=I, NLIN;
For LEQP NLIN=I
For EPQP NLIN=28
Table 2 (Continued)
32
FILE NAME RECORD DESCRIPTION RECORD FORMAT
IOTP
Temporary
Storage)
IOCE
([Ce-l] Matrix)
IOKE
([Ke] Matrix)
IOAE
([Ae] Matrix)
lOBE
([Be] Matrix)
Same as File IOPR
- or -
Record 1 - EPQP only
[Ao]N partition of [Ae]matrix
i((ABIN(I,J),I=I,168),J=I_I68),,28224 real data/record
Record 2 -
[AT/N partition of [Ae]
matrix
[((ABIN (I, J), I=l, 168), J-l, 168)
28224 real data/record
NOTE: Records 1 and 2 are repeated NTIME times
- or -
Record i
Displacement Vector {u} (UI(K,I),K=l,168) i168 real data/record
NOTE: Record is repeated for 1=2, NTIME
Record 1 - EPQP Only
ICe -I] matrix
_(CE(I_J),I=I,168),J=I,168 .
28224 real data/record
Record i
[Ke] matrix partition
_(AKE(I,T),I-I,336),J=I,336)112896 real data/record
NOTE: Record is repeated (NTIME-I) times
Record i - EPQP Only
[Ao] N partition of [Ae]
matrix
((AE(I,J),I=I,168),J=I,168) "
28224 real data/record
Record 2
[AT]N partition of [Ae]
((AE(I,J),1=169,336), J=1,168)
28224 real data/record
NOTE: Records i and 2 are repeated (NTIME-I) t_mes
Record 1 - EPQP Only
[Bo]N partition of [Be]
((BEl(I,J),I=l,168),J=l,168) '
Record 2
[B7]N partition of [Be]
((BE2 (l,J), I=I, 168),J-I, 168)
NOTE: Records 1 and 2 are repeated (NTIME-I) times _
Table 2 (Continued)
3_
FILE NAME
lOAf
IOAO
(E7 CoeffArrays)
IOFO
(Integ. Force
Vector)
IOKF
"([KF] Matrix)
lOSE
"([Ae] • [Ce] -I
[Be])
IOUL
(U, V_ W,
RECORD DESCRIPTION RECORD FORMAT
Record 1 - EPQP Only
Arrays AC, ATI, AT2, AT3,
AT4, All (7, 7, 28, 4)
|(AC, AT1, AT2, AT3, AT4) I
All dimensioned (7, 7, 28, 4)
27440 real data/record
NOTE: Record is repeated (NTIMES-I) times
Record 1
Vector {F)
(((VLOAD(I,J,K),I=I,28),J=I,3), ;
K-l,4) i336 real data/record
I-GRID, J=D.O.F. (u,v,w,)
K=0, O, T, T
NOTE: Record is repeated (NTIME-I) times
Record 1 [((ACB(I,J),l-l,168) ,J-i,168)
Partition (M,N) of the 28224 real data record
[KF] matrixNTIME
NOTE: Record repeated ( l (NTIME- (I-l))-I timesI=I
Record I - EPQP Only !((ACB(I,J)_I=I,168)J=I,168)
Partition (M,N) of 28224 real data/record
[Ae]" [Ce-I]'[B e]NTIME
NOTE: Record repeated ( 7. (NTIME-I))-I timesI=i
Record I
Displacement/velcoity
vector from the previous
iteration {u}
(UNEW (I, J), I=l, 168
NOTE: Record is repeated for J=2, NTIME
Table 2 (Continued)
34
SLAVE FINITE ELEMENT FOR
NONLINEAR ANALYSIS OF ENGINE STRUCTURES
USER'S MANUAL
I.O INTRODUCTION
The purpose of the SFENES program is to provide the user
with validation of the basic matrices needed to compute the
transient displacements of a group of non-linear elements and to
provide for element stress recovery unpon convergence of the
problem. In addition, the element matrices routines have been
provided to compute resultant displacements, checks for conver-
gence, output displacement and stress and perform element stress
recovery. The program is limited by the following factors:
I. The only element currently provided is the quadri-
lateral plate element with either linear elastic
analysis or non-linear elastic-plastic analysis.
2. Only a single structural element may be analyzed
(multiple time intervals).
3. All input and output is in terms of the "local" coordi-
nate system.
4. A maximum of 25 time points (solution times) may be
requested. Output displacement times are unlimited.
The following pages describe the program and its input/
output features.
35
2.0 SFENES OVERVIEW
The Slave Finite Element procedure is described here.
Reference to Figure I will aid in the description of the solution
algorithm. The element input data is interpreted and stored for
later reference. All of the required spatial definite integrals
are computed and stored as is the one time computation of the [C]
matrix. The input element lead data (if any) is combined and
integrated over the time intervals. The force vector {F} is then
stored for later use in computation of {u}.
The iterative procedure starts with the computation of the
matrices [Ke] and either [Ae] , [Be] for the EPQP case or [Se] for
the LEQP case. For the EPQP case the initial iteration assumes
that the structural element is elastic for all time intervals but
for each subsequent iteration the elastic and/or plastic regions
are computed. The structural matrices are then assembled for
global time. For the EPQP case final time assembled [KF] matrix
is computed as [KF] = [Ke] = [Ac] [Ce ]-l [Be] and the matrix
-lmultiplication [Ce] [Be] is stored for later stress
computation. The linear LEQP case simply involves the time
assembly of each of the [Ke] matrices as computed over the speci-
fied local time intervals. The [KF] matrix and the {F} vectors
are then reduced based upon the input boundary conditions as well
as the removal of the tows corresponding to displacements at
times TO and TN (rows 1-84) and rows ((N'168)+1 to (N'168)+84)
where N = the number of input time points minus I (I<N<24). The
reduced [KF] matrix and {F} vector are used to compute the new
-l
36
t
(S_T)
CO._ll_rE:[_1, [_], [me]AT AL_.T_SAND SAVE
i
ITL"/ ASSL'_LE
[1_ ]- iX e]- [ae]
[Cel-l[Se]
_'D [Ce-I] De]
t
iI
COMPUTE:[_1, [Se]AT ALL T7.1_SAND SAVE
IT_E ASSEH3LE
[Kf]=I_e3Ah_ SAVE
FIGURE I.
SPATIAl. ASSL_,_LY
i. APPLY B0t_"DARYCONDITIONS
2. _OV£ 'l'st TOAND Tlq DISPLACE-MENT R_ D.O.F.p:f] *SD {_)
TICO_UTE: ,{u) = [_1""
---(r)SAVE
SERIES LOGIC
{u} vector ([KF] {u} = {F}). The updated value of {u} is checked
for convergence and then stored for the next iteration.
The vector {u} and the stress matrices [Ce ]-l [Be] or [Se]
-Iare used to compute the stress vector {a} = [C e] [Bee] {u} or
{a}=[Se] {u}. The displacement and stress vectors are then
stored for use in computation of the [E7] matrices for the next
iteration. After each iteration the displacement and stresses
are printed for the input time intervals only. When the problem
converges the displacements are also printed at the requested
output interval. The iterative procedure continues until conver-
gence or maximum iteration is achieved.
38
3.0 QUADRILATERAL PLATE DESCRIPTION
One finite element is provided in SFENES and that is the
quadrilateral plate element. Figure 2 depicts the local coordi-
nate grid labeling and the orientation requirements. The
analysis procedure permits transient analysis of the plate as
either a linear elastic element (LEQP) or as a non-linear
elastic-plastic element (EPQP).
39
,-4
0
II II
II fl
II fl
XH II
II II
,,-4
,-4 _-IM XH I1
X XII II,-4 e'_
X
N
FIGURE 2. QUADRILATERAL PLATE LOCAL GRID IDENTIFICATION
40
4.0 INPUT OVERVIEW
The input requirements and options are described below. The
following general rules must be observed.
I. Each input line consists of 8 fields of 10 characters
each. In some cases a field is subdivided for integer
or alpha input.
2. Integer data and floating point "E" format data must be
right justified in their respective input fields.
3. One of the material prop inputs is required.
Listed below is a brief summary of the input options and
notes regarding order and required usage.
TITLE Title information
TIME (Required and must preceed and load input)
The number of time increments +i and the values of
beginning/end of the time increments.
Contains material properties and local grid point co-
ordinates for the linear plastic quad plate element.
Contains material properties and local grid point co-
ordinates for the linear elastic quad plate element.
Defines element body force, pressure and traction load
(must be preceeded byTIME input option).
Defines any initial stress component values (at TIME =
o.0)
Defines any initial displacement and velocity component
values (at TIME = 0.0)
Displacement and STRESS output print selection (Default
= Print All D.O.F.)
EPQP
LEQP
LOAD
ISTRES
ISISP
PDOF
41
PGRD
ICND
CONT
END
Local grid number output print control (Default = Print
All Grid Points).
Boundary conditions, grid identifications (Default=
None Bounded Out)
Execution control parameters - maximum iterations,
convergence criteria and output format.
Require last input for the element.
42
5.0 INPUT DESCRIPTION
Figure 3 contains an illustrative example of typical user
input. A detailed description of each line and field of input,
that may be entered for each of the input options summarized in
Section 4.0, is contained on the following pages. Input record
description contained on these pages includes:
I) Input _ Code, i.e., "TIME"
2) Record Format, i.e., Field Usage and Mnemonic
3) Record Example, as contained on Figure 3
4) Field Description - verbal explanation of each field in
the record along with data type, limits and defaults if
any.
5) Qualifying Notes
All input is formatted and is currently read from logical unit 5
"lOIN".
43
-- . _
;PIE :.; 03-':- - " C.O -. 0.0005 0.OOIO - . .\: . ..,... ....... .,:,.[TLE " " C2 :-:" " ..- " -. .... ... .. ,-"
C_LEHENT LEOP TEST OF DUI'PUT " ' " ........ ':
.;'.-'-_":_-_':_.133102/ 86 ._ :-.-.-.-".":._'-.-,-":_.:,':.,_:',:"."!:.-.-'_.:i.":i::.:'.':..'.":_'.._.'-' -,--r-..:-','_:_.,,:_:_.-?'--'-_.:-'.-.,'.:/'_-.g:.-._;-_•._- ' ' _.-, .I-...,,- -'_'._--_.-,,_: ,..,'" ".:,. ,i' ,_'-_. ..: "-"-'_ "' _ '"_': "" ',_ : • --':-_'--"'_-,"_;"';'°._,;-£,_:,_--'..'..,-". 2_ .._': _,.'_.._
)RD ,. __,=_,-0 ....... C_O _ ..,_ . . _ -....... . ..... ........,,_
3RD' • 16C.03RD 1610.0)RD .... I$1C.O
JAD .'.i-,-._.22-1 1" . " - _:"0.0 "
;TRES C2 :
1 1
lO, C13.010,0
013
0.0 1,0 -"0.0 1,0 ,..o.© 1,0
.. .._._.-__- , ..- p . • :. . • -. " "._.._:--. :"_._'i, :- .:"
0 0.0 ..- 0 0 0 0 .-10000.0 0 0 0 I .--.
, C,_,O.OC213.C
_ZsP c_
C.O O.C 0.0 0.0 0.0C. 0 13.0 0.0 0.0 0.0
:_ C,_O.O "' C20.13.
" ClO;,O -OF
1RO
C.O0.013.0
1
C.C13. CCoO
' O.O " 0.0 0.0'C.O 0.0 • 0.0
0.0 0.0 0.0
1 1 1 1 1 1 1 1 1 1
a
MD 17
1I
1 1 1 1 1 1 1 1 1 1 11 1 . 1 1 1 1 1 1 1 1 ]
_IL,
1
_TD
1- 22
3 1
22'7
_-- 5 62E
o_._0_1- c.cool
11 12 13 1_ .16 17 18 20 21
FIGURE 3. INP_UT SAMPLE
../ .i. i.
#
o
...
44
• , ;.. -.. , ,
• . . .
!
!
hln"
-I0W
v
bJ
n_Z 0
v
v
v
I-
A
t-J Z
I- I-
^ _,v v
A
v
F-Z
II
I
IIIIIIIIII
IW0
s_
b'}00
S
00
.. Q. D.
t'OO
.J
Z WC ZX _
W I-
0
I-
0
,,J
ZW
Z00
_Jwd_ZU.
.JW
h .j
_d_Z(D
v
zz
W
Z
00_
_W
_I
_Z
Z_
_Z_
WW_W
_II
^_
II
_Z_
45
WJI-.@,-I
!.-
'3. ,,"Z 0
U
,'rW
...... Z
.t.,,.
13..J
t,.I.0
U WZ I-
<[
I.LI..1 "TI'-- rJ;,-I
I-.- 0
31
I..IJ_JL.3.ZCX
I II II II II Ii 1I II I! Ii I
/
III
I II II II II II II ii II Ii I
_8313..0"
I- .-Z_,,,itO
...... W'r.,N J U
0l..d
90
I--n
fJ
W
¢3_iWl--I
11
I--
ILlT-,-Z0U
.._1
"-'ZLL.
JILlW£Q
I..I..J
r_
_ZU
Uzm.v{D,-iz
I,-,I
-'l--
I.IJ_LOJLUI--l-Z_
:30C).J>-ILLO_I.LI.-
ZJ-- LLI
:Z::_I--
0ml--
W_Ld.J _: n"t-U_:
I- Ld "r; _IU
U ,.._ -r
n-
_-C]U
Z_
&._-__l_Z_Z_:
"1"LIJ LLI O_:]: "r _1
_0
s,-I
hiJ
_U_-Z
{'4
46
IN_UT - EP_P - ELASTIC PLASTIC QUADRILATERAL PLATE ELEMENT
FCF;PIAT :
EP_F'
I
ICORD
EXAMPLE:
I
IEF QF'
I : I I ' I I i
NL I IE IG IAMU IRHO IALPHA IAJ I
I I I I I I I -I
I YSTR I NU I I I t I 1
I I I I I I I I
IGIXENTER IYENTER IZENTER IN I I I " I
I ; I I I I I I
I
|CORD
I
ICORD
I
ICGRD
I I I I I
011 I2.0 II.1538E÷7 0.3 1.000-"2588
I : I I I
IZOO0. 12.0 I I I
I ......... _I :.......... | I
1310.O IO.O IO.O 11.O I
I I I I I
1610.0 110.0 IO.O II.0 I
I I I I I
14110.0 IO.O I0.0 II.O I
I i
ICORD 15110.0
I I
I I I
I0.2 I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I.......... I
I I I
I.......... I i
-I.......... I I I
II0.0 IO.O II.0 I
I I I I
FIELD DESCRIPTION:
CARD FIELD FIELD
NO. LABEL NO.
CONTENTS
1 EF'OP 1
I NL 1
I E 3
1 8 4
1 AMU 5
I RHO 6
1 ALPHA 7
I AJ 8
,2 YSTR 2
2 NU 3
3 - o CORD 1
3- b IG i
3 - b XENTER 2
3 - b YENTER 3
3 - _ ZENTER 4
3 - a H 5
THE ALPHANUMERIC "EPQP"
CODE TO FERFORi_ LINEAR OR NONLINEAR (ITERATIVE) COMPUTATIONS;
(INTEGER, O0 = LINEAR, 01 = NONLINEAR)
YOUNG'S MODULUS (REAL > 0.0)
SHEAR HODULUS (REAL > 0.0)
POISSON'S RATIO (F.EAL, O.O<AMU.:O.5)
MASS DENSITY (REAL)
MATERIAL PARAMETER IN PLASTICITY LAW (REAL)
MATERIAL PARAMETER IN PLASTICITY LAW (REAL)
NOMINAL YIELD STRESS (REAL)
ALTERNATE POISSON'S RATIO (NOT USED) (REAL)
THE ALPHANUMERIC "CORD"
THE LOCAL GRID NUMBER (INTEGER, 13<IG<16)
THE LOCAL X-COORDINATE OF GRID POINT IG (REAL)
THE LOCAL Y-COGRDINATE OF GRID POINT IG (REAL)
THE LOCAL Z-COORDINATE OF GRID POINT IG (REAL)
THE THICKNESS OF PLATE AT CORNER CONTAINING LOCAL GRID POINT IG (REAL>O.;
NOTE: 4 CORD CARDS ARE REQUIRED, ONE EACH FOR LOCAL GRID POINTS 13,14,15 AND 16.
IN THE LOCAL COORDINATE SYSTEM GRID POINT 13 MUST BE AT THE ORIGIN AND POINTS
13 - 16 MUST ALL LIE IN THE X-Y PLANE.
4T
I-Z_,,iEI,IJW
I,I
dr,
J
i,Il-<E.J
Q
!-.I
i-
J',,.U
rr'
,',_i .7.I--I
J
'3.13l.lJJ
i_
nZI-,I
,T.
o11
O
tF
D
n-UJ
ZLU
L9 N
IIIIII ,,III i..I .._I :,II >
LUp-
Z
x
II
-IIII
O. _I Ii'r I
Ld 0 1I U I
.J
E
x'uJ
|"
!
I-IIII
" |
III
I
IIIIIII
_'9 O C: i C, O
OOO
r'J83 O O O O
.3 ':'
,, .q O C=," - S
0 0
o .=. 8 .5
,3.
..J
43,,,-I ,,-,,I
P, l,m
m" b3
'Z r.,"O OL.} U
48
OI,-I
p-
U
W
.JWI,-t
ii
I-ZIMl-ZOU
/
'-' ZLL
..J..J I,ii.l.I,"" <I"11 /
I::1
ZU
.J
uJOE
Q
t--Z
0
J
JJJJ
EEEZ
Z
vZ_ZO
_000v
0,_ Z__
,:J_ U_ZZZJ
__000
ZD _Z Z{_{JJJJ_
_Z_UUUU_j O_JO00O={_ _JJJJ_
_0_ ZZZ
__._ 0Z
_"4ii4..iI--I
..-r
ii
.J i--
z 7_
s--,,.d hl.J EL
h-
I ZO
C
.Jr3hl
I LI.
I-- <I:
Z (:3
IIIIIiIIII
II II _ II II II II
I II II _ II P I _-l _ II N i NI Z II >" I'>"I _' I .?,I X I X
; I I! I !i I II i II i _ i :_I I _ I b.I ILL I b_I I W I _I I E3 I E3! I ',;...11 i].2
II
> > Ii-- _ I> > I
> > I
> > Ix x I
IIII! > >ILL. l..l.I _'-I LIJ WI 0 0I _ {.2
II
_ I ,I.,-I ,..,i! N
_ I >
X I x....... i II il II
L_II4
Cl,-.I
"_ LL hbJ
U CJ
•-.,i
P_C
_J
II
E.Zi--I
LU
>.I--
LU--I,-r,
I--
I.'E0Li.
:'r"ElLi.
I!IIIIIIII
II .--I "tI
I .'.'
I
> I-!
U. I
A
LLNII 11 II il
.I
&H
LT.
A
>
I-'4
v
LL
n
" o""t3t-..I I-.4
4_ "-"h
l--I
J
O
,R
II
,.., I• I
4,_: I
O I•-_ II I
II I. _ ll ll
.3,3,C00
0
"4
t'.l
II I. li NII
.Jn
x 0
49
0I,--i
I--
1="4
LIJ
_J
1--I
LL
t--ZUJI-Z
_ZLL
UJ_
I,L1
CZL3
-'_ -'_ tN IN IN l'4
0,_ -P "0 _,- E
50
LLO
_JDJE>
I i iI i 0 1I I --_ I '_"
II r.'_ II I !II I 1I I _ I
iIIII1II
-I--, [ ....I.....I-
NI='11"4
i-I
"r--4- i--II 1=I £4
•"_ II III
II1I :"4
IIi
I I_'4 I I
_" ! I•" I I
I t'q I I•-_ I I
I Il I
"----'t--7II
I_ I
[,I II
I II II II i
tO I II I!I I
i,,I--i
Jn
E
_9I.-I
-J.J
Zm
l.-.JUm
I-0
1.2U/,'r_.
m_m
a.m
(D
row,4
0../
Wt._
I.u_-
mU
WO"r.b.
ZO_,-r,
mLUO
W
LW
.J]E
ZZ0
_LO,'r
[UU
LL0C
LU
_.T-.
-JZ
UJ_
-_,-rOIL_03LO:r0_
W_W
_WW
--- E.,0_P-OW-_--O
['4
0_-0
•-_ i:4 t"3 _"
6-Z
I,.,'
>-p-
Z
F-
r3LU
,Y0LL
Z
, .-',
0
P.l
t:l
.J
-- _0
m
_j ,
_Z
J,/jJLU_
LL.J
,._,_
(J
5[
W830:Z:P
0F-
E(=J
]EI.-4
0l
01ZOI--I
I--
=
]EOU
hi
E{3LL
LLC3
ILl
E
E
h£LZ
_'7
Z JO ,'r,,', <£X t--,',1
EO
zu; u.
I.-_ +--. m
0I-
{'4
J
t-
÷ _
t'4 _ C_+_* ..JE_-- E iii
--- b.
ZLdH
00
_.J
_j ,-r,
i, j
_Z_J
O::r__ v v
A _A_
Z
ZZZ
OOO_ Z
OOOOOO0
J_J_JJ 0
_ZZZZZ_ 0
_111111
I.d
_ZILl
m$-I
I--
£LZ
CCCCCC_
Illllll
Z0
Z0LJ
Ld
O3
..J
11'-I
Z
I
O_UJn_
_r
Z C
IIIIIII
N !>- I
IIIIIIII NI X
III!I
I!I >-! XI _0
NN83
>->-L0
X
X
f.0
Ld r,
1.13 x
0
_9 --*
+
C_
S
C,
t.'_ _
IIIIII
• I 00 1l,-jI ._
0 0C,C: C',
0
,", 00o ,_
I '."4 I _ I',,II :_' I 0 0I II I103iI _ Ii _ II F-- II f.,O II _ I
52
0
I-
I-,-I
fJ
LU
._ILU
I.,
O01--ZUJ
Z0_J
.J
_Zb.
CIJJIj.ILIJ._,-., ,_I..I- J
_Z1.2
1..1.1
I-
t,-I
01
1"4
l.U
'l-t,J
'!-I.-
£4v
v
E
Zv
0
_2
mmzm
_m
m
_SJJJJJJ
__ZZZZ_Z__
ZZZZ_Z
W___
_X_N_NN_OX_NXX_
_X_NXX_
++_+++÷
II}1111
F-ZLUZ:WU(Z.J
LL0
L_
.J(3::)
.JCI,-I
t--
ZI--i
I
Z 0LL
.J_-
I
Z
LO
v
.IJ'0l:I
d
o
E
I II II II I_! !>I II I_I I_I I _t I=
LOI-=I
v
IZl
I _ I (_I Z I _I I
I 1_1 ×
IIIIIII
@ I O
dJ.-,iSIIII
-f!I! 0 0I, S d
lP., l,f"}0 0':, C,0 O,-', 0
..4 dI !
0 0
IIIIIIII 0 OI_..4 c;
I:LtO
I=-I
{3
I-n
Ed{JO3UJ
I
r_,JW
LL
53
{ni--zbJI--ZOL_
.Jw__Zb.
=tj,'lli,.i ,_
LL.J
_d(ZZ
=
H
COU
n-
Z
I
JE,
"I-F-
A
Z
Z
Z__Z
Z
_ 3 __Z JJ
B_ E_E_U ......3_JJJ
_ZZZZZZ
&OJJJJJJ
J_
H_O00000
_Z
_Z_JJJJJ
_ZZZZZZ
_ZZZZZZ
Z__Z__000000
_U_U_U_U_0111111
^^_3>
^^;&&E:>
_Z___
++ ++
Z2ZZZZZIIIIIII
A
JJC
h-Z
II
b-
([b.
Z0
h-n0
Z
O0tOb3
b-03
Z
b-ZW
IllU
JnbO
!
b.0
n
Z
!IIi
I
C_Z
0b.
I NI _-II _I.I
x
x_9&
f.l.
I >-I _-I _,'_
II xI xI O3,I &.I
II JI LLII Z>II Z_I .JI l.dI Z_i
I_.I II_ IZ_ I
II
I% II
I_ II
I Z_I &.I I._
r,
0
n
I 0IIIIi 0IIII
0
IiIII ,,_IIL1
C I
|III
0
.Jn
x r_,
0
b-O.
(J
bJ
JL_
b_
01I--ZbJ
O(3
13.J
_Zb.
_,-,j.JLdk,k,I_,,-,, _LLJ
t-,,
_Z(J
&0
(J
b_
Z<["I"nJ
W"I"
A^pZZZ
ZZZ
ZZZ____ZZZZZZ
II II _ __ _ _
OOOZZZ__
....... II II II 000000_ ZZZZZZZZZOOOm m m B B IIB II II_ ........
ZZZ
II II fl _ _ _ _ _ _ZZZ __
_v_ _ _ II II II II II
_ZZZ__ _
W___
_>_ZZZZZ_ 000000ZZZZZZ__
O&&&JJJX}NXX>
('4 f'4 £'4 ('i('4 ("4 f'4 P4 ("4 ,.',! £4 (':,1
54
JJE!--ZI.-I
EG.
li
I-.J
LIJ=
.J1:3E
ZOU
{-.Z
E
ELd=
7_
=
rr"{.5
.J
UD/
rrf.9
F-- C"7 _"',3- _-7-. E3
LL
_" 80 I•-_ (',1 I&. n I
II
r$ I'_ I('1 I
r, EL I1
I
.,-i b_
(j_ Q.
rl EL
I?" t.')EL (q
13- ('4EL
n
I 43 _,I i_. £41 "-III In 13"I EL "_III
I _"I _ -"I. 13.III t'9 I'_I _I ELII
I (4 43I EL --_I Q-III _ b'JI _ --'I 13.II
IIII"III I::IIII £L
.FM
"Pq
..J
| _ v--i
Iir
q_l ,.,..s
I .,-, -" II II II II II -" O II II II II I
v-I ...-I
T .... "" ;, "IIIII _-q .,-4
IIII
.J£L
<_XL_
.,'r_96.
55
0
I--_Li.=i
rrU
L[J
.JLdIii
LL
{nt-ZL_F-Z0U
_J,,,c;_ZLL
=JJWI..I.I_
LI..J
EZU
ZZ
_E_Lm
OOZZ
I1 !1
O0
i1_. ii.
t--I-"ZZ
a..rl
II II
I_,.m
I I
mf.n,-r. n-LLI__'
:3::3ZZ
!.- I--
O0,', n
i._rrLgO
=
I_ -.I g
r_jU_.E3D, JJ
U_{:3 LL1-4 I.L b. _-'
LUJJ 83:EOO :3:3 rr' tr ,-_Z F-- P-_ZZ I-,"1"{30 "1"
_j
ZZLIJ _.-i i.-_
i.- I:L _ b.I
oo o
•_ I I ,'r
13..I LUI ,-- L_
I::I,--_'_ ILlE ,._,.-_ I--
.'t(4 t.O LU
l-IDZ
1:3
ILlP)Z
0
WZ0Z
PJ
W
Z0
Z
Z
0
Z
o
I
zL_
l-
B.Z
Z
II
I IIIII
I III
<£It"
o
I
I Z
Z
I I
f.'_J•-" IZ
C'4•-" IZ
Z
I
Z
I--I
I ,_"I _._IIII I")IIII
4] IIIII
I/3 III •!I
f,,I II II II II II i
iN I II II II I
I_ I
III
0 I['q I
III
t.3I..=I
,o.,-=I
r-,I II!II
_q 0:] I
III
......t",l i
II
J
x
b,
z
56
0
)-O.
r_
.JU_
k-Z
Z0U
I=.J
_ZLL
lid
i, j
_ZU
to
z
0
_ zz
Z_'ZZ
Z _
_ Z_
J^O0_EE
_v
ZZ=O
:E_
Z _ZZ
"Z_
_ZZ
=ZEi_=
_Z_JJ
_Z_
n-,m
_Z
vZZ !I ."--
Z ,,,,_,,,..ir.JE{ ----__Z ZZ
hitrI--I
13IJJtrv
rr
l--hiT
C£L
.J1:3
I--Z0U
Z0
OIJJ
LO_J
D
n
I-ZOO
r, ,-_Z 0
LL
I.--JL,dICI
ir.CI-I--I
CCU
UIr.,t.
Z00
0f
I,L,I
,,,-4
IIIIII
("4. Ii JC I0 I
I
J(.I.
E Zx 0W U
0
I--Ir.,L
(-1
Wr.,
..JI,.#
I.L
5I
I'--ZbJI,--Z0
,..I
_Zb.
j.'HW_
I._-I
U
Uh, ZLU bJ[..IxIJJ
:>LU Z
0Z (J
LI. _ _
P'j _jLd
I-irv.
i.- m
_ H -Jh _
I--1--Z mmw
x _ _j
0 O_
Z ,-. J_
_ _ Z
__Z_._
Z _ Z _ ZO_Z__
__Z_
J ¢ 0 W il II_ J W ,
_Z_ W_
£4 C',I I'0
F- F- FZ _ J0.,_ U ,.'r" LLIUT I:L U
IIIIIIIIil
Zl,--I
l-
_J
W
0
_ aJ
L_ W._ID.
<Z
l.tJ| ......
C_Z<Z
Jl--C
Z 0 Zb. W
58
6.0 OUTPUT OVERVIEW
Typical output is illustrated in Section 7, Figure 5. An
echo print of the user input is always printed first. The echo
print is followed by a group of program controlled output which
contains:
I.
2.
3.
Computed local coordinates of analysis element
Labeled material properties, as input
Tables giving element load values in the local coordi-
nate system for each input time slice
4. Table of input initial stress and displacement values.
The third data output grouping is output each iteration and
contains the displacement/stress data computed that iteration.
This output is only at the input time slices. This data is not
present for the LEQP case since only one iteration is performed.
The final output consits of displacement/stress data at the
requested print time increments upon convergence of the problem.
The printed format is operator controlled for this grouping.
59
7.0 OUTPUT EXAMPLE
A quadrilateral plate of constant thickness is sued to
illustrate the input-output format of SFENES. Table I provides
the required input to solve a linear quad plate problem and
Figure 4 shows the geometric layout of the problem plate. Used
input data is illustrated in Figure 3 and each input record is
described in Section 5 of this report.
Problem output is illustrated in Figure 5. A description of
this output is contained in Section 6 of this report.. The output
contrived here is only partial (unbounded D.O.F. only) in order
to conserve space.
6o
TABLE 1.
QUADRILATERAL PLATE MATERIAL PROPERTIES, COORDINATE INPUT,
LOAD EQUIPMENT AND INITIAL VALUES
(1) Material Properties
G = 1.1538 X 107
p - .2588 X lO-3
1J = .30
(2) Spatal Coordinates
Gr id No. X
]3 0
14 lO.O
15 lO.O
16 0.0
Y
0
lO.O
10.0
lO.O
Z
0
0
0
0
Thickness
1.0
l.O
1.0
1.0
(3) Time Coordinates
0.0
0.0005
O.OOlO
(4) Element Load
Pressure Load on Top Surface of
-lO,O00t or -lO,O00t in W dlr
(5) Initial Values
Stress = 0.0 at all grids
Displacement = 0.0 at all grids
61
FIGURE4
QUAD PLATE DIMENSIONS
Y
20.. 26 27 ! 19
+ " LOi : 311/ ,11 _28 31 _23
1 i,_/_- _V _ X
LOAD AT GRID POINTS 1-12
DIRECTION +Z
VALUE -]O,O00t
62
....-
"-r' ""_" _w _ ,,, m o I,,, m o- i+ mq m_ I
0
0
0
u_
C)4.
_J
00
0
ad!
o0_¢00¢ 0
OOl
OOC 0
001 0
OO¢ ¢_
OO¢ ¢_
_ f0 II
+ .
0 ¢
0 I
_ C0 l 0
OO¢ r_
/'4r
O(4..I.LPL
O¢O¢ -..,O(
O¢ .-'*O(
r_
,,0 ,4" '_ r_l
I
/
oO.0
00
O0
I
I
n
I
III!
IIII
,mo
O0I
i .
• I
a*.a
•,.* _.(_0 !,.d
¢>0
C0¢_C
OOC
ddd
I
I
G. C "!
n
I
0t,
4U
e_
C_
CI
bCC
C
.11"¢0 CNC
C
NP"
hi
,-aN
I-
L
63
i "
1
n
b_
'i
j!
2
• a
r_
_.JOI
IJ W
• 0
D
00
@
0
C
12
4,
0
g_
0 0
0
_ ou_ i
I
i[
I
I
I
!
I *
ti
!
0
i
0
0
i
II
0
I
!
!
t
i
't
I
i
If,J
I
1
0 0W i
1
iII
l
III
1 "-[
i ""
!
i
i
i
1
!
!t
,i
I
*_ I,_ I n°_ g !
!
i
I
• I
m m
L_
H
..JC3
II
.JoU
ff
,=ul[;3
U
P
(;3
U
f_
II
.J
(:3qJ
0
!
+4. ,I. 4-+u..I uJ u3 uJ u.
C_O _o'o _OO O,O_O •OC) C_O'G _OO O, 0', O _
I I l l l
C
,.=
.iv
CO0 ! 00_
• oU. • • i
0
0
l
0_3 00_• IpL • • q
001 O._C
II
,ii
O( 00_ 00¢ 00_• • • • • o •
O( 00_ 00¢ OOI
1
O( O0 00¢ 00'
O( O0 00¢ O0
0
• I
!
f
1
At!f
I
L
ml
Z
C3
(3
_qp_
Il
21
JooJ• • • q
(_ooG
:D
c_oo(:• • • q
c_ o o (:
e • • 4
_ooc_
31
4 • • 4cJ o o c_
t
a 0 ""* N• q • • q
_ooc_
• I
00(
oo(
ooc
ooc
OOC
ooc
ooc
OOC
oocl
• • q
oo(=
OOCI •
• i i
OOC
ooce • q
OOC
OOC
OOC
ooc
OOC
I III
e • t • • 1
._,.
O0
O0
O0
O0
O0
oo
oo
O0
I !_IJ.P
0"00_0 -0"0"
oo
. . -_._s0-q_q
61
:" i'] F,-.
I
iI
,I
!
I!
I
I
!I
i
I
I
I
I
I
N
'T
i,..i
c_
_,_ N_I.+ ,i
31
i
+
i
iI
I
1
!
I
i
; !
++
I
+
I
_J
L.,
4
Om
!
• • • |
• • 41,
• -* _D,-+ ,-_'-JO' ,OP" '1 +,_ _ P-,O
,O ,O b'_ + O<r ,,YO"
,+ : I_ IP, I_ .:1" Psi O1_
, OP" +.4.,,I, r,P I_ _ +,.,I +,.i
• • e • • • • •OO O O_ OO' OO
' I I ! I I I !
• ,d *-,I I +,.4 +iJ , +,,+O0 00¢_00' O_
I I I . I I I _'I,U I_ l.q U.I UJ I UJUJ
_ W 0'1 _,,J _ F"- ,"d C
O0 00¢]00¢ _0
ml ml_( ,.,I _1 _ ,..I O0 00¢ OOC O0I 1 I . I I I I'1"
I,IJ_ LLII.Ut. tUU.ItJ, IJJt.IJ'4', N,,.4f NO,It _IPIC
O IDI' P- 1%1_I OIP
I'.-_ NOD_ P""*C ,ir,,-_
_N_ _off)¢ _ NO_F'II _'O'" "4"'4_ Ir_*-* .
,oo, _ '''gg0¢ OOC
7' P?_ 777_?UII _UJIn UJUJU. _IJLLI
I t I I
4_ I I t I
LUt I1+ ijj I ,,ij lJJ_', t_Ot =O0',
0", 10 P- _ (l_ _,.+ ( IDNI,' 0"¢ _ _ l"J lr_ IL'X , _,,I '+
fit( _ ,,O _ ,,4" CO ( ,,.* f_
• • • • 4 • • • •
, I I I I I
LUL UUU _¢ _'Wf_( Of%l_ t'U u'_ °"
• r'_¢ "¢NNQ0¢ i'_ =''.
• _¢ _ ,e c_ ,._ _, ¢ 0,4+
,,_lr d ID ,4,t <1" r"- (: "0
( :_ -..+ _ ._ N erl f_ ,.9 ,_ rtr,
¢ _OC :) 0¢] 00¢ q)O
I I I I I I Il_u J I.u l_J Uj IJJ LI JUJ
• OC ) O'C_ O" OC _00¢: _ 0_C30" 0¢ " O"
¢ )OC )OCI OOC )0
• "r
i
';_" ?..._'.
I
___/ ....
,,+ _ • • ¢ ,..
_._ _-|
69
+:";: +' ;+;_ ,+ T'-I
+__ .._._.+._ % "_____¶
7 ....
1
=
+_; ''_ 3",,i ,,ii __ q
iI
!
.+ ,
I
I •
4P
C=w,s
¢'E
i
7O
J
Z
u
[
t
q
I!!
I!
I! .I
2
=1
71
_" ,D ,7!i -
_---_---_ j _.-_--
• i
I
P
. g_ m a_ i
v_
_D
Z
r_
06t_
r_
ID
q
I
!
[
(
C
C
C
C
GI
moP,
_O4
_OC
• ° _
_OC 00000
lt!
r;
_d. o '
_ _ O_D o oo
!
|
i
!
,!• !
!
i
i
i
!
i
72
i.
-I '
i
II
I
!t ,
!
I
I
I
I
"_-i ;__,r,
.i v r
-J
L_
p-
E_N
L
.Mmq a_el-ae ......... N
/
i: c_c ooc c o Ioo I" :" ¢JC OO¢ ¢ O |OO
+ 4 + ,I, 4 + 4, 4_ + + :UJIb. UJLU{_+ UJU._UJu'UJ i
-a_ ] .Of,,, rqrr_E ,,O ,.,.. _ .,/' R I
. 4= O,-it_ .4"_4 N,-i, ,<r_li • • l • • ( • o 4 • Ii I
¢ ooc oO¢: oo¢ oo +': ' I I I I I I I I I I
I '
OC OO¢_OOCOO 1
• • I I I I I{ I I I_ I I ]uJu. I, uu,,ful wu.tu.l_w I
...+.., 4_1,..I _ ._._r+_ 00_
• , _ • , • ._ • ,
C OO¢_ OO¢ OO¢:tOO
O000C OOC _OI I I l I I I I I I
IMI.i I.UUlMILIJUJI,_ tllUl
IpC O _ V, c0 _ -I _l" ,0f--_ _O,d u",,P,,-ot RCp.
. P'-4 ID P-C,_',- U'_' _0,-I
C ODD-- ,'tl-I-_ ¢10 (_l_',P .-*'a
C OOC OOC OOC OCD
?'; ??,'; _'?_ ??LUtJL t,liJ t.IJ _ UJ t,.._ U, UJt,Up'_ I'. N,,.,*O m,,,?' C m,_
• O_ NmO u_ _.:1 f"O
' IMP- NO'P. ._ U'_.4 ¢t_'4"- f_ tt_rt ,.*,._r 0"O0",{ F"I ,..ill O,,..Ir, _,0
! C O¢_l_ P...-I-:.-dNP_ P_IN
i Ill Ill l l I lI
Wu'+,t 4"q' _'_ 4 ,41",4"OC OO¢ O COOt II I I I I I * I I
uJIJ.' LtJ I.U IJ. _j I,.IJ UL IJUUJ
C'_,£ mO'o 00,4 P'-4"
_* li'l_ O" _"l,.. 0,0-- r*.- r_:; I'1 I". 14%1%10' .*,40"¢[ O" I"..
C O4%11" *.dN_' 4"4"4 V_t_q g • 4 • I i • • _ • •
¢ OOC 01_,_ OOC O0
•_ oc Ooc oOC _o
I ! I I I I I I I t_JLL UJ_JL¢ UJ UJ u. I.UIM
:_ r_ P.. ,-_ N 4 ¢,'l ,.-, m _ 0 i
N O' I"- N C _ ,_ I/' _0 R i
C O _'l *- N _tl" U' ,0 I_" _- _ 0 _• • i • • 4 l • 4 o ii
¢ r_lO_ OO¢_ O OC_ OO
_0 00C_ OOC_ O0I I I l It I I I I I ,
I,,U I.U l,,IJ I.U I,,_I u ' P,.U uu I.U I.U J
IJU 0¢_ 00"C:_O"O( IP 0"3[: OC_ 00"_0" O< 0'0" t
• - C_C 00" CliO( 0"0" ]
J _C O_'C3 _ O( 0_¢P t
c ooc ooc oo( oo
.... • ,- - • ._ _ ._ : 2 .'l -_ ++_Z..+-.
+,]_ +,._+,,+±+.;-+
_--- ---
+
L---+-_,'__"+JY.+
I
I
o
i
ql
I
p, :;
.J
J
II!
I
• o
n|
I
00_00_ ii
1'i
-t1I
, .
i
iI •
i
' iJ
i
i
i
; I
' ii '°
i I
i1I
I
iv
I
!
i
!
|
$
• ¶o .
I
r
..... _ _-_
II
• o - _ •
,__._:____-¢- ii-_
I
I
__m.
I
: I
II i
i
k
!
I
,J
0
<:;2+
Iv(3
31
I
qde eo
• • II • • OT • •
oo °°o;ooI I tl ! I II/ !_ UJ U.4 W [- LU _U W
:_ ,0 ¢N ,4" '_ into _'_, O, (:_1 w r,'t e_| ,4. _0
• eq • • e_ e •
_ t_ U._ _ LL_ L4J I,sJ _,(.f
rl _f'_ ,-4 ,
_i ,.-i I_ ,, ...¢ I_I _ ,i=
:_.-J .,,,_,~ ~• o" • _ • •
p?,_ '°°°°,I I lie I
l",n
;gggggi;_g; LU UJ u._ I.U I.IU' l.IJ
i ..... } ...... +'°
!
' iI
!
1 ii t1
I
!
I
!
1
II
ii
I
i
+'iI....+i+........r++.++l
,it
i
!
I
i
i
I
•; r--_--T
+,,_'
+
/
r _.
I
]
.J
L..
7
N
L_
+
c: oom oO¢: ooc1
+ ,,i •
• a
¢_ OO¢= OC_¢100C• • i • • 4 • •
¢_ oo,', ooc: ooc
°
.le
q ooc= oo_ ooc• 4 • • i • • q • •
, G oooooc: ooc
'
._ 3ooaoo¢:oo¢..,: ooo_;¢;¢1 " '¢)0¢
+
_ oo_._._oomoocl+
+t°°°°i0 rJ 0 aD ,.__UO_
0 0 C3 ¢_
ooNo_• • • ii • II
! °°¢_° °c_
OOC
OOC
I I I
OOC
O0
O0
O0
O0
O0
O0
O0
O0
O0
O0
O0
O0
! It,,IJ *J_
O" _.P'C;' qT'
0"_
O0
, ,, ,,__ _,_',.__.__ -
.;-__ :----_-
, + ,._ ._ _ :-r, .,__._..__._ _._
_-._-_1,---_ -:-._-;.,
T7
,;.--
I
. I
m
7
0N
a"
L ,_ L
II
C OOC OOC!OOdCO
c ¢;_c c;c;c c;c;c_¢;F
I_ 00¢ OO(= 000 O0
3
:P
5I--
p
i
C OO000000C_IO0
c __'__
i
?_,°°°°°,_°°I I I1 I t !U.' IJ. I_L_ IJ.I LU 1.1_
OC 00' O" o0_0_0"O_ ou'Oo" 0 0,_,
0000,00_ 00_o, 0_
OC 00_00_ 0_,0" 0"
00_ 00_ 000 Oo
':l '----%-...12.,,..'
!
1I
II
t
ti
1 '
i
!
I ,
iI
1
' i!i
i
II
!
|
t
_7-i_£ --=--" ----
78
+_, -" i:". ",_ ;;"'__ ,'__
!
|!
!
u,.._
2_
.- _...
/it
i . .I
,¢
00¢ OOq: OOC O0
c;¢;¢ (;¢;c dc;c d¢;
,:,o.o.¢ o o.,: o_,: o.o.C OOC OOC. OOC O0
=)
C OOC OOC OOC OC)
C OOC OOC OOC O0
I
3
C OOC 00( ¢_0¢' C:)O
q: OOC: 00¢
dg_¢dgcOOC 00
¢
• ¢
O*"JC OOC 00_ 00
OOC OOC OOq_ O0
OCO0_ 00_00
00¢H0¢>¢ OOC 0¢_
m-._.
i
:It _ __-e_
- 1
Fl-,_
_ 1 _ ]
, 1
I
, I
I
,,,P
,4'i-I
e-,,N
0
i I _
._coocooJooooo t
© oooooooocoo i
ili i J i
= oo_ oo: =oo. oo I
I
. i i
" _oo_.oocooCoo l
:!:_ j
: C OOC 00¢ 00000, I
I
i , i i
! t
I'
i.;
,i!
]
J'e_.,.T_¢_..
-j
J
=r
o
.... - ._-_:,,.o .... ,7.-F_-o_
" O, +-4 +,,4 ,
" 'b 4' '_
U.JI IWIJ IJ.J I
0 _ , 1_4_1
3 4"_ 4'N
E +, It, _'_
• • O •I OOq OOt
• " I I !
• - ff'lq t_, P'I q
OI OOq
. t I t" i.lJI uJUJt
P-I 0', Jl i_P P'-Oq
:p ID( N "r' *
,t', I'.-.4"I
Of tr, Of
• • l II
( OO( 4OO1
fqf _l_l
O( 004
iii L
P-P C,OL
"+"( O,IP_
( OOC 00(
?, ,:p?,I.UL UJ tu _.
_'P O--*t10., f"- I/'_ I+
3 _r P',- f_' c
u'_¢ _D *J" *O_ 00"¢
( O,1"- rq,4",
, 77'0¢ 00¢
• I I IUJL I,,U t4J _,
" b'_¢ O,O_
r-r r_l ,l" I:_ ,,,_¢ NOr
( Or_l¢ ,"_N¢
C OOC OOC
P-P ,0,0_" r.JC ¢_0¢
"' I t I IuJU IM uJ t,
" _< ,O --d _
fM,4 N_<
¢ ONf" ,_-_-
fqff _q'_ _ rOC ¢_0C
,,,,d 0 , ,
+4.,
U._ L
0',_- O0 _
00¢ O0
l I ( I I
OOC 04)
I I I I IIJ,,J tl.l U UJUJ
¢0 ¢ID + 4_ ,,,0
,,,T a0 ¢ I-.,4',,O r_ _', P-1.4,,o ,,,O C I%11",,4
•o ...,* ,,,I l%clo
• • 41, l
00¢ O0
I I
OOC O0I t I I l
LJ.; I.l..; t.l I,IJ ?.L;
0 t'Jff f_U _,
0" 000 0_W
_-e=o
oomp?
• • • 11 •
??9,?°
I I I I
ulrJl
V', P,,- _'t ,,G
OOC_O
g C:,G,
I I I] I I
!
0_0100
I I II I II,_ u,J u.l uJ LIJ
_" OC:(C_U'
O" ¢':' 0" 0"_'C, 0'0"_ P"-o:I,E O,
• t q • •
+,p,", ,+ +- . ;... +," v I[ ,;'[
l
I
I
i
I
p
• i' i
t
0
I
I
I
,0
0
¢
¢
¢
¢
lIiI
• i
iI!
I
i
i "
I!
,tI
,!i!
,i
---._ -.._-
!
¢
!
!
II
!
I
I
1
_'-_ l _--_----_- _
82
_7
.\
f
B_
n_
..I
Zlm
F_l._._..o;:.:::--_'-_.':_. ", ,',__z_"__t_
i̧ iii ! /I_! ,ii!!_/ i¸¸
k OOG 00¢ OOC O0 I "
i ooc ooc ooc oo
_ooc ooc, ooc;oo |
_;_ _,:;_ _;,::_ _ J
/
, __oo°°°°°_°°_°° |
, I /
°°°°°°°°°1 °° |(_C OOC OOC O0 |t I' I I I * I I I e /
t,UU. tJJ UJl._ U.I UJ U. uJ t.LJ I
._,°_,_,_: _.°_,_. _
........ ii
• r
83
,,.__
_ 1_
--_o
"r' ._
r .
1
1 .
i _.b
r
i'
I ,
.!
I
.3 _)
..J
q:l
..,,I
7
r_
+
!
:m+
' 00¢
00¢
:D
• • 4
q [_0¢
q _00
• ( _00
U
._ " J
" + c ;d 1
I
O0
I1
i
00000
t r
oo_oo_oo j,+++ ++_++ +
+
i
+
_oaooooo
00qo01g0_o_ooc oo
I
Ii
t
Oe
!II
I
rI
e0
,-i ._Jc !? ,oo _o_o
o_
. • f • • I+_-+]:T+
I
++j.._,+,_+lu+,,,-oi+..,_::++_
!
I=;+
I
II
_.-+;_,+.._.++
I
1!
84
I
Iu
!
I!
!
i1
iIi
o
!
-+
+
1
j
I
, ...
i
I
1I
II
I
I +J
7NL_
._lIM
1
"_:
1
31
i •
_>
i
q
q
I
q
I
r- (
(
(
IJ
E
C
l:
L '_ '_'_!
"_"'Z_:,t
85
_ _i,_.__.-_
.l_
I
IP,, I
I
I
L
o IN
7
'!
¢_
9a
a
I
X,
I
• !
1
" I
lj °-
OOC• • q
00¢
000
OOC
000• • e
_00
000
00¢
00(
00¢
00¢
00¢
OOC
oool_o• • er
0 t'_ (210 0
o._.o,o.o.o.!o.o.OOC O00CO
_OC OOC OOC: O0
• • qd 1
ddd oo_oo
0000000
_,,_, ,_, ,_,_ _,_,L 7w
O0 _ 0 _ 0'_,
• * * o¢ * • • i e e.
- -, - --]. --1 -_-
86
...9
i
i
N
EfTL3
=R
( •
_oo c
0_0_.o oo_..C C 0 OOC
_o._. oo0..00, OOC
=)
=D
=3
¢
¢
e_
C
¢
_, ,! ,q
, _o oo0oo( (_1 • • • •. OOC O0
( OOC OOd O_'_C OO
c _Jde c_cJ .....00¢ O0
Or)_ O0 OOC O¢'J
OOCO0 OOC O0
OC O0 00c O0
! ! i I ! I I !tJJ u. UJ bJ LIJ d.I _ UJ U./
OC: _' O" C) C 0"0 _
OC OO _ 0 _ OC 0_0 _
gd_ dg .....O'_C O0
._.__! ._ ....
8"'
!!
!
,i
• !I
_-_-_ . _---_--,-_ _- p f_ •
• , i
I
i
.J
7_
l.t"
J
31 •
C 00( OOC
OOC OOC
3_333_
:_ .'+
0 DOC4 • • q
0 _,00
• o
J_
o _oo
a=oo
:)4=)O
:) I
!
• _o_
o_• ''d• 0t_
.J00i
; O0
i
%.
D_3C
i
DO0
• • 4
=oel!i
q r &._..--..--;
oo_oo
22132i
++
00_+00
I
I
33333
i • ".; +,t -+..+
_-++_ +:m_:++_++++_ ,.+;.++_,.+._,;.+_.!+-ii '
I'
I + +
+
I
j i
i
+. i
, I
, I
)0_0 O0
,°j+2°° , rl88
II
]
IiII!
_____.
I
i
+
+
+ .
+ ,
J
!. i
¢
..!.
1
_: o¢
Oq
4, .
101
f_Ji• oq
--. -4:1
Q'l
0o(l
O(
_. I
' uJLor
,,0ewu
_ o_r
t ooc
! i
0¢I I
L_LI
"_ . e,,la
If_c! O_ _
m •
,o?5
Y5WU
_u_ _¢
_e
• •I OOC
I !
OC
I I1
UJUw.-_l
., f'-f_...,0
( ONf"
¢ OOl:
I I
! I
_ ,,..J ¢
d ,0,-
0 ¢ OOC
_C
. • • q¢ _0_
OC 00_OC 'OOC
4.4' 4,4,4
_ '_
O_ OOCi I I I I
I I t I
• • • •
O0 00_
I I ! I I
?? °°_! I I
?? °°_I I I
?? ??'_U4 14.,I UJ I,_ I._
fe_O _r_f_
??_, ??=,
I I I I I
tl_ LL_ U.I UJ UJ t_.
e • • q •
I I II I I I
ooauo_
I I II I I I
aoor,I _m 4
N I_"_ Vl .0 f-- h• • • • • q
I I II I I I
_¢_CI0 OC
I I II I I I
D_C=C_OC
e • q • w ¢
• • ) . N
O0
t/JUJmU_
OOI I
OO
I I
t_U_h-0,
OO
I I
OOO I
LUUJNf_
h-_r,,-I,-4CON¢_rq
??
??L_UJ
N_
r,..O
m_
! t
??_U,J
• •O0
I ;
_U'_O0
I I
,._4"
! I
'_r_
L"
• I
I
o
1
• i
I
I
i "
I
1.
• II
89
.I
!
] i'.
Ii
eM
t:l
I!I
I
_ .
I
I '
B
• (
I
LI ;
: l
_ c! "
¢_ C
I
Cq
mg_
00
" 0
O0I
0!
UJ
0
J-Jl
!
Oq
Na
,01_f0_
?,U.JL
Ne
!
NCOu
F-e
_u0'1©
_Na
I I
U'_U
Or.! !
• ° t
t It I } _ I
,, ,_??
NN_O"
44 4"p? ,_ ?
? ?;?U UJ LU U-' sLI LtJ I_ UJ
,oNm_mmN N_ o" ,/" ,o _, _! ,e. N
I I t
_ OC:IO 0I I I I / I
O,l,,,l,,
I I| I I11 IJ LU I,_ ._ I.la U._ LU I._
i 41' 41_ _ _0 t"! eM e_l
• _O _,_:_ _ _ ,._'__ _
OC o00,'30C, 0 o! I I | II I I il
I I 1 | I ! | ! III
' C_',o _ o_0o100". o'.O_ t_'.1_
I
I
I
w r, ,,,, ,_ i
90
i
I i
i i
!
i
i
!
I
1IIIIIIi
I
ItI
Z
I
I
I
h
, r
r.
__..;_
J_-_-E_
.t
I
l
i
N
g!
• I
• !
. !
' i
I
i
N
I
. " . !
.. " !
• i
:r
!
!
.- OCO_
. ,b 4
_JtL
u_r,
. 0,_
QO_S. " co_
¢ C),,*F• • q
¢ f_O¢
Nr_0¢
! IuJ_
i ; *0,_
I_tw,.
( 00¢=I I
_q,u
OC:I I
UJLL
• 0_<P<P
. _a,4
m,#
?7
_0
! !
I I
_ 4",-
Om
' • e e
_ ¢ OOr..lI I
! I
o I
! !
i
00¢
?o°_oo_
_oo_o_! I f;l
ee_e
I I II I I (I I I
! I I J I !
, , _ I I _1 t
_ o_ o e_
I t
i
I
I
I
II
!
92
t ,
i .....i....t
I
;
!
t
Ii!
ti
i :!
?
i"
I •
i
i
I
. __,._._:
• I
• n
i- I
!
q _ r
f_
N
m
• k,
3
3m
C 00¢ OOC 0(:3¢
¢ g_¢ _d¢ ddc
¢ OOC 00¢ OOC
uJ
i-
- - _,_ ,,,,,,,,-
C_:O Q Q" OC
• _. •r c • .,_
_. (
i
1.1, i
1
J i "
I "II
i
I
1
1
(G
q..
¢ OOC
i II t , I
: ! i
! f
!
!
i
!
i
i Ii
I
I
'i
,!
i
ii
!
I '|
!
I
'1
f, ,.-
j....
• "] :'t
' • i1
d'
I
.... •
4'
£ " .
b
• ,-,-.,1
i
_/
L..
Z
C'3
',,._
I
r
_ C Oo
• C O0ii
l O0
• COO
ii
" i
[
_ooCO0
00! !
, U.J I,_ :
'_17't,J 0t_
£ 00
0C7
f..
!
I
II
!
i
i
!
i
i-. _
r_
I
#
I
i
r_o..
N
)<tn
_,(VI
J
.4
w Am
O0
uJ_J
.00
,-d 0
I I
N_004. 4,
_JUJ
%Jl_."O
_aw4
??
_7ll,dJ
_0
_I,IP
_0
_0
ULIJ
D_
tOC I).-_
_WP_
..fC J J"
q= >0
I
>0,
>0"
)0
• q
!!
!
• a
..° _ _
!t
.1
o !I ;
9B
I:
" I
i :: !
i
1
i
I
!
[
I
Iwl
Z
M
• f%/f_OC
' 4. 4
: I_kx
C'C
-. _;." OO
NIN• OO
_-.i gO
,00"
O0
• 00
_UIJJ
_eF
W'J.
I . I'l _"
| • -0_ "
i .4f_
- _O• _" 4'
_U.,I
• _,11_
40'1
I J,l_
.t >O
; I
)O
, 4.
_UJ
IN
._,.
m
I
!:_J
1 •
• r
;i1
_o-_
i
!
1 ;I
]
t
"- 98
_ _ ;13 -"
I
t?
I
|,!
_-_-i_-.'__'.
. ,;.]
i- 'i
_-..'!
• i.qI
I
..]
._)
L_
7
N
iIilli /_#1
':l_ I
I_Ima /4'o I
I_I'_ I
I_-_I., ,,:t_: I
O0
I l_mlI>- I_,o II>" li_-._ I -
I" I_II <J_.Ii]ooi/ /&& I
/= /_1/ _ /_1
00
I I_I,,.-q,lmI_ Io_ I
I_ IO_ II" IO_ I I
I> I_; II <I_,_,I 1
L;l°°i]
;:,___
I
...,-
7-
¢_i.i
L
iIi
),.
¢00
00_1- 4.
_ Nt'-
! I
NN
.lul
Ib. _Q"K NI_
NN
."*(%1
0OO
WW
M N_e'__ O4"
IT'J _"
q • •
U.J_
Cl ,IP '_
d 00OO
e !
_'°
I
1
!
I00
_ J
t
t
L-
7.
e-e
r N_ _m¢.wM_ eo_.m J o
• 00
.... 4. @
cdc_ "• I !
uJL/J _ .
,_., _"'c0
odd
O0
• UJLIJ
.I_ ,.d
0,.._
0
- &'.4 r_
,gd
4..I.wUJ
cc_
C_Of _
C O0
00
I ILII 14J'--I U"
I,U O_
C,m_"
--_ .=, _-:_, _ ....
]01
--; ;. .:o __]_
II
_._--,__-*_- ______-s
....__ i_t
i -
I
I4
! i .
sj.
i:- I
• !,; |
n- I
I i
I
n
n
.I• II
t
gO
7
• ¢
¢
n
I
I
!
,i
i!l:i I ! ,
I _ I
I
,
' ii
i ., I' iI I.I !.
i
i
102
i
i ' '
i
!
I
i
I
t
Ii
!
IIi
. , r
I
IiII
1
0',
Z
C_
(._
• !!.
Nf',' OC
- " + 4
• i,I.J U
)" . li_¢
I/I IC'CU_I*.
• I" OG
(,. I !
- l%1 I_i
U.lU_
'4 O'I_
ml ,.4_,mr_l
O0
O04, +_ttJ
-ql'_
'_ 00"
_0
_0
J 11"4"
! !
_0
f _...4
I
!) kJ
,_,
C 0
III!
103
.. 1̧
I
i
_J_ i_-,q __;I
II
mw
Q
I
0g-I
=[
N
r_
__ _ ,i;e iw mo °
N¢_I• 00
4. +
_,1 ,ID<D:_ .dr.-_ w,.,, P.-" i_,iP
el'"OO ..
-. , I I
OO
W_
.._._
OO !
OO• .4.4.
UJUJ
K 0"_
U_ IDP,-¢00
ql • g
clo0
N_
!ww
I , (=1,4:,-..,
! OOO
II NN
J oo1 u_u_
q • 0t=OO
+ 4,
'_ _._ _._
i P"_
|1 . q • •
I coo
! IU,J_
'UJ O@"
C_Oi i • •
._-2--ff-/I
...!_:_',',:i:_......._ _ ..... "_......... I ............. ! .....
I ,iI
i
I
i
104
• I
t
!
v I
7.
0ul
_°
- 00
IJuUJ
• y'_l_
,ID .,,I
N)(
( OO
NN
OO4" 4"
_UJ
K e_i ,-4U_ 0,0
4,0
e., I_-C, "* N
C_OO
I_P'I
I.UUJ
O,0N l_ ti'_e,a 0,0"
,0,.d
(: "-* N
(,_fe,IO0
+ 4tuuJ0,0
t4 ,0,-4
N.f
C_ ..i N
_dd
UO
+ 4.UJ_J
X cO_
N,4P,D,,O
(%11_
O0
! !U,IU.I
1" 01_
0@"
cdg
e_ _ q m
105
_-_-_-.;-_ -_
,_ -_! _=-'_-i
i
J
N
Z
,r',,,
!
i
),,,.
C
X i
Kt_
I
a
),,,,O)_
aE
),,,.)..
ad
!
I)(: I)(o
c
0I
0
_NOO
_N
I!OO
Oo01
OO
NN
OO
WW
N_
N_$1
OO
N_
W_
iiO0
N_
a_
iI
I!
_[i ;'_
fI
)
Ii"t
9
!
) - . •
I
I
L.
r_
Z
m
...... _ : _1._..... _-_
J
+ !i
I. OO
_J
NK4q)
OO
OO
C OO
¢ OO
¢ OO
t_
¢ O0
ccJcj
)<
¢ OO
¢ OO
OO
...dO,
5" O_*
*-- O¢ _
e *
C OO
_.",.C_ji_,: ,,_ ,+,,'""=,.
_-_-_-.___.g+,
_L_.
!
Z
0
0
• i
(
q
(
¢
(
(
C
J
!
C
C
A
O0
O0
O0
÷ +UU_
NO
DO! !
,UUJ
%lr,_
??U_
'q4"
?°_0_0
D_
q_
)0
I
t I
J
IJ_
e •
I
I
I
i
!
108 "
I (
l
-- 4W
!
J
V
tr_
..o
3_
(3N
i_ i. •
_r_
b')
C
N
J
c
14:
I
III!!
1iI
i
OO
4 4
uJuJ
f_N_O--*
N_
NNOO
4 +t;JUJ
f_..d
OO
OO+ 4tUUJ
)< <_,-*
f_lr_
"*O
t.lJ UJ
_O
;" ..C NU'_
O0: 00
wul
_ -'°m.8"0_
• t
,,O-_
_f,,.
COO
I !
_'3m
! !II,J_
r c _
109
L....
L
I
_D
0
. /
UJUJ
O0
iii,_, o ,
)¢4_
" . • e ,
• . - O0'g" IUJI.U
X .- ,11_ IDO
,00
.iwao_
C O0
04. I
! I
O0
4 4..LI IJ.I,.. p,.
X !+'1P"
CIO0
I
O0
I-JuJ
u,- 0_'
C _'_
egg
. - ..... ,-..
lilI I
!,
i
Y
L,.
l".,,
'.,,..
_ N ,,, _., e _. g . .o "" " ".... ¢
:r?; :'
I'" '|
II"ii "I ' '
bOO _'
N
• 1I O0
oo .:
¢
¢
C
4 '
Ci
¢
X
¢
¢
zI... -
¢
C
O0
o.0.O0
O0
O0
O0
O0
O_
O0
I
!
,. ,, _, _,.-_:'_
111
l
I
I
I
I
I
,_ '5 '_ _,_"_r
I
II
IIII
II
n
!
I
I
II
|
?
!
1
Z
0
' O0
_UJ
N OgO
O0 '-• u
N_NO0
X _0 _
N_
_0
_04
0_
,_ . 00
P?
• p_PO
,I ,d.lP
JU__0,,I
. _
i •
4 _,4Pip
!
C _
_ g
+ i
+
• .
° "
++
.-+• ..
i.+"
t
+
t
u
I
i
i
_J
0N
t.i
1
• fel(_"': O 0
+ 4
i
' 1
°_wm
==: _'_ ";'l i" "r-E
114
1
II ;i
I
i
I!
I
:1
H i' i, i
;
I
i
!
!
1I
!
i
-!
J
_)
Z
¢ O0 ':
NNO0
WW
Ne_
00
,,_,_
<1"0"
_U,J
edgi !
O0
. ,,tO,,
cd_! !
Wu_.... _0
eg,_• . ! I
O0
_ _uLJ
"_0'
_ o0,
I= V_ O"
_= ....
I
u
I15
_-_--_
• -_--;
!
I
• r
1
- i
I
i
i
I
i
Ii
• iJ
• i
I
: F
lw,
N
!
!
I
I
116
,__,:
_,r_
L
i• I
• I
J
N
=,,
r_N
I
-'_,. _ ; . _-r'_
117
=-_.:,i_i_ _":
I
!
__ _-rr _-,:-_: i
= _,
i
!
I
I
L
"4"N
C_
I
, m_]........I---I1
t
I
-!
o ;
118
._' .',_ ?_I- 'h ;" _,d'4"6"6
|
;
Ii
iI,I
i
r.
% • i
,r.
i
• I
J
Z
N
o"
!
_T
119
J..E_
i
• I
I
!
I
I
.°
J
,0
N
gZ
o-q
IIi
l
i
121
F_
+.,I++:-+,_++_
,+
.+• +
• +,
++++"
:"'. I:..!!i I
¢:;'
+
:.T :
• _2+
:.:,. ,
+i
!I " 1• _.: +t ,, i
1
i
• i
| . 1
. , ,
i
• j
i
"it:P,, : + I
ed
Z
M
,lb
I
t
(
1
C
c
e_|
o
r,_f0¢
)(-J
)0
Jq._
_0
JLU
tf_
,fe_
'e,p,,.
,0
II, U
N
0I
N
e_r_
0
!
0
4.
,0
0
0
I
0
I
7"
I
tIIJIII
Jf iJ
I
t
122
i
i?-_: ._'_?
I.
i _ .
.....)
Form Approved
REPORT DOCUMENTATION PAGE OMBNo.0704.0188Pubic rel:x)¢_ busden for this oo_flon o/i_forrnatk_ Is eMlmated to average 1 hour pe¢ response, _,dud_ng the time _r rev;ew_n 9 insb'_'_,'mwc:hk_ existing data sou¢ces,
Oa_dng and maintain;rig the data needed, and con_O _ Nr_ewln9 _ c_ of information. Send o0mrr'4¢_ mg&dlng this bucd4m e|Uma_ o¢ any olher aspect of this
oo_lect_on of infon'na'Jon, including suggestions for redudn 9 _is burden, to Washington Headquarters Serv_ea, D;md_ate fo_ information Opere_ons end Reportl. 1215 Jefferson
Doyle Highway. Su;te 1204, A,'tington, VA 22202-4302. and to _ Office ot Management and Budget. Paperwork Reduction Project (0704-0188), Wsshin0ton, DC 20503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVEREO
October 1991 Final Contractor Report
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Slave Finite Element for Non-Linear Analysis of Engine Structures
Volume B--Programmer's Manual and User's ManualWU-505-63-5B
i
S. AUTHOR(S) C=NAS3-23279
D.L. Witkop, B.J. Dale, and S. Gellin
7. PERFORMING ORGANIZATION I_IAME(S) AND ADDRESS{ES)
Bell Aerospace-TextronP.O. Box 1
Buffalo, New York 14240
9. SPONSORING/MONITORING AGENCY NAMES{S) AND ADDRESS{ES)
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135 - 3191
8. PERFORMING ORGANIZATIONREPORT NUMBER
None
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
NASA CR- 187225
11. SUPPLEMENTARY NOTES
Project Manager, C.C. Chamis, Structures Division, NASA Lewis Research Center, (216) 433-3252.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified - Unlimited
Subject Category 39
12b. DISTRIBUTION CODE
13. ABSTRACT (Maxlmum 2OOword:)
The programming aspects of SFENES are described in the User's Manual. The information presented here is provided
for the installation programmer. It is sufficient to fully describe the general program logic and required peripheral
storage. All element generated data is stored externally to reduce required memory allocation. A separate section is
devoted to the description of these f'des thereby permitting the optimization of I/O time through efficient buffer
description. Individual subroutine descriptions are presented along with the complete Fortran source listings. A short
description of the major control, computation, and I/O phases is included to aid in obtaining an overall familiarity with
the program's components. Finally, a discussion of the suggested overlay structure which allows the program to execute
with a reasonable amount of memory allocation is presented.
14. SUBJECT TERMS
Computer code; Nonlinear analysis displacements stresses time; Shape functions; Nodal
representation; Four-dimensional; Solution algorithm
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATIONOF REPORT OF THIS PAGE OF ABSTRACT
Unclassified Unclassified Unclassified
NSN 7540-01-280-5500
PRECEDING PAGE BLANK NOT FILMED
15. NUMBER OF PAGES
124
16. PRICE CODE
A06
20. LIMITATION OF ABSTRACT
Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18
298-102