Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown

Katoh, S.

English

NASA Technical Reports Server

ADDING STXESS PLOT FUNCTION TO NASTRAN 
Shunich i  Katoh 
TBM-Japan 
ABSTRACT 
Stress p l o t  f u n c t i o n  was developed and added t o  t h e  NASTRhN level  15.5,  
t he  l a t e 6  t level a v a i l a b l e  a t  IBbI-Japan. Computed stress d i s t r i b u t i o n  can be 
d i sp layed  by t h i s  f u n c t i o n ,  with v e c t o r s  showing t h e  p r i n c i p a l  stresses of t h e  
f i n l t e  e l e m e n t s  over  t h e  s p e c i f i e d  p o r t i o n s  of t h e  s t r u c t u r e .  
First, NASTRAN i s  reviewed i n  the a s p e c t  o f  p l o t t i n g  c a p a b i l i t i e s .  Stress 
t e n s o r  field i s  examined i n  p r e p a r a t i o n  of stress d i s p l a y .  Then t h e  stress p l o t  
function as added t o  t h e  NASTRAN i s  described. A sample p l o t o u t  by t h i s  func- 
t i o n  i s  shown, 
PLOTTING CAPABILITIES OF N A S T W  
There i s  no q u e s t i o n  t h a t  p l o t o u t s  are much more effective t h a n  p r i n t o u t s  
f o r  t h e  users t o  grasp global state of  computed r e s u l t s .  P l o t t e d  o u t p u t s  a r e  
often i n c l u d e d  i n  a n a l y s i s  r e p o r t s ,  
NASTRAN has e x t e n s i v e  p l o t t i n g  c a p a b i l i t i e s .  The l eve l  15.5 can g e n e r a t e  
t he  f o l l o w i n g  k inds  of p l o t  (ref.  1 )  : 
1. Undeformed geometric p r o j e c t i o n s  of t h e  s t r u c t u r a l  model. 
2 .  S t a t i c  deformat ions  of t he  s t r u c t u r a l  model by e i t h e r  d i s p l a y i n g  the 
deformed shape (alone o r  superimposed on t h e  undeformed shape) ,  or 
d i s p l a y i n g  the displacement  v e c t o r s  a t  t h e  g r i d  p o i n t s  (superimposed 
on e i t h e r  the deformed o r  undeformed shape) .  
3 .  Modal deformat ions  r e s u l t i n g  from r e a l  eigenvalue a n a l y s i s  by the same 
o p t i o n s  s t a t e d  i n  t h e  above i t e m .  
4 .  T r a n s i e n t  deformat ions  a€ t h e  s t r u c t u r a l  model by d i s p l a y i n g  either 
vectors or the deformed shape  for s p e c i f i e d  p o i n t s  of t2me. 
5. X-Y graphs  of t r a n s i e n t  r esponse  or frequency response .  
6.  Topolog ica l  d i s p l a y s  of m a t r i c e s .  
Structure p l o t s  ( i t e m s  1-4) a r e  a v a i l a b l e  by e i t h e r  o r t h o g r a p h i c ,  perspec-  
t i v e ,  o r  s t e r e o s c o p i c  p r o j e c t i o n s .  Users can s p e c i f y  p o r t i o n s  of structure t o  
be p l a t t e d  by SET d e f i n i t i o n  c a r d s .  Var ious  pa ramete rs  can be  specified o r  de- 
https://ntrs.nasa.gov/search.jsp?R=19780024526 2020-03-22T01:55:35+00:00Z
f a u l t e d .  
Exanril~ing t h e  above l i s t ,  we n o t i c e  t h a t ,  i n  s p i t e  o f  v e r s a t i l i t y  of the  
NASTIUN p l o t c i n g  c a p a b i l i t i e s ,  we canno t  g e t  s t r c s s  d i s t r i b u t i o n  d i s p l a y ,  which 
i s  often more necessa ry  than de format ion  d i s p l a y  and is d e s i r e d  by many XASTlbIN 
users. 
Contour  p l o t  f u n c t i o n  i s  r e p o r t e d  t o  have been  added t o  the  c u r r e n t  l e v e l  
NASTIIAN, t o  w h i c l ~  the  a u t h o r  doesn'  t: h a v e  a c c e s s .  It i s  u s e f u l  for d i s p l a y  j ng 
a s c a l a r  Eield (n s i i lg le -va lued  f u n c t i o n  o v e r  a E ic ld )  such a s  temperature  dis- 
t r i b u t i o n ,  b u t  seettis t o  be i n s u f f i c i e n t  f o r  u v e c t o r  o r  t e n s o r  F i e l d  such  as st- 
r e s s  d i s t r i b u t i o n .  A f t e r  some s t u d y ,  t h e  au tho r  developed t h e  stress p l o t  func-  
t i o n  as w i l l  b e  i n t r o d u c e d .  
STRESS TENSOR FIELD 
S t r e s b  d i s t r i b u t i o n  i s  a  censor  E i e l d  o v e r  a s t r u c t u r e .  And d i s t r i b u t i o n  
of p r i n c i p a l  stress i s  a complete  e x p r e s s i o n  of t he  field. Numerical ly ,  n st- 
r e s s  t e n s o r  a t  nny p o i n t  of a s t r t t c t u r e  i s  d e s c r i b e d  w i t 1 1  a real symnretric ma- 
t r l x  i n  reference t o  an  ortt-rogonnl c o o r d i n a t e  s y s t e m .  T h e  e f g e n v a l u e s  a n d  the 
u n i t  e i g e n v e c t o r s  of  t h e  matrix arc t h e  magnitudes and t h e  u n i t  d i r e c t i o n  vec- 
t o r s  of  t h e  p r i n c i p a l  s t r e s s e s  a t  t h e  p o i n t .  Let  t h e  e x p r e s s i o n  " p r i n c i p a l  s t -  
ress v e c t o r "  mean the u n i t  e l g e n v e c t o r  multiplied by t h e  c o r r e s p o n d i n g  e igen-  
va lue .  Becnusc t h e  o r i g i n a l  m a t r i x  i s  coniplerely represented by the  e i g e n v a l u e s  
and eigenvectors, the stress tensor i s  con~plece ly  e x p r e s s e d  by t h c  p r i n c i p a l  st- 
r e s s  v e c t o r s  a s  deEined above ,  
T h e r e f o r e ,  s t r e s s  d i s t r i b u t i o n  can  be d i s p l a y e d  w i t h  p r i n c i p a l  s t r e s s  vec- 
t o r s  at a number oE p o i n t s  \ d e l l  scattered o v e r  t h e  s t r u c t u r e .  S o l u t i o n  of a fl- 
nillc element s t r u c t u r a l  program l ike  N A S T W  gives  us  ready n ~ a t e r i a l  for  such 
d i s p l a y  with the  p r i n c i p a l  s t r e s s e s  a t  each structural element. 
TMG STRESS PLOT VUNCTION 
Overview 
I r  o r d e r  t o  a s s i s t  NASTUN u s e r s  i n  t h e  i n t e r p r e t a t i o n  of o u t p u t ,  t h e  s t -  
ress plot: functlko~l was developed and added l o c a l l y  t o  t h e  N A S T W  l e v e l  15 .5  at  
IBM-Japan. I t  was not  designed as a p o s t p r o c e s s o r  b u t  was i n c o r p o r a t e d  into t h e  
s t r u c t u r e  p l o t t e r  of rlle NASTKAN i n  o r d e r  to  u t i l i z e  t h e  v e r s a t i l e  c a p a b i l i t i e s  
of t h e  e x i s r i n g  s t r u c t u r e  p l o t t i n g  r o u t i n e s  and t o  niake t h e  expanded usage  s i m -  
p l e  and  n a t u r a l  e x t e n s i o n  keep ing  un l fo rn i i ty .  Any of t h e  o r i g i n a l  capabilities 
were not  d e l e t e d .  
By this f u n c t i o n ,  compurecl s t r e s s  d i s  r r i b u t i o n  i s  d A s p l a y e d  w i t h  p r i n c i p a l  
stress v e c t o r s  oE t h e  s p e c i f i e d  f i n i t e  e l ements .  The p o r t i o n  of the s t r u c t u r e  
i s  drawn u n d e r l y i n g .  Compured p r i n c i p a l  stress v e c t o r s  are drawn on each struc- 
tu ra l  e lement  . 
St resses  t o  b e  D i s p l a y e d  
For Lhc one -d in~r ;n s ionu l  e l c t ~ l e n r s  ROD, CONROD, TUBE and U h l i ,  t h e  a v e r a g e  ax- 
in1 stresses a r e  d i s p l a y e d .  Fo r  chc two-di t i icnsionnl  e l e m e n t s  TIUEbI, TIIPLT, 
'CliIAl, TKIA2, QDP1EP1, QUlrEELt,  QDPEbL2, QDPLT, QUAD1 and  QUAU2, t h e  p r i n c i p a l  f i b e r  
r t t r 'csses  ilie d i s p l a y e d .  2 1  o r  22 con b c  . ;paciLicd t o  c n l c u ~ l n t e  r l ~ e  sLrcss a t  
tllc cori :espor~dit lg f i b e r  d i s t a ~ l c e  f rom t11c wid p l a n e  t o r  e a c h  two-din iens iona l  
clemet~l: that: h a s  bend ing  s t i f f n e s s .  ttr niakes p o s s i b l e  t o  t a k e  t h e  stress due t o  
t ; l l c \  Lending nlotuent ns well os t h e  nicnlbrnne s trcss . in to  c o n s i d e r a t i o n .  
L c  i s  difficult f o r  v i e w e r s  t o  g r a s p  t h e  d:Lrect.ions of the three p r i n c i p a l  
stress v c c k o r s  of n ~ h r e e - J i m e n s l o u t l 1  s t r e s s  t e n s o r  by nleans 0 1  t h e  two-dinlen- 
b i o n a l  d i s p l a y .  The c o n d i t i o n  chat t h e y  are niu tunl ly  p e r p e n d i c u l a r  i s  a h e l p f u l  
but i n s u f f i c i e n t  i n f o r m a t i o n  t o  r e s t o r e  t h e  t h r e e  t l i r c c t i o n s  u n i q u e l y .  F o r  
~ h r e c - d i m e n s i o n a l  e l e m e n t s  TETRA, \$EDGE, HEMI and HEXA2, n c o n v e n i e n t  method i s  
recon~mentled i n s t e a d .  Users u t r n c h  ti~o-rlimei1siolia1 e1e111enLs on a p p r o p r i a t e  sides 
of t h r e e - d i n ~ e n s i o ~ z a l  e l e m e n t s ,  and  specity t11e two-d imens io t~n l  e l e m e n t s  r a t h e r  
rlian t h c  t h r e e - d i ~ n e n s i o n a l  e l e n l e n t s  f o r  p l o t o u t  o f  s t r e s s e s .  1P t l lc  two-dinren- 
~ i o n a l  e l e m e n t s  a r e  tl1i.n enough, t h e i r  s t i1 f t ~ e s s  i s  c o m p l e t e l y  n e g l e c t e d  i n  t h e  
con ipu ta t i on  ot o c c u n ~ u l n t e d  s t i f f n e s s  because o f  the f i n i t e  p r e c l s i o t i  of cotuput- 
e r  a r i t l z m e t i c .  By t h i s  t e c h n i q u e ,  s t r e s s e s  are  o b t a i n e d  on s i d e s  r a t h e r  t h a n  
at t h e  c e n t r o i d s  of  t h e  t h r e e - d i m e n s i o n a l  e lement r i .  
The Eunct iomal  ~ i iodulc  PLOT was m o d i f i e d :  five e x i s t i n g  s u b r o u t i n e s  DPLOT, 
PALUPL, PLOT, HEAD and Dl'nlJ i n  t h e  utodule were m o d i f i e d ,  a ~ ~ d  Cwo GETSTR and 
DRWSTR ware added .  'l'he nwrtber of i n p u t  data b l o c k s  f o r  t h e  module was i n c r e a s e d  
by o n e .  The Nodule Property L i s t  (PPL) and t h e  R i g i d  Pornlnts  were iuud i f i ed  ac-  
c o r d i n g l y  ( r e f .  2 ) .  The t n o d i f i c a t i o u  of R i g i d  Format 1 c o u l d  have  been  expressed 
i n  the Eol lowing form o f  ALTER p a c k e t  i n  Esecutive C o n t r o l  Deck ( re f .  1 ) :  
AL'l'ELI 1 5 , 1 5  
PLOT PLTPAR,CPSETS,ELSETS,CASECC,BGPI~T~EQESIN~~IL~,,/ 
PLOTX~/V,N,NSIL/V,N,LUSET/V,N,JU~I~~PLOT/V,N,PL~~LG/V,N,P~~L~ $ 
ALTER 123 ,123  
PLOT PLTPAR,GPSETS,ELSETS,CASECC,~~GPDT,~IN,SIL,PUGV~,,OES~/ 
~~LOTXZ/V,N,NSIL/V,N,LUSET/V,N,J~LL~PLOT/V,N,PLTFLG/V,N,PFILG $ 
ENDALTER 
I n  t h e  new tenth p o s i t i o n  o f  i n p u t  da ta  b l o c k  s c c c i o n ,  s u b s t i t u t e d  i s  t h e  
daLa bloclc O E S 1 ,  which c o r r e s p o n d s  to u s e r ' s  r e q u e s t  f o r  element stress o u t p u t .  
T l i i s  i s  t h e  source which s u p p l y  computed s t r e s s e s  co t h e  f u n c t i o n a l  module. 
New Parameters 
S e v ~ r u l  p a r n n ~ e t e r s  were added f o r  use i n  p l o t  r e q u e s t  p a c k e t .  Tliey a r e  
l i s t e d  and  e s p l n i n e d  subsequently, i n  t h e  same way as the e x i s t i n g  p l o t  pararne- 
ters are i n  reference 1. 
,. . [EIA)iIllUEI STRESS s] ... , 
. . . [PENS t , c ]  . . . k3 * * -  
blhYIblUI1 STRESS ca rd  is  interpreted by the n i o d l f i e d  PARMI subroucinc. I t  
m u s t  u l w a y s  b e  inc luded  Ff s t ress  is to be plotted. The value of s r ep rcscn t s  
tl-re length to which the maximu~n a b s o l u t e  p r i n c i p a l  stress is  scaled i n  car11 sub- 
case. Xtr rriust be specified in units 01 s t r u c t u r e .  l'liis card f o r  stress p 1 ~ L  
corresponds LO the HNiZPllJlJ DEFOlUAI'ION card  for deformation plot. 
New parataeters in expanded PLOT logical card are i n t e r p r e t e d  by the s ~ o d l f i -  
e d  PLDT subrout ine .  
Non-zerc inCcgers  following the new keyword STRESS refer to subcases char 
are t o  be p l o t t e d .  Zero ea request u n d e r l y i n g  drawings I s  not used i n  stress 
plot request because stress p l o t  alwny s includes u n d e r l y i n g  drawings. 
l ien1 nul~tber Lol lowing t h e  lreywords PVLXibiilEi STlESS is used as t h e  ~mximuln 
principal stress value in sca l ing  the stress v e c t o r s  for all s u b c a s e s .  Each 
subcasc i s  s e p a r a t e l y  scaled uccording its own mnsiniua~ if this item is absent. 
This p a r s r t t e t e r  i n  PLOT card  f o r  stress p l o t  corresponds to the hlkYIblLIbl DKFO1Ul.A- 
T I O N  paralileter i t 1  PLOT card f o r  dcformacion plot. 
'lbo integers E o l l c v i n g  rlie l c c y r ~ o r d  PENS idcil~ify pens to be used Co draw 
tensile and compressive p r i n c i p a l  srress vec tors  respec~ively. P e n  s e l e c t i o n  
had been activated f o r  o u r  plotter r o u t i n e  beEorc.  Pen 1 is always used f o r  
underlying d r a w i n g s .  
Z1 and 22 s e l e c t  f i b e r  d i s t a n c e s  from t h e  mid planes o f  two-dirnenslonal 
c l e n ~ e n t s  that; hnvc Lending s c l f f n c s s ,  where stresses are to be c a l c u l a t e d .  
fleadings 
For o frame of stress plot, In the bottrotn l i n e  "STATIC STlUSS .. . " is 
written instcad of ''STAOfIC DEFOR. . . . I * .  Tn the cop line "EN-STR." wit11 the 
~~taxirllul~r absolute principal s t r e s s  vnlue is w r i t t e n  ills rend of "FkY-DEF. I' with 
the tnasinium absolute component of defornra t ion.  These are done by tile modi f i ed  
subroutine . 
Underlying Drawings 
Underlying drawings of structures for s t r e s s  plots are written by the modi- 
fied DM\? subroutine l i k e  t h o s e  for deformat j .o t~  plots. Therefore, parameters  
applicable t o  u n d e r l y i n g  d r a w i n g s  are  common. 
Plo r  oi i'r i n c l p u l  Stress Vectors 
Computcd p r i n ~ i p n l  s t r e s s e s  arc i ~ t c h c d  and p l o t t e d  b y  the oddcd subrou- 
I: Lncr; CE'l'S'l'K and DRWSTR u l ~ d @ r  corlLro1 oi L I E  niodif iccl PLOT s u b r o u ~ i ~ ~ e .  A p s l n -  
c i p a l  stress v c c ~ o r  is p l o t t e d  i n  t h e  shape  of at1 arrow havlng heads nc b o t h  
~ n d s .  The u!-ruw is l o c u ~ e d  60 tl\ltit t h e  11llddle p o i n t  oi the  s h a f t  expcdleacly 
co inc i r l c s  wit11 the g r a v i t y  ce r l t c r  a i  t h e  v e r t i c e s  uf  t h e  f i n i t e  clcment.  'i'hc 
c l i r c c t i o n  o f  t l ~ o  arrow is  t t i o L  ol  lie p r i r l c i p u l  s t r e s s .  The length 01 t h e  stlait 
is propor t  iot lak t o  t i ic  nagnitudc LIL ~ l r c  pr iuc . ipu1  s t c e s r .  The s i z e  o f  chc 
hc ,~ds  is a l s o  pra l )o r t  i o n u t c  . 
'l'he heads a r e  ou tward  ii tlie p r l t ~ c l p i l l  stress is  tensile, dnrl inward Lf 
coaprcssivc.  tlcndt; arc drawn r ~ o t  a6 fix-iil~lglcs b u t  a s  t r a l ~ ~ ~ o i t l ~  i n  order  Lo 
a v o i d  i n d i s l i n c t n e s s  ol; p o s i t  i ons  u i  t he  apexes of triangles when p l o t  Led. It: 
i s  wel l  known that i l  sl iui ' t  loolts t o  have dlfrcrene l eng th  i f  triangular heeds 
a re  u t t n c h e d  i n  iwo ways, outward and inward  f o r  coii!pnrison. To a v o i d  t h i s  op- 
t i c u l  illusion, outward llcnds are drawn s l e n d e r ,  und i ~ ~ r ~ n u d  ollcs Elac. When t h e  
a b s o l u t e  values of t e n s i o n  and comprcssiotl a r e  e q u a l ,  the  outward  and  t h e  inward  
I~eads with e q u a l  areas h s v c  t h e i r  c e n t r o i d s  e q u a l l y  apa r t  Eroilr t h e  c o n n e c t i n g  
p o i n t s  wi th   he shalts. 
Pro j cc  Lion 
Strcss urrows are p r o j e c  Led  o r ~ h o g r a p h i c a l l y  o r  pe rspec  tivcly a l o n g  wi th  
under  ly iug draw iugs . 
Upon r e q u e s t ,  p ro jec ted  sizes o f  arrows cull be r e r u i n e d  t~ b e  proportionare 
t o  the mngnitudcu oh p r i n c i p a l  sLrcsses as belore p r a j c c t i o a .  Then users  can 
compare ntagrlitudes of p r i n c i p a l  s t r e s s e s  by l t i ~ n s u r i n g  t;he p r o j e c t e d  s i z e s .  Fo t  
ilaturtzl npptlaranccs viewing paranlc ters  s i l o u l d  be s o  s p e c i f i e d  as t h e  ~ r o j e c t i o n  
p lane  d o c s  not ttlalic l a rge  angles  a g o i i ~ s t  s i g n i f i c a n t  p r i n c i p a l  stresses. 
Figurc  1 w a s  d r s t ~ n  by t h e  stress p l o t  i u n c t i o n .  l i c l n t e d  part  o f  t h e  p l o t  
request p n c k c t  was as follows: 
OUTI'U'I' (~'Lo'I') 
SET 1 L\LL 
+ . .  
IIEr\S1'ECTIVE l1ROJEC'I'1 ON 
hLIS7 b1W1 STRESS 10.0 
VIE\# 0.0 45.0 0 . 0  
I:I N U  SCAI,E SE'I 1 UKLG 1 
]'LOT STATIC S?'r&SS 3 SET 1 Zl ORIC 1 PENS 
Pen I ( b l a c k )  \\rns used f o r  h e a d i n g s  and  ut~derLyilzg d rawings ,  Pen 2 (blue) 
fq>r  t e n s i l e  p r i u c i p a l  s t r e s s e s ,  und Pen 3 ( r e d )  lor cou tp rc s s ive  ones. 
Utilizing existing capabilities of: t h e  NASTRAN structure p l o t t e r ,  stress 
rlot func t ion  was developed and incorporated i n t o  t h e  N A S T U N  l e v e l  15.5 w i t 1 1  
relatively little e f f o r t ,  But it p r o v i d e s  e f f e c t i v e  means for us t o  grasp glo- 
bal s t a t e  of cornputed r e s u l t s .  
REFERENCES 
1. blcCormick, C. W. (Ed .) : The NASTMN User's Manual, NASA sP-222(01), with  
Level 15.5 S u p p l e n ~ e n L ,  May 1973. 
2 .  The NASTMN Progranbner ' s  Manual., NASA SP-223<01), vitlt Level 15.5 Supplement, 
May 1973. 
6/28/78 MAX-STR, 6, 18534240 
TEST 
CENTR [FYGAL FORCE 
STATlC STRESS SUBCASE 3 LOAD 300 
Figure 1. S f i P L E  PLOTOUT 


Adding stress plot function to NASTRAN

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