It is demonstrated here that complete checkout of a basic substructure can be done under the special circumstance of a sliding connection with offsets. Stiff bar connectors make this possible so long as the bar coordinates are aligned with the displacement coordinates at the sliding surface

Butler, Thomas G.

English

NASA Technical Reports Server

 91"-20510
MODELING OF CONNECTIONS BETWEEN SUBSTRUCTURES
Thomas G. Butler
BUTLER ANALYSES
The focus of this paper is on joints that are only par-
tially connected such as slip joints in bridges and In ship
superstructures or sliding of a grooved structure onto the rails
of a mating structure as shown in the sketch.
¼ "!
!
"9
In substructure analysis it is desireable to organize
each substructure so as to be self contained for purposes of
validity checking. If part of the check is to embrace a connec-
tion, then all of the elements of the interface that it sees in
22
https://ntrs.nasa.gov/search.jsp?R=19910011197 2020-03-19T18:32:36+00:00Z
MODELING OF CONNECTIONS B_ SUBSTRUCTURES
its mate should be included within its model. In the case of the
groove/rail structure, shown above, it will enhance the checking
if the rail points, to which the shoe points will connect, are
duplicated in the substructure with the shoe. Thus a complete
job of checking out the shoe substrucure can be done in Phase 1
with statics and eiqenvalues and not protract the checking proce-
dure of basic substructures into Phase 2.
To implement such a scheme, referring to the sketch,
points R1 & R2 are included in the shoe model. The connection
from $3 to R1 and from $4 to R2 are made in Phase 1 and now
become available for complete chekout of the shoe substructure,
including its mating with the rail. To make this example
general, postulate that the planes throuqh the :our points are
not parallel to the coordinate planes. In e[fect there are
offsets. Generally, one llKes to plan to avoid havlng
out-ol-piane offsets, butexiuencies do crop up whlch forces the
analyst to face up to such realities. Often such interface
connectlons involve MPC s or elastic ties. fn any case a
_equirement of Substructure Analysis is that points that are to
be connected in Phase 2 must be available in Phase 2; i.e. they
cannot be condensed out or constrained out in Phase I.
Therefore, if an MPC is used, the connecting points must be the
independent degrees of freedom in the MPC relatlenship.
The needs of this joint are that there will be no rela-
tive translation in either transverse direction and no relative
rotation about the long axis of the rail. In terms of the
indicated coordinate system, translations in x and z directions
must be constrained together and rotations about v must be
constrained together. Just a pair of connectin_ points will De
used herein to carry on the discussion. A sketch will be use_ to
Z3
MODELING OF CONNECTIONS BETWEEN SUBSTRUCTURES
assist in the discussion
multi-point constraints.
RAIL
'v
X
J
: Z4.Y
of making the connection by means of
f
f
I
701Z
I
Include rail point 243 in the Shoe Model. h_en Phase 2 COMBINE
operation is invoked, NASTRAN will recognize that rail 243 = shoe
243. As remarked above, since point 243 is going to be commanded
to connect in Phase 2, it must therefore be an active available
point for joining; and must therefore be an independent point in
an MPC relationship. Now following the needs of this joint,
constrain point 7013(X,Z,#) to 243(X,Z,#). The constraint
equations for translations in X and Z are:
7013(X) = 243(X) - c x 243(#) + b x 243(_)
7013(Z) = 243(Z) + a x 243(#) - b x 243(@).
But 243(_) and 243(@) are rail rotations which are not sensed by
the shoe. If 243(4,6) are included in the shoe model they would
be independent shoe rotations which will engage in the MPC
relationship but would have no elastic path out to other parts of
24
MODELING OF CONNECTIONS B_ SUBSTRUCTURES
the shoe. Thus, if nominal mass were added to these rail points
to keep the eiqenvalue matrix from being singular, an eigenvalue
check for rigid body modes would show the shoe model to fail.
One might argue, why not leave the rotations in until they are
connected during COMBINE, then they are no longer disjoint. I
cannot afford to leave the 243(4,6) rotations in the shoe model,
because after connecting with the rail these rail ro_ations must
no___ttbe transmitted back to the shoe. Moments in the shoe/rail
configuration about the two transverse axes are produced only by
couples of forces not by local rotational bending. This rules
out the use of MPC's during Phase 1 in this case. There are
other cases of connections between substructures in which MPC's
in Phase I would work. The case in which there were no
transverse offsets would work. A NASTRAN run o_ a simple model
demonstrates these results in Appendix A.
The alternative is to make a stlff elastic connection,
but not so stiff as to cause matrix ill-conditioning. If a bar
instead of elastic scalars is used, it will be modeled so as to
be fully connected in all 6 dearees of freedom at the shoe end,
but only partially connected at the rail end. At the rail end it
must allow for sliding along the rail and not transmit rotations
to the shoe about the rail transverse axes. This implies that
pin flags must be used at the rail and to inhibit these freedoms.
This stiff bar connection can be implemented the wron_
way or the riaht way. One gets trapped into modeling the wrong
way by forqettinq that pln flags are applied to ba____rrcoordinates
not to the displacement coordinates, f fell into this trap and
will show you what happens. Then I will follow it up with the
correct way to model it.
25
MODELINGOF CONNECTIONSBETWEENSUBSTRUCTURES
BAR CONNECTION
WRONGHAY
 sT<
io? g ,
2,4,6
Y
Include the rail grid points in the shoe model and apply SPC's at
the GRID level in d.o.f.'s 2,4,6. Connect the shoe point to the
rail point with a stiff bar. Note that the connection from shoe
GP to rail GP produces bar coordinates that are skewed with
respect to the displacement coordinates. Thus when bar element
coordinate 2 is pinned, a component of force still develops at
the rail end o2 the bar in the Y displacement coordinate direc-
tion, and so the eigenvalue check for rigid body modes fails once
again. The listing in Appendix B of a simple model, incorporat-
ing this wrong approach, shows the constraint forces in the rigid
body modes in freedoms TI, RI, & R3 to be non-negligible. Then
the elastic mode shows large constraint forces in these freedoms.
26
MODELINGOF CONNECTIONSBETWEENSUBSTRUCTURES
BAR CONNECTION
RIGHT WAY
D_r_ Z
I
¢ej_L ¢ O,cl,s,et
¢< A
Dos,"); .),
Offset the bar at the shoe end so as to terminate the bar at the
rail end so as to be perpendicular to all displacement coor-
dinates at the rail end. This connection passes the eigenvalue
check for rigid body modes. Appendix C is a listing of a simple
demonstration problem of the joint modeled the light way. Note
that the constraint forces in freedoms T2, RI, & R3 are negli-
gible in rigid body modes as well as in elastic modes.
27
MODELINGOF CONNECTIONSBETWEENSUBSTRUCTURES
CONCLUSIONS
This paper has demonstrated that complete checkout of a
basic substructure can be done under the special circumstances of
a sliding connection with offsets. Stiff bar connections make
this possible so long as the bar coordinates are aligned with the
displacement coordinates at the sliding surface.
Z8
MODELING OF CONNECTIONS Bh_ SUBSTRUCTURES
APPENDIX A
RUN WITH MPC CONNECTION
29
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33
MODELING OF CONNECTIONS BETWEEN SUBSTRUCTURES
APPENDIX B
RUN WITH WRONG BAR CONNECTION
34
GRID
P0 INT
ID. TYPE
71 G
72 G
P O I N T S I N G U L A R I T Y T A B L E SPC 0 MPC 0
SINGULARITY LIST OF COORDINATE COMBINATIONS THAT WILL REMOVE SINGULARITY
ORDER STRONGEST COMBINATION WEAKER COMBINATION WEAKEST COMBINATI0
i 5 4
1 5 4
6 ROOTS BELOW 1.973921E+01
E I G E N V A L U E A N A L Y S I S S U M M A R Y (INVERSE POWER METHOD)
NUMBER OF EIGENVALUES EXTRACTED ...... 7
NUMBER OF STARTING POINTS USED ....... 1
NUMBER OF STARTING POINT MOVES ....... 0
NUMBER OF TRIANGULAR DECOMPOSITIONS .... 1
TOTAL NUMBER OF VECTOR ITERATIONS ..... 34
REASON FOR TERMINATION ........... 7_
LARGEST 0FF-DIAGONAL MODAL MASS TERM .... 0.13E-06
6
MODE PAIR ..........
NUMBER OF 0FF-DIAGONAL MODAL MASS
TERMS FAILING CRITERION ........
(_ 1 OR MORE ROOT OUTSIDE FR.RANGE.
SEE NASTRAN U.M. SECTION 2.3.3)
0
REAL E IGENVALUES
MODE EIGENVALUE CYCLIC GENERALIZED GENERALIZED
NO. FREQUENCY MASS STIFFNESS
NASTRAN INFORMATION MESSAGE 3308, LOWEST EIGENVALUE FOUND *
AS INDICATED BY THE STURM'S SEQUENCE OF THE DYNAMIC MATRIX *
• (THIS MESSAGE CAN BE SUPPRESSED BY DIAG 37) *
****************************************************************
1 -7.963921E-08 4.491420E-05
2 2.852769E-08 2.688150E-05
3 9.751177E-08 4.969911E-05
4 1.989545E-07 7.098997E-05
5 2.305249E-07 7.641507E-05
6 3.321909E-07 9.173054E-05
7 7.002442E+06 4.211578E+02
2.016630E-01
1.250841E-01
1.946527E-01
1.088651E-01
2.362906E-01
1.223466E-01
1.515952E-01
-1.606029E-08
3.568360E-09
1.898093E-08
2.165920E-08
5.447087E-08
4.064244E-08
1.061536E+06
35
ID 0FFSET,CONNECT
APP DISP
SOL 3,0
DIAG 8,21,22
TIME i0
CEND
FREE-BODY MODAL STUDY OF SHOE/RAIL CONNECTIONS WITH BARS JAN 20,1991 PAGE
[_]RONG _AY WITH CONNECTOR BAR SKEHED TO RAIL.
2
CASE CONTROL DECK ECHO
TITLE = FREE-BODY MODAL STUDY OF SHOE/RAIL CONNECTIONS [_ITH BARS
SUBTITLE = WRONG WAY WITH CONNECTOR BAR SFd_MED TO RAIL._ 3 RB MODES.
OUTPUT
DISP = ALL
MPCFORCES = ALL
ELFORCES = ALL
SPCFORCES = ALL
SUBCASE 1
LABEL = BARS PINNED AT RAIL END. NO OFFSETS AT SHOE END.
METHOD = 3
BEGIN BULK
SORTED BULK DATA ECHO
---I--- +++2+++ ---3--- +++4+++
CBAR 1 i 71
CBAR 2 2 71
+TIE UP 246
CBAR 3 2 72 14 13
+TIE DWN 246
CMASS2 131 0.i 13 4
CMASS2 141 0.I 14 4
CMASS2 711 0.I 71 4
CMASS2 712 0.I 71 5
CMASS2 721 0.i 72 4
CMASS2 722 0.i 72 5
EIGR 3 INV 0.0 1.0 6
+ALLMODEMAX
GRID 13 0
GRID 14 0
GRID 71 0
GRID 72 0
MAT1 1 3. +7
PARAM COUPMASS 7
PBAR 1 1
PBAR 2 1
ENDDATA
---5--- +++6+++ ---7--- +++8+++ ---9--- +++i0+++
72 1.0 1.0 0.0 SHOE
13 14 +TIE UP
6 3 1.-3
+TIE DWN
3.0 2.0 2.0 0
3.0 17.0 2.0 0
0.0 0.0 0.0 0
0.0 15.0 0.0 0
0.28 2.4-4
1.0 1.0 1.0 1.0
i00.0 100.0 100.0 i00.0
31THETA
14THETA
71THETA
71PHI
72THETA
72PHI
+ALLMODE
246
246
RAILIPT
RAILIPT
SHOEIPT
SHOEIPT
36
SUBCASE 1 EIGENVALUE = -7. 963921E-08
REAL E I GENVECTOR NO 1
PT ID. T1 T2 T3 R1 R2 R3
13 3.308091E-01 0.0 5.615981E-01 0.0 9.189782E-02 0.0
14 -6.346744E-01 0.0 -9.552183E-01 0.0 9.189782E-02 0.0
71 3.910763E-01 -5.288029E-01 1.000000E+00 -I.011211E-01 6.503133E-02 6.436E-2
72 -5.744071E-01 -5.288029E-01 -5.168163E-01 -I.011211E-01 6.503133E-02 6.436E-2
EIGENVALUE = 2.852769E-08 R E A L E I G E N V E C T 0 R N 0 2
PT ID. T1 T2 T3 R1 R2 R3
1 -1.806720E-01 0.0 3.554041E-01 0.0 -1.205854E-01 0.0
14 -7.829153E-01 0,0 1.000000E+00 0.0 -1.205854E-01 0.0
71 1.403818E-01 -1.730800E-01 4.690333E-02 4.297306E-02 -8.839797E-02 4.015E-2
72 -4.618614E-01 -1.730800E-01 6.914992E-01 4.297306E-02 -8.839797E-02 4.015E-2
EIGENVALUE = 9.751177E-08 R E A L E I G E N V E C T 0 R N 0 3
PT ID. T1 T2 T3 R1 R2 R3
13 -7.289532E-01 0.0 2.853720E-01 0.0 -1.817658E-01 0.0
14 3.520157E-01 0.0 2.345846E-01 0.0 -1.817658E-01 0.0
71 -8.096893E-02 -6.163144E-01 -7.029006E-02 -3.385834E-03 -2.055022E-01 -7.2E-_
72 1.000000E+00 -6.163144E-01 -1.210776E-01 -3.385834E-03 -2.055022E-01 -7.2E-[
EIGENVALUE = 1.989545E-07 R E A L E I G E N V E C T 0 R N 0 4
PT ID. T1 T2 T3 R1 R2 R3
13 3.17775iE-01 0.0 1.764639E-02 0.0 -2.180602E-01 0.0
14 -4.354112E-01 0.0 3.30i453E-01 0.0 -3.180602E-01 0.0
71 1.000000E+00 -9.989289E-02 -9.057981E-01 2.083326E-02 -2.929949E-01 5.02E-2
72 2.468137E-01 -9.989289E-02 -5.932992E-01 2.083326E-02 -2.929949E-01 5.02E-2
EIGENVALUE = 2.305249E-07 R E A L E I G E N V E C T 0 R N 0
PT ID. T1 T2 T3 R1 R2 R3
13 9.812109E-01 0.0 1.000000E+00 0.0 -I.272332E-02 0.0
14 8.707730E-01 0.0 5.573768E-01 0.0 -1.272332E-02 0.0
71 7.983168E-01 4.514050E-01 8.229362E-01 -2.950821E-02 -2.407710E-02 7.363E-3
72 6.878789E-01 4.514050E-01 3.803130E-01 -2.950821E-02 -2.407710E-02 7.363E-3
EIGENVALUE = 3.321909E-07 R E A L E I G E N V E C T 0 R N 0 6
PT ID. T1 T2 T3 R1 R2 R3
13 -7.600989E-01 0.0 1.000000E+00 0.0 -3.662173E-01 0.0
14 -3.776701E-01 0.0 3.752712E-01 0.0 -3.662173E-01 0.0
71 -1.461953E-01 2.568173E-01 -1.776728E-01 -4.164859E-02 -3.932845E-01 -2.6E-
72 2.362335E-01 2.568173E-01 -8.024015E-01 -4.164859E-02 -3.932845E-01 -2.6E-
EIGENVALUE = 7.002442E+06 R E A L E I G E N V E C T 0 R N 0
PT ID. TI T2 T3 R1 R2 R3
13 -6.670417E-01 0.0 1.000000E+00 0.0 -6.548009E-01 0.0
L4 5.839078E-01 0.0 -8.773038E-01 0.0 5.701413E-01 0.0
71 6.416196E-01 1.446323E-03 -9.644380E-01 2.011386E-)I -5.263158E-01 1.14E-I
72 -5.595077E-01 7.3097SOE-03 _.305104E-01 5.448166E-02 6.091975E-01 4.62E-2
37
EIGENVALUE : -7.963921E-08 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T1 T2 T3
13 0.0 2.806213E+01 0.0
14 0.0 -1.530662E+01 0_0
R1 R2 R3
-2.590351E+01 0.0 -1.726900E+01
-4.709728E+00 0.0 -3.139819E+00
EIGENVALUE : 2.852769E-08 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T1 T2
13 0.0 2.551103E+00
14 0.0 -2.551103E+00
T3 R1 R2 R3
0.0 1.177432E+00 0.0 7.849547E-01
0.0 -I.I18560E+01 0.0 -7.457070E+00
EIGENVALUE = 9.751177E-08 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T1 T2 T3 R1 R2 R3
13 0.0 -1.275551E+00 0.0 1.876532E+00 0.0 1.251022E+00
14 0.0 5.102206E+00 0.0 I.I03843E-01 0.0 7.358950E-02
EIGENVALUE = 1.989545E-07 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T! T2
13 0.0 9.566635E-01
14 0.0 -5.102206E+00
T3 R1 R2 R3
0.0 3.017170E+00 0.0 2.011446E+00
0.0 4.121012E+00 0.0 2.747341E+00
EIGENVALUE = 2.305249E-07 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T1 T2 T3 R1 R2 R3
13 0.0 1.020441E+01 0.0 1.964840E+01 0.0 1.309893E+01
14 0.0 2.793968E-09 0.0 -5.077676E+00 0.0 -3.385117E+00
EIGENVALUE = 3.321909E-07 FORCES OF SINGLE-P01NT CONSTRAINT
PT ID. T1 T2 T3 R1 R2 R3
13 0.0 -2.551103E+00 0.0 -3.532296E+01 0.0 -2.354864E+01
14 0.0 -2.551103E+00 0.0 -1.236304E+01 0.0 -8.242024E+00
EIGENVALUE = 7.002442E+06 FORCES OF SINGLE-POINT CONSTRAINT
PT ID. T1 T2 T3 R1 R2 R3
13 0.0 -3.846585E+01 0.0 -2.479790E+04 0.0 -1.653193E+04
14 0.0 -I.149591E+02 0.0 2.221343E+04 0.0 1.480896E+04
38
MODELING OF CONNECTIONS BETWEEN SUBSTRUCTURES
APPENDIX C
RUN WITH RIGHT BAR CONNECTION
39
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Modeling of connections between substructures

Abstract

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