I LIBRARY COPY · 2013-08-31 · • i library copy nov24 1967 r,_anne9 spacecraft center houston,...
Transcript of I LIBRARY COPY · 2013-08-31 · • i library copy nov24 1967 r,_anne9 spacecraft center houston,...
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• I
LIBRARY COPY
NOV24 1967
r,_ANNE9 SPACECRAFT CENTERHOUSTON, TEXAS
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Z' -I
• Og WUO_I AJ.l'll_)¥d
SID 67-498
STUDY OF APOLLOWATER IMPACT
FINAL REPORT
VOLUME 5
USER'S MANUAL- NO INTERACTION
.MW.1967
(Contract NAS9-4552, G.O. 5264)
GPO PRICE $
CFSTI PRICE(S) $
-,,.;' Prepared by-v, Ha...4_.opy (HC)
_: J.P.D. Wilkinson Microfiche (MF)
(Author)ff 653 July 65
/ F.C. H_
Program Manager /Structures and Materials
Approved by
L.A. Harris
istant Manager
e and Technology
NORTH AMERICAN AVIATION, INC.
SPACE DIVISION
https://ntrs.nasa.gov/search.jsp?R=19680002458 2020-05-19T18:32:46+00:00Z
PRECEDING PAGE BLANK NOT FILMED.
FOREWORD
This report was prepared by North American Aviation, Inc., Space
Division, under NASA Contract NAS9-455Z, for the National Aeronautics and
Space Administration, Manned Space Flight Center, Houston, Texas, with
Dr. F.C. Hung, Program Manager and Mr. P.P. Radkowski, Assistant
Program Manager. This work was administered under the direction of
Structural Mechanics Division, MSC, Houston, Texas with Dr. F. Stebbins
as the technical monitor.
This report is presented in eleven volumes for convenience in handling
and distribution. All volumes are unclassified.
The objective of the study was to develop methods and Fortran IV
computer programs to determine by the techniques described below, the
hydro-elastic response of representation of the structure of the ApoUo Com-
mand Module immediately following impact on the water. The development
o£ theory, methods and computer programs is presented as Task I Hydro-
dynamic Pressures, Task II Structural Response and Task ILl Hydroelastic
Response Analysis.
Under Task I - Computing program to extend flexible sphere using the
Spencer and Shiffman approach has been developed. Analytical formulation
by Dr. Li using nonlinear hydrodynamic theory on structural portion is
formulated. In order to cover a wide range of impact conditions, future
extensions are necessary in the following items:
a. Using linear hydrodynamic theory to include horizontal velocity
and rotation.
b. Nonlinear hydrodynamic theory to develop computing program on
spherical portion and to develop nonlinear theory on toroidal and
conic sections.
Under Task II - Computing program and User's Manual were developed
for nonsymmetrical loading on unsymmetrical elastic shells. To fully
develop the theory and methods to cover realistic Apollo configuration the
following extensions are recommended:
a. Modes of vibration and modal analysis.
b. Extension to nonsymmetric short time impulses.
- iii -
c. Linear buckling and elasto-plastic analysis
These technical extensions will not only be useful for ApoUo and
luture Apollo growth configurations, but they will also be of value to other
aeronautical and spacecraft programs.
The hydroelastic response ol the flexible shell is obtained by the
numerical solution of the combined hydrodynamic and sheU equations. The
results obtained herein are compared numerically with those derived by
neglecting the interaction and applying rigid body pressures to the same
elastic shell. The numerical results show that for an axially symmetric
impact o£ the particular shell Studied, the interaction between the shell and
the fluid produces appreciable differences in the overaU acceleration of the
center of gravity of the shell, and in the distribution of the pressures and
responses. However the maximum responses are within 15% of those pro-
duced when the interaction between the fluid and the shell is neglected. A
brief summary of results is shown in the abstracts of individual volume s.
The volume number and authors are listed on the following page.
The contractor's designation for this report is SID 67-498.
- iv -
INDEX FOR FINAL REPORT
"Apollo Water Impact"
Volume No.
4
5
6
9
10
11
Volume Title
Hydrodynamic Analysis of Apollo
Water Impact
Dynamic Response of Shells of
Revolution During Vertical ImpactInto Water - No Interaction
Dynamic Response of Shells of
Revolution During Vertical Impact
Into Water - Hydroelastic
Interaction
Comparison With Experiments
User's Manual - No Interaction
User's Manual - Interaction
Modification of Shell of Revolution
Analysis
Unsyrnrnetric Shell of Revolution
Analysis
Mode Shapes and .Natural
Frequencies Analysis
User's Manual for Modification of
Shell of Revolution Analysis
User's Manual for Unsymmetric
Shell of Revolution Analysis
TO
Author,,
Li and T. Sugimura
A.P. Cappelli, and
J. P.D. Wilkinson
J. P.D. Wilkinson,
A.P. Cappelli, and
R.N. Salzman
J. P.D. Wilkinson
J. P.D. Wilkinson
J. P.D. Wilkinson and
R.N. Salzman
A.P. Cappelli and
S.C. Furuike
A.P. Cappelli,
T. Nishimoto,
P.P. Radkowski and
K.E. Pauley
A.P. Cappelli
A.P. Cappelli and
S.C. Furuike
E. Carrion,
S.C. Furuike and
T. Nishimoto
- v -
PRECEDING PAGE BLANK. NOT _LI_ED,
ABSTRACT
This volume is a userts manual for a computer pro-
gram which determines the dynamic response of a shell
of revolution during a vertical axially symmetric impact
into an incompressible fluid. The Program uses the
theory developed in Volume 2 of this report where nointeraction between the fluid and the flexible shell is
accounted for. The hydrodynamic pressures are deter-
mined on the basis of a rigid-body theory, and are applied
to the shell as a forcing function. The results are intended
for comparison with similar calculations derived from
Volume 3 and the UserWs Manual of Volume 6 where the
hydroelastic interaction is accounted for.
- vii -
PRECEDING PAGE BLANK NOT HU_ED.
CONTENTS
I.I
Z.l
5.1
6.1
7.1
LIST OF ILLUSTRATIONS
LIST .OF TABLES
INTRODUCTION .......
l.Z Load Map . .......
PROGRAM FLOW DESCRIPTION . . .
2.2 Program Deck Setup .....
RESTART .........
INPUT DATA FORMAT.
4.2
4.3
4.4
4.5
DECRD Subroutine.
Data Deck Setup .
Call DECRD (DA) . .
Boundary Conditions .
4.5. 1 Top Boundary .
4.5.2 Bottom Boundary
Call DECRD (GDA). .
Call DECRD (CDA). .
• 6 • • • • •
SAMPLE PROBLEM . . ....
5. Z Sample Input Data for the Start from Zero
5.3 Sample Input Data for the Restart" . .
5.4 Sample Output .......
WARNINGS AND RECOMMENDATIONS . .
6.1.1 Choice of Time Interval . . .
6. I. 2 Number of Iterations . . .
6.1.3 DECRD ......
PROGRAM LISTINGS ......
Page
xi
xi
9
13
15
17
18
20
21
22
22
25
28
29
33
35
42
49
81
81
81
81
82
- ix -
PRECEDINGPAGE BLANK NOT FILMED.
LXST OF ILLUSTRATIONS
Figure
1
ZFlow of Executive Program 157 DR
Model of Sample Problem .
Page
• I0
54
LIST OF TABLES
Table
I Description of Links.
Page
1
- xi -
t
_ ,? 1.1 INTRODUCTION
The computer program for the calculation of the dynamic response
of shells of revolution during vertical impact into water when no interaction
is present is written entirely in FORTRAN IV and makes use of the overlay._'.J!!':J:feature of that language. The program has been checked out in NAASYS, the
NAA adaptation of the IBM 7090/7094 IBSYS/IBJOB system; and uses the
-_ NAASYS library routines shown in the load map, pages 4 to 8, inclusive,• _ of Section I.Z. r
The NAASYS input tape is Unit 5, the output tape is Unit 6. In addition
to:these files, the program uses Units 8, 9, I0, and 11 as scratch tapes,and Unit7 as the overlay tape. NAASYS itself is stored on Unit I.
The program is made up of an executive program and eight links, all
of which are called by the executive program. A brief description of eachlink is shown in Table I below.
Table I. Description of Links
Link
No.
0
2
3
4
5
6
7
8
Name
Executive
GEOM
CDAFIT
ACCN
DEFLTN
PATH
INTLDS
PSUMS
PIX
Purpose
Reads general data, DA, and controls flow of
execution of other links
Reads geometric parameters. Prints all geometric
input and calculated values
Sets up stiffness parameters
Computes hydrodynamic pressures onthe shell
Calculates the deflections due to the pressures
Controls flow after computation of deflections.
Computes velocities and accelerations
Computes internal loads
Outputs all computed quantities
A dummy subroutine for a CRT Plotter
- 1 -
1.2 Load Map
PRECEDING PAGE BLANK NOT FILMED.
- 3 -
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-il
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u.I UJ U.I UJ UU UJ; UJ
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Z Z _- Z Z
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Z:' Z Z Z_ Z Ziml_ i.i iml
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• • • •
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ON
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h-
ua
i
I
F
N _ 'N ffl 'N N N 'fit I_
E _ ..I
Z-- iZ uJ Zxujr_ luJ _- u4_
UJU ]14J Lu U4
i
-o I-."
Z Zua_ IJu
IJuZ IJLI
"1"
Z --,Z Z ZuJ [ P_u._ uJ l.u:_
_00 _0 _n 0
TU. Z U EQU UUW '_
N ;
.f
_z
m
Z Z :
_. '_ U_ I
I
II
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0 _-
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°•._ 0
f15 wr_
Ill 8
uJz
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J
-8-
, k
Z. 1 PROGRAM FLOW DESCRIPTION
An overall flow diagram of the executive program 157DR is shown in
Figure |. A listing of the complete program is shown in Section 7. I.
- 9-
"\
I,/
• i I
S
i
READ TITLE ]p, Vo and W
L J _ t i
- 10
Ti_ - 0Rewind scratc
tapes
Read shell data
Set time
interval
TDEL
r
20
call GEOM
reads and computes geometric
parameters
2Sl'-Rewind Unit 8 1
D
Figure 1. Flow of Executive Program 157 DR (Sheet 1 of 3)
- 10 -
TFILT, O
ii I
@
I , .,x, _oI1_ I i
I,c,alCRmT I! read and set up
I stiffness! pa_ters
&-_- oO L-T .0
<0
Figure i.
I
call ACCN
calculate impact
pressures
-1 40 ,
Call DEFLTN
calculate
deflections
I Call PATH
determines program
Computes
velocity & accelerations
>0
Flow of Executive Program 157 DR (Sheet 2 of 3)
- 11 -
.:H
/..0
I jT "¸
outputs co_uted I
_0
_r .ooi
721LT.001
_0
90
= 0
80
Call PIX
Punch outputFor a restart
©Figure 1. Flow of Executive Program 157 DR (Sheet 3 of 3)
- 12 -
2.2 Program Deck Setup:, J
As explained in Section I. Ij the deck is set up in overlay regions.
Each region is denoted by a $ORIGIN control card. A list of the setup is
shown below. It includes the control cards and deck names. The order of
these decks must be kept in the given sequence.
- 13 -
I
• j,.
_rO1 Cards_ L_,: ..
":._.,"Sm_'rc
$ORIGmSmF'rc
:,$1BFTC
$1BFTC:SO.Gin$IBFTC _
$LBFTGSO.GIN$IBFTC
$1BFTC
$1BFTC
$ORIGIN
$IBFTC "
$ORIGIN
$IBFTC
$ORIGIN
$OBFTC
$ORIGIN
$IBFTC
SDATA
157 DR
MMPY
MADD •
CHAIN = - _ .
_TaY. •
c_...cnA,_TC0DSENTP
CHAIN..
ACCN2
PMAXX
CHAIN
157DRI
MSUB
INVRS
CHAIN
WHERE
CHAIN
157DRZ
CHAIN
FS UMS
CHAIN, SYSUT2,LNK6
REW
Subroutine s, , , Lu ,,
Main program
ADD"..
GEOM
CODIMA
CRVFIT
CODI/_A
ENTERP
ACCN
PMAXL
DEFLTN
MSU
INV
PATH
INTLDS
SUMS
PIX
- 14 -
3. I RESTART
In many calculations, it may be desired to restart the program at some
time t s without recalculating all the response quantities from zero to t s. In
addition, if it is desired to calculate the response atmore than about IZ0 time
intervals, it is necessary to make a,restart (see Section 6. I. 2).
For a run from zero, the following indicators are set:
: o.oPNCH = I. 0
Here, the condition RESTRT = 0.0 means that it is a start from zero. The
condition PNCH = I. 0 means that at the end of the job certain quantities will
be punched on cards to be used as data in a future restart. Thus, part of the
output from this job will be some cards containing the arrays
TIMX
ZP(K, L)
ZZP(K, L)
Z3P(K, L)
OMGZ(L)
This punching is done by the executive program 157DR.
In order to restart the job, the following indicators are set in the
input data:
RESTRT : i. 0
PNCH : i. 0
Here, the condition RESTRT : 1.0 means that the punched output data of the
previous job is to be read as input data. The indicator PNCH = 1.0 means
that there will also be punched output at the end of this job. If PNCH = 0.0,
no data will be punched and no future restart will be possible. The punched
cards are put at the end of the data deck. They are read by subroutineCRVFIT.
- 15 -
pB,EGED|NG pAGE BLANK NOT I:iLI',AED-
4. 1 INPUT DATA FORMAT
Data are entered into the program by three subroutines.. The
executive program 157DR reads the hydrodynamic data, and the DA region
of the shell data. Subroutine GEOM reads the GDA region of shell data,
and subroutine CDAFIT reads the CDA region of the shell data. The regions
DA, GDA, and CDA are read by means of the DECRD subroutine.
- 17-
4.2 DECRD Subroutine- ....7.. 06 3.......
The data in regions
DA, GDA, and CDA is
read by means o£ the
DECRD subroutine, A
descrip_on of the sub-
routine follows, together
with a listing in i
FORTRAN IV.
DECRD Decimal Read
le Description. When a minus sign isencountered in column 1 of aDECRD data card, that card will be
read and then reading will beterminated.
The index of a DECRD card must
be wri_en to the extreme right of
the first 1Z-column field.
2. Extent: 78 locations.
3. Call Statement:
CALL DECRD (ARRAY)
, . Z. 4_3 _5 .....
2 O. -6 5 - _E + O.Z
• 4.9: . . . .E 2; I , " i "':/ ;;, * ;,,
- 7... 8_ 9.5. E. 2_
- 0 . 0......
2.9 75 ....... +3
1.2 3. 4. _ . 20 00
The first card will result in informa-
tion being stored as fo_ows:
ARR(1) -0. 7063E 01
ARR(Z) Uncha_ed
ARR(3) 0. Z435E-00ARR(4) 0. Z065E 04ARR(5) 0. 4649E 04
The - sign in column 1 of the second
card signals that this is the last cardto be read under control of this CALLDECRD statement. This card has
been written to illustrate some types
of errors (or possible errors) inwriting the data. The informationwill be stored as follows:
0
o
e
where ARRAY is the name of the
read array to be read. This argu-
ment may be subscripted.
Error indication: If the index field
is zero or blank, the comment"BAD DATA CARD" and the con-
tents Of columns 73-80 Of the
defective card _11 be printed. Thejob will be terminated,
Example: Assume a CALL DECRD(ARR) statement and the followingdata cards:
ARR(I I)
ARR(IZ)
ARR(lS)
ARR(14)
ARR(15)
O. 7896E Zl (Exponentmislocated or
incomplete. )
Unchanged (Treated as
a blank. )
Unchanged (Treated asa blank. )
0. 2975E 040. IZ34E 03
When no decimal point is written, asin the last two items, the data is read
by the E12.8 format: the number ofdecimal places is counted from thebeginning of the exponent field, if any,or from the extreme right of thefield.
0
- 18-
000
n-U
U
kJualzalo
kJ
u-im i
II
i
_o_o___o o
A
d5 r-_O
0
if5 U ,.--_
I.--- J _ O
o N
O,-'_ -J_0 "_ ,..0_-, u.,_, Urn
_-0_
_o_
!1
I
I
o o o55 5 _
o
oO
uJ@
A
I--
Z
o o
_ ocI--u o
_ O
,-, t5 l
I--
U_ O
o+ Z) u
7,_ "_}
" e
_°_, _ _o3 _nO
<
$<,r-t
<I.-
123
_tn
on-
_D_ _'_ L_
ob
I
i
- 19
It
2.
3.
4.
5.
4.3 Data Deck Setu p
Data decks should be stacked as follows:
Three title cards (which may be blank,
A card with VIN, RHO,
DA, general shell data,
if necessary).
WT.
read by executive program.
GDA, geometry data, read by GEOM subroutine.
CDA, section properties data, read by CDAFIT subroutine.
The data in groups 3, 4, and 5 should have a minus sign in column 1of the last card.
The following tables show the nature of the DA, GDA, and CDA decks.
:J
- 20-
• f
4.4 Call DECRD (DA)
DECRD
Index
1
Z
3
4
5
8
II
IZ
14
16
17
18
Z5
Z6
Z7
Z8
Z9
30
33
36
37
4440
4476
Name
EN
AO
HO
BO
SIGO
POI
SPRL
UK
WK
TAU1
ENTI
PI1
MASS
CFE
CZ
SKFE
SKZ
SUM
TFI
RESTRT
PNCH
EMI
EMIN
De scription
No. of points along shell meridian
Reference length (in.) ]
Reference thickness (in.) _ For luo_t casesReference Young's Modulus (p_ _i ,_e.tto _.. C_
Reference stress (psi)Pois son's ratio
Location of spring along meridian
Spring value in _ direction
Spring value in normal direction
Length of total time interval from zero
Total no. of time intervals from zero to TAUI
Print interval (will always print last interval)
Mass density Ibs. secZ/in 4
Coefficient of viscous damping at each station in
_direction
Coefficient of viscous damping in normal direction.
Spring constants of shell under elastic restraint in
_direction
Spring constant at each station in normal direction
Fourier summing increment (always -I.)
(Always -I)
0. for start from zero, I. for restart
0. no future restart; I. restart cards are punched
See description of top boundary cDnditions in Section 4. 6.
See description of bottom boundary conditions in
Section 4.6.
Last card must have a - sign in Col .umn I.
- 21 -
4.5 Boundary Conditions
4. 5.1 Top Boundary
When the boundary conditions on the top boundary are of the following
kind, a special flag can be used to specify them:
free:
roller:
fixed: = u e = W =_E = 0) = 3.
simply supported: = u e = W = M E = 0) = 4.
complete: = _g = 0) = 5.
In these cases, DA(4440) = 1. El0, and DA(4441) is given the value
1., Z., 3., 4., or 5. as shown above. Other special boundary conditions
may also be specified. As an example, the full boundary (which is also given
above) can be specified as shown in the following data sheets.
A
¢Ng = u e = W = ME = 0) = Z.
A
(u_ = u e = F_
- 22 -
x_ _ i!:!_i?_:!:i:i:!:!;i?_;_:i?i::i'i::::::i::::ii_
ft.
_Z ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;i;i?i'!'!:i'i'i":i'!:i:i:i'!:!:i:i:_:iii::'i!'!i!i:i'_
0
P=l
i!iiiiiii!ii!iiiiiiiiiii!!iiiiii!!iiiiii!iiiiiiiii!iiiiiiii!_-:._,_._._._.:,_,_,_._.:._,:._.:.:,_._.:._.:,_._,_,_.:.:._._.:._._,_,_._._,_._._._._,_._._,_,:.:._._._,_._._._,_,_,_._-_,'.:.:._._._,_._._._,_.:._.:.:,_._,:.:,:._,:.:._._._,_,:,_,:._
!i!i!_iiii!i!!iiiiiiii_iiiiii!i!i!i!!iii!iii!i!_ii!iiii!!iiii'_,_'_'i'_';'_'_'_,_._,_-_-_'_._o_._._._,_._.;._._._,_,i._._..
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::iii!iii_i!!!iiiii_i!!ili!i!!iiiiiiiii!iiiii_ii!_i_i_i_i_:_'
_::::::::::: :::_:} ::::::::::::::: :::::I_.
L_
I
_°U
iiiiiiiiii!i!ii!iiiiiiiiiiiii!iiiiiiiiiiiiiiiii!iilg!iiiiiliiii::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::
o
O_
- 23 "-
_i;_!:___iii!_i_j
t_
_ , uJ..I
!_ o•t,,l ,1_
_ o,o , _
n: _ ,-_ t_ o
o_ _ _ _
f_ :!i!!!!!i?i!iii!!_!!!!!!!!!!!i!!!!_!_!i!!!!!_!!_:!i!_!!ii_:::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:.:.:.:.:.:.:.:.:.'.:-:.:.x..:.:.:.:.:.:.:..:.:-:_..:._,
" !iiiii!iiii!iiiiiiiii!!iiiiiiii!iiii!!ii!!i!!ii!!ii::::-:':::-:::::::::::::::::::::::::::::i::::::::::::1 :'!':'.'!i!'ii.!!'i'?iiii!iii:iii'iii!!iii?!ii!'!!iiiii:_iii:ii::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::i_iiii!iiiiiiii!ii!!iiii!!i?!iiiiiiiiiiiiiiiii!iiiii!i!iii!i!il
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::I_.., ',:::':':':'"'°_'":':':':':':-:-'-'":'/-:':'-_'_':"-':t_
• C 0
- 24 -
4. 5. Z Bottom Boundary
The same selection of boundary conditions is available here as for the
top boundary. This time, the indicator specifying the free, roller, fixed,
simply supportedj and complete conditions are set as follows:
DA (4476) = 1. El0
DA(4477) = 1., 2., 3., 4., 5.,
according to the bottnd_y condition desired. An example of Other possibleboundary conditions ia giveni_ the data Sheets below. The exampie here isthe free boundary (the same as in Section 4. 5.1), "
°. .
L. i .-..= • • ....
, • i m | '_
i--I. _!'!,,_!_ii_....i̧'__, .__
_ _ r ¸ /' _LI_.
D _
_l _
¸¸i¸¸,t4 ¸ '
c_
t_
_G
_o•I /:fJLI _-'
_ ":':':':""'":"":........""''"""'"_':" i:':_:::i:_:i:::::::::_:::::::::::::::::::::_:_:::-'::::i
LID _ .:-_:-:-.:-:':-:-:-:-:-:-:-:.:-.--.....:....:.:..;.
_Z _ :<o*,:.;ot,_o_,,o_;_,:,:o:o:,. ;,:,:.; ,,:,.,.,.,.,..__!::_;!:i:!_i:!:_:i:!:i:i:!:!:!:i:!:!:!:!_:i.i_.:!:!:.:.
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- 26 -
i L
- 27 -
4:6
DECRD
Index
1
.2
3
4
8
9-208
209-409
Call DECRD (CDA)
Namer
GMI
EN
PFLAG
ZA1RCAXL
!
ROFF
PI_O
PHIN
EM
RIPT
XIPT
De s c riptioni .....
Geome_ indiCato r:
1. = cm_- Cylinder
Z. : S_=S- toroid
3. = genezal discrete point
4. : a l,b_az_:_%mctions
No. of station points
Print indicator; # 0., prints all data
For GMI = 1. ; radius at station 1
For Gh4I = 2.
For CdMI= I.
For GMI = Z.
For GMI = I.
revolution
For GMI = 2.
in degrees.For GMI = Z.
in degrees.For GMI = 3.
For GMI = 3.
For GMI = 3.
maximum)
; radius of curvature
; axial surface length; off-set distance to center of curvature
; angle between generator and axis of
; initial opening angle from vertical axis,
; final opening angle from vertical axis, _
; number of RI points given
; discrete radii (200 points maximum)
; discrete XI - arc length, (Z00 points '
The last card must have a - in Column 1.
- 28-
J.,.
4.7 Call DECR D (CDA)
The various tables are set up in this region as follows:
TAB (I) = No. Of stations given along meridian (i. e., stations
at, which value s change).TAB (Z) = Station, No. 1.
TAB_ (3) = Parana_er value at Station No. 1
T C4)=•Nextii,t t o, no.TAB(5} = Next partier value
.... .|" ,,/ . • .
[Stations and parameter values interlaced.
The last station must be the Nth station parameter value because
CODIMA interpolation routine will not extrapolate.
If +1.0 x 1010 is placed in TAB (1) the following parameter value is
constant (uniform over all stations EN) and its value is placed in TAB (Z).
4
29 -
DECRD
Index
i _ I
2
4
5
6-41
Name
DTB
De s c ription
Extensional Rigidity
No. of stati6ns given, if = 1.El0, then a constant
_e_'tenStonal.lrigidity is given in 2' Stati6aNo. :[:"
ifCDA (:I) =r:1" _'_10, then this is a constant value of
e_tens ional: :rig idit y.
Val_ofextensional rigidity between Station I and nextstation
Station No. Z.
Value of extensional rigidity
Follows same pattern to DTB (20), value of last rigidity.
- 30 -
y
DECRD
Index
42
43
44 !
45
46
47-81
83-125
124-164
165-205
206-246
247-287
288-328
329-369
370-410
452-492
493 -533
534-574
575-615
616-565
657-691
The last
EKTB
Follows
EITB
ALFTB
DNATB
TTB
ENTB
EMTB
PNTB
PFB TB
DZOTB
VZOTB
QZOTB
DFOTB
VFOTB
QFOTB
Flexural Rigidity
Delcription
No. of stations given, if = I. El0, then a constant flexural
_isidityis given in 43
Station.No. 1
" if CDA._4Z ) = 1. El0, then this is the constant vs_lue of
• ae 1.rig di - • .V__exural rigiditybe_ween station 1 and next
station
Station No. 2
V_lue of f!exural rigidity
same p_ttern to EKTB (ZO), value of last ridigity.
COntinueai above for the following quantities:
Young's ,modulus (E)
Coe£ft of thermal expansion (a)
I/Z shell thickness (h/Z)
Temperature gradient through shell (T)
Membrane thermal load
Bending thermal load
Normal pressure on shell (at reference surface)
Meridional surface pressure (at reference surface)
Initial displacement in normal direction.
Initial velocity in normal direction
Initial acceleration in normal direction
Initial displacement in g direction
Initial velocity in _ direction.
Initial acceleration in g direction.
card must have a - sign in Column 1.
- 31 -
5.1 SAMPLE PROBLEM
To demonstrate the use of the computer program, and to illustrate
the format of the input and output data, the sample problem shown inFigure 2 has been calculated.
The problem concerns the vertical impact of a flexible body of
revoi_itibn_on0isti_g of a shallow spherical shell to which is rigidly attached
a heavier mass eo:_m_t_the_ur combined weight is 10,000 Ibs. The radius of
curvatuze of the_ shel_ middle surface is 175.6 ins., and the openin E angle is
19, 53°. ::, The shell _eXt6n_i_ and flexural stiffne S ses are both set equal to
3, 33 x l06 ibs/in. ,: Which c0r_esponds ton sandwich shell havin E 0.05 in.
steel facings and 1.9-5 in, honeycomb core. Other shell properties are asfollows: Ma,s per _it!s_e _rea = 9. 7 x 10'4 Ibs. sec. Z/in. _; Pois,on'sratio = 0. 33, and m_duius of elasticity E = 29. 7 x I06 psi. The initial impact
velocity is 30 fps. The hydrodynamic loads are computed on the basis of
the rigid-body theory ofVolume2 ofthis report, and are then applied as a
forcing function to the shell of revolution. A full discussion of the numerical
results obtained is given in Volume 2. Sample data sheets follow.
- 33 -
b
//
/
tI
II
II
II
II
II
I
/I
I
V
IX
.6IN.
Fp
Figure Z. Model of Sample Problem.
- 34 °
5, 2 Sarnple Input Data for a start from zero
In the present problem, we shall use a time interval of . 0001 seconds
and make a run to I. 0 milliseconds. Because it may, at some future date,
be desirable to make a restart at I. 0 ms. (to avoid recalculating the
response from zero), we shall punch some quantities on cards to make this
restart possible. They will be part of the input in the future restart. Thus
we set RESTRT = 0.0, and PUNCH= 1.0,
Sample input sheets are shown below for the start from zer ° .
- 35 -
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- 37 -
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- 39 -
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C:, •
- 41 -
S. 3 Sample Data for the Restart
In order to restart the problem at 1.0 ms., the following input is
required. Note that the time interval must be the same in all runs. The
changes in data are indicated by the arrows in the data sheets. Note
particularly that RESTRT = 1.0 here. The output cards obtained from the
previous run are placed at the end of the data deck. They are read insubroutine CDAFIT.
The output quantities will be identical to those from the start fromzero.
42 -
-rU
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- 48 -
5.4 Sample Output
The following pages show the output resulting from the start from
zero of the sample problem. Letters in circles correspond to descriptions
below.
®®©@@®®®©®®®®®®®®®®®
First Title Card
Second Title Card
Third Title Card
No. of Stations EN
Radius of curvature, ins.
Offset distance from center of curvature = 0
Closed apex, therefore PHIO initial opening angle is zero
PHIN, final opening angle is 19. 53 °
Station number
R(1), normal distance from shell to axis
W(THETA) nondirnensional curvature in 8 direction
W(XI) nondimensional curvature in _ direction
RHOX(1) R(1)/AO = P/AO
GAMMA (1) p '/p
DTB, the extensional rigidity (constant over shell)
EKTB, the flexural rigidity (constant over shell)
EITB, the Young's modulus (constant over shell)
ALFTB, thermal expansion coefficient (zero)
DNATB, I/Z shell thickness (constant over shell)
TTB, temperature gradient (zero)
- 49 -
U
V
W
X
EN
AO
HO
EO
SIGO
ENFO
ENFL
POI
THETA
PIXI
SPRL
UK
VK
WK
EMK
TAUI
ENTI
PI 1
ENTB, membrane thermal load (zero)
EMTB, bending thermal load (zero)
All these other quantities, read by CDR, are set to zero.
See Sections 4.4 to 4.7 for descriptions
= number of stations
= reference length
= Reference thickness
= Reference Young's modulus
-_ Reference stress level
= always zero
= always zero
= l=)oisson's ratio
= always zero
= always zero
= location of spring along meridian
= spring value in _ direction
= always zero
= spring value in normal direction
= always zero
= total length of time from zero
= Total no. of time intervals from zero to TAUI
= point interval. Here PIl = i, and output is pointed at
end of enc interval
- 50 -
TAU2
ENTZ
P12
TAU3
ENT3
PI3
=0
0
0
0
0
=0
(always zero)
MASS = mass density
CFE = coefficient of viscous damping at each station in direction
CZ = coefficient of viscous damping at each station in normal
direction
SKFE = spring constant of shell under elastic restraining in
direction
SUM =- 1. always
ENI
DEL
BCITP
BCIBM
Y
= I. , open shell; = 2., closed shell; set in GEOM
= distance between station points
= boundary condition indicator - top boundary
= boundary condition indicator - bottom boundary
Full Tables of
D
EK
E1
ALF
DNA
Extensional rigidity
Flexural rigidity
Young' s modulus
Coefficient of thermal expansion (zero here)
1
_- shell thickness
- 51
T
ENT
EMT
®
®
®
@
®
I
U(1)
V(D
W(I)
M(PHI)
M(THETA)
M(PHI,
THETA)
Q(PHI)
temperature gradient through shell (zero here)
membrane thermal load (zero here}
bending thermal load {zero here)
Full Tables of PN, PFE, DZO, VZO, AZO, DFO, VFO,
AFO, all of which were read as zero in GDA. [See Section 4.7
for their descriptions I .
is self-explanatory. It shows the time (t), rmximum radius
of the pressure profile (c), and overall vehicle velocity (V).
Maximum pressure is given in BG, and depth submerged is
not computed here.
is a column showing the station number from the apex (1) to
the boundary (120).
is a column of the total pressure acting at each station point.
Because the maximum radius of the wetted surface is 3._ ins.,
and the distance between each station point (DEL, see _)is . 503 ins., the wetted surface only extends to station 8.
Beyond this station, no pressure is applied. Note that the
maximum pressure always occurs at the edge of the wettedsurface, in this case at station 8.
This page contains columns of response output. The columns
are as follows:
Station points along shell meridian
Tangential displacement (ins) of middle surface in _ direction
Tangential displacement of middle surface in @ direction.
Here zero because problem is axially symmetric.
Transverse displacement (ins.) of middle surface (positive
outward).
Meridional bending moment M% (in Ibs/in.)
Circumferential bending moment M@ (in ibs. /in. )
Twisting moment ME@. Zero here because problem is axiallysymmetric.
Shear force O_ (Ibs/in.)
- 52
Q(THETA)
@1
N(PHI)
N(THETA)
N(PHI,
THETA)
SIG(PHI)
SIG
(THETA)
SIG(PHI,
THETA)
@VEL(U)
V L(Vl
VEL(W)
ACC(U)
ACC(V)
ACC(W)
Shear force Qe- Zero here because problem is axially
symmetric.
Additional columns of response.
Station point along meridian
Meridional membrane force N_ (Ibs/in.)
Circumferential membrane force N 8 (Ibs/in.)
Twisting force N_8. Zero here because problem is axiallysymmetric.
Stress_g (psi) on outer fiber of shell.
Stress °-8 (psi) on outer fiber of shell.
Stress _O on outer fiber of shell. Zero here because problem
is axisymmetric.
Additional columns of response.
Tangential velocity in _ direction (ins. /sec.)
Tangential velocity in 0 direction. Zero here because
problem is axially symmetric
Transverse velocity (ins sec.), positive in outward
direction.
Tangential acceleration in _ direction (ins. /sec Z)
Tangential acceleration in t9 direction (ins. /sec 2)
Transverse acceleration (ins. /secZ), positive in outward
direction.
- 53 -
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- 80 -
O. 1 WARNINGS AND RECOMMENDATIONS7. 1 PRO(
0. 1. 1 Choice of Time Interw_l
The proper choice of the appropriate time interval zXt is important
for obtaining good results. If At is too large, the response will be highly
damped and inaccurate. On the other hand, ifA t is too small, the program
\\ill take a large amount of time to run. In the sample problemAt of 0. 05 ms
\vas used, which gave good results.
0. 1. 2 Number of Iterations
There is an unidentifiable bug in the problem which makes it necessary
that a restart be made after about 140 iterations through the shell program.
Should 160 iterations be exceeded, the program will "blow up." Therefore,
it is recommended that the job be run in segments of roughly 120 iterations
betxveen restarts. The method of restarting is explained in Sections 1. 3 and5.3.
o. 1. 3 DECRD
The subroutine DECRD is in the NAA program library and consequently
does not appear specifically in the source decks. In installations without
this program in their library, the subroutine should be inserted in the zero
link behind the subroutine MMY.
-81 -
7. 1 PROGRAM LISTING
- 82 -
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