The application of NASTRAN (level 16.0.1) to the static analysis of a sonar dome rubber window (SDRW) was demonstrated. The assessment of the conventional model (neglecting the enclosed fluid) for the stress analysis of the SDRW was made by comparing its results to those based on a sophisticated model (including the enclosed fluid). The fluid was modeled with isoparametric linear hexahedron elements with approximate material properties whose shear modulus was much smaller than its bulk modulus. The effect of the chosen material property for the fluid is discussed

Lai, J. L.

English

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STATIC ANALYSIS OF k SONm DOMX RUBBm WINDOW 
S. L. Lai 
BFGoodric h Company 
SUMMARY 
The application of NAS'IIRAN (level 16.0.1) to the static ana,lysis of a 
sonar dome rubber window (SDRW) is denionstrated. The assessment of the 
conventional model (neglecting the enclosed fluid ) for the stress analysis of 
the SDRW is made by comparing its resalts to those based on a sophisticated 
model (including the enclosed fluid). The fluid is modeled with isoparametric 
linear hexahedron elements with approximate material properties whose shear 
modulus is much smaller khan its bulk moCL-&us. The effect of the chosen 
material property for the fluid on the results obtained is also discussed. 
INTRODUCTION 
The SDRW (or window) of a ship (fig. 1) is a rubber composite structure. 
It is used for protecting the sonar device inside it and giving a small mount 
of t h e  transmission loss to the acoustic wave. The rubber composite used for 
the SDRW has steel wires of cross-ply construction as its structural reinforcing 
members (fig. 2). The maximum mount of the reinforcements used in the window 
is subject to the specification of its acoustic performance requirement. 
The internal pressurization of the window its enclosed fluid (sea 
water) becomes necessary to generate its additional structural stiffness and 
rigidity. Designers prefer to have the internal pressure being greater than 
the external pressure induced from a ship's operation. However, the maximum 
allowable internal pressure depends on the amount of the steel wires used in 
the window. Under some severe loaeing conditions such as slamming and impact, 
external pressures on some areas of the window exceed its internal pressure. 
The enclosed fluid is, therefore, expected to play an important role on sustain- 
ing its structural integrity. 
The conventional model, in which the enclosed fluid is not included, is 
adequate for analyzing the vindow of a ship under a normal operation. It does 
not give us satisfactory results as the window is subject to severe loads. So, 
more reliable results arc only available for this severe loading situation, if 
a s~phisticated model which includes the internal fluid of the window, is used. 
In this paper, simple models instead of complete and complicated models w i l l  be 
presented for demonstrating the application of NASTRAN to the static analysis 
of u SDRIJ. 
https://ntrs.nasa.gov/search.jsp?R=19780024540 2020-03-22T01:54:43+00:00Z
The c o i ~ ~ p l c t e  lr~odel for a type of n SDRW i s  ellown i n  figure 3. This modal. 
i s  f o r  n coniplete window structure wl~ich i s  at tached t o  the s h i p  s t ructure .  
The enclosed f l u i d  i s  not  included i n  the modd.. it has been used for t h e  
prelinrinary evaluation on t h e  ~itructural in teg r l ' t y  of the SDRW sub jec t  %o 
various s k a t i c  loads. They are: hydros ta t ic  fo rces ,  i n t e r n a l  pressure ,  forces  
induced fro111 t h e  weight of  $ha window, .the enclosed fluid and other  hnrdwases, 
steady s t abe  hyc21.odyneniic fo rces ,  tho  equivalent s t a t i c  fo rces  induced from 
the  slmnnline; and impact on tl!e window, and the combination8 of some loacis as 
n~cntloned .
The window i s  1nodeXed w i t h  q u a d r i l a t e r a l  and t r i a n g u l a r  plate  c lononts  
(cQuAD~ and C T R M ~ ) .  Their  anisotropic m ~ t c r i a l  p roper t i e s  (m'112j a r e  obtained 
based on the rubber co~nposi?;e theory ( r e f .  1 and 2 ) .  Some proper t ies  a r e  
obtained wi.bl t  .I;he use of Walpin-Tsai equations ( r e f .  3 ) .  The uppropriatx? 
bounda~y condit ions aye implemented with SPC or SPC1, The loads on %he window 
can easily be i n p u t  with GRAV, PLOAD2 and FORCE. 
The r e s u l t s ,  obtained froln %ha conventional model for  t h e  case of t h e  
window under no~mal  opera t ional  loads ,  arc satisfactory. However, excessive 
and unreasonable deforma+bions coinpared t o  the observed a r e  obtained i f  t h e  
window i s  under severe loads. Thus, the ex te rna l  loads  on some a reas  of t h e  
window are grea te r  t han  I t s  in.t;ernal loods. Its m a x i m u m  displacements a r e  
greater t h a n  the  th ickness  of the  window. A bet ter  niodel i s ,  therefore ,  
required f o r  obtaining more r e a l i s t i c  so lu t ions .  Af te r  sone considerat ion,  a 
f e a s i b i l i t y  study of t h e  model which includes the  enclosed f l u i d ,  was made. 
SOPHTSTICATD MODEL 
It was developed by adding i s ~ p a r a m e t ~ i c  l inear  hexahedron elements 
(CI~IEXL) f o r  the  enclosed fluid ,to t h e  conventional model. These elements 
are considered as a s p e c i a l  i so t rop ic  s o l i d  wliose shear modulus being much 
smallcs than  its bulk ~nodulus. Because of N A S T M '  s l i m i t a t i o n  on MATI., i t s  
approximate Poisson's r a t i o  chosen t o  be very close t o  .5 (ref. 4 )  and Young's 
modulus, which i s  determined with t h e  cliosen Poisson 's  r a t i o  and its exact 
bulk modulua, a re  used. The con t inu i ty  of t h e  t r a n s l a t i o n a l  displacements of 
the  corresponding g r i d  po in t s  at t h e  f l u i a - ~ t r u c t ' u r e  interfaces a r e  constrained 
with MPC. The f l u i d  boundaries are constrained with SPC. 
A demonstrated model has b e ~ n  developed f o r  evaluat ing t h e  f e a s i b i l i t y  
o f  using a complete sophis t ica ted  model for  the  s t a k i c  ana lys i s  of the SDRW 
structure. This  demonstrated model i s  shown i n  flgure 11. Two loading cases 
on t h i s  model a r e  considereci i n  this paper. They a r e :  (1) a uniform i n t e r n a l  
pressure, and (2) a combined load of an i n t e r n a l  pressure and a non-uniform 
external. pressure induced from t h e  slamming. 
SAMFLED PROBLEM 
The s i ~ n p l i f i e d  s o p h i e t i c a t e d  model used for  khe dcmonstrn-Lion of NASTRAN's 
c a p a b i l i t y  on the SDRW a n a l y s i s  i s  shown i n  figure h .  Two c i r c u l a r  arcs arc 
for  the  window s t ruc tur t ; .  Thei r  din~cnsiuns a r c  given i n  f i g u r e  4. The in1;ernal 
pressure i s  22.4 (27.1 f o r  t h e  comnbined load case) ~ / c r n ~ .  The maximum e x t e r n a l  
p r e s s u r e  is  40.3 ~ / c m ~  exerting on one side of the window. The minimlurn thiclr- 
ness of the  window ~tiodel 13 1.27 cm. 
The r e s u l k s  obtained from t h e  sophiskicn.t;ed model w i l l  bs coinpared t o  
t h o a e  fron~ a s i m p l i f i e d  conven t ion~ l l  model. They w i l l  a loo  be compared t o  
t h o s e  from t h e  same ~no.:el w i t h  a i r  as t h e  enclosed f l u i d ,  The Young's modulu~ 
and t h e  Poisson's r a t i o  used for  sea water  i s  ,1368 ~ / c n i ~  and .h999999. Those 
f o r  a i r  i s  .841t-11 PI/crn2 and .4999999. 
RESULTS AND DISCUSSION 
Only t h e  c r i t i c a l  r e s u l t s  ob ta ined  w i l l  be d iscussed  i n  t h i s  s e c t i o n .  
Tbcy a r e :  displacements ,  reaca t fon  f o r c e s  and moments, snd  nlcrnbrane s t r e s s e s  
(more i~nportrznt information t h a n  eleltient s t r e s se r ;  f o r  designing rubber  
ccmposite slruc.t;ures). The membrane skresses are obta ined  tlsru a post-processor 
excluding .the bending s t r e s s e s  i n  element s t r e s s e s .  The cffec-1; of t h e  approx- 
hate Poi s son t s  r a t i o  used f o r  t h e  f l u i d  (ma water )  on t h e  r e s u l t s  from the  
s o p h i s t i c a t e d    nod el w i l l  also be discussed.  
Fro111 t h e  r e s u l t s  given i n  t a b l e  1, we can f i n d  t h a t  t h e  enclosed water ,  
which has a r e l a t i v e l y  h igh  compres s ib i l i t y ,  can s u s t a i n  the window shape under 
the severe l o a d .  Due t o  the low cc -~p le s s i - tg i l i t y  of' a ir ,  t h e  window f i l l e d  wi th  
air from .I;lie sophis . t icated model y ie lds  r e s u l t s  about t h e  same as those  from 
the convent ional  one under both 1oadi.ng c a s e s .  A s  the  window i s  under an 
i n t e r n a l  p re s su re  which gives a small  deformation,  t h e  convent ional  model shc~uld 
be good enough for analyzing the window. Under t h e  severe load ,  t h e  sophis ' t i-  
cated model should  be used. Its enclosed f l u i d  can: (1) decrease  c r i t i c a l  
d i sp lacements , reac t ion  f o r c e s  and membrane s t r e s s e s  on t h e  loading  sicis and 
i n c r e a s e  those  on t h e  non-loading s i d e ,  ( 2 )  decrease c r i t i c a l  r e a c t i o c  moments 
s u b s t a n t i a l l y  on t h e  loading  s i d e ,  (3)  move t h e  maximum displacement and 
membrane s t r e s s  t o  t h e  non-loading s i de  o f  t h e  window, 
The e f f e c t  o r  ;he approximate Po i s son ' s  r a t i o  chosen f o r  t h e  enclosed 
f l u i d  on t h e  c r i < i c a l  r e s u l t s  a r e  given i n  t a b l e  2. A smal l  increment i n  the  
Poisson's r a t i o  f o r  s ea  water i n s i d e  t h e  window can: (1) inc rease  c r i t i c a l  
displacements ,  (2)  change reaction fo rces  and moments n e g l i g i b l y ,  and ( 3  ) 
i n c r e a s e  membrane s t r e s s e s  s l i g h t l y .  
FINAL REMARICS 
NASTRAN h a s  been used a s  a des ign /ana lys i s  t o o l  f o r  khe SDRW. S a t i s f a c t o r y  
r e s u l t s  can b e  obtained i f  a proper  model i s  used. For t ime and cost-saving 
purposes, a conventional model which only includes t h e  window structure can 5e 
used. If the displace~nents  of t h e  window exceeds i t s  w a l l  th ickness ,  a sophis- 
t i c a t e d  model which includes t h e  enclosed f l u i d  should be used f o r  obtaining 
b e t t e r  so lu t ions ,  The method a s  demonstrated i n  t h i ~  paper gives u s  reasonably 
good r e s u l t s  conpaired t o  those from engineering experience. The approximate 
Poisson's vatio of' Lhc enclosed f l u i d  i s  recormnendea t;o bc .h999999. Wit11 t h i s  
approach, a cos t ly  d i f f e r e n t i a l  s t i f f n e s s  o r  o ther  approaclles may be avoideti. 
The method developed by I h e r s t i n e  ei; a l .  (ref.  9 )  hr~s been considered,  
This  neth hod can assure the continuity of normal displacements and pressures at 
the i n t e r f a c e  of the window and the enclosed f l u i d  from t h e  s t r u c t u r e  and the  
f l u i d  elenen-i;s. The technique implementing t h i s  method f o r  t h e  titled subject 
i s  being developed. 
1. Brewer, H.IC.: S t r e s s  and Dcfornhations i n  Multi-Ply Ai rc ra f t  T i res  Subject 
t o  I n f l a t i o n  Pressure Loading, Technical Report UPDL-TR-70-62, June 1970. 
2. Brewer, H.K. :  Predic t ion  of Ti re  S t resses  and Deformations from Co~nposite 
Theory, Ti re  Science and Technology, TSTCA, Vol. 1, No. 1, February 1973, 
pp. 117-76. 
3. Halpin, J . C . ;  and T s a i ,  S.W. : Environmental Factors  i n  Composite Material  
Design, Al?MT,-~~-67-h23, A i r  Force Materials  Laboratory, Wright-Patterson 
A i r  Force Ease, Ohio, 1968. 
4. Fung, Y. C.  : Foundations of So l id  Mechanics, Pen t i ce -Ha l l ,  Inc . , Englewood 
C l i f f s ,  N. J., 1965, pp. 129-130. 
5. h e r s t i n e ,  G.C . ,  e t  a l . :  The Dynamic Analysis of  Submerged S t ruc tu res ,  
NAS1CRAN: User ' s Experiences, NASA TM X-3278, September 1975, pp. 419-429. 
TABLE 1. CRITICAL RESULTS 
Loading Cases 1 2 
---- 
Displacen~ents (cm) 
A .463 12.81 -13.38 
B ,463 12.70 -13.27 
C (loading side) .4h6 .379 -. 26 
C (non-1 aading side ) .446 .605 
Reaction Forces (N) and Mofrients (N-cm) (P) (P  1 ( M) 
A 2.22-t-lr 1.35+4 2.974-5 
B 2.22.1.4 1.354-4 2.95+5 
C ( l oz  =ing side) 1.734-4 1.66+4 8.14+3 
C (non-loading side ) I. 73+4 2.26-1-4 2.8133 
Membrane S t r e s s e s  ( ~ / c r n ~  ) 
C (loading side) 
C (non-loading side ) 
where A i s  f o r  t h e  window model, B is for t h e  window-air nzoael, and C is fox 
t h e  window-sea water model. 
TABLE 2. EFFECT OF POISSON'S RATIO ON CRITICAL RESULTS 
Loading Cases 
Reaction Forces ( N )  
D 
E 
F 
Membrane S t r e s ses  ( ~ / c r n ~  ) 
n 1,642 
E 1,673 
F : . (03 
where D, E and F are  fo r  Po i s sonTs  ratio being equal t o  .4999, .499999 
and .999999 respectively. 
Figure 1. A Sonar Dame Rubber Uindow 
t r # .  * * a .  - 0  . . * I * .  I . .  a * . .  - 0  . D  w *  .. 
Figure 2. C r o s s - P l y  Construction o f  Rubber  Composite 
\ %  
F i g u r e  3 .  N A S T R A N  Model o f  A Sonar Dome Rubber Window 
R i g i d  Boundary 
1 4 4  c m  4 
FRONT VIEW 
Figure 4. A Simplified S o p h i s t i c a t e d  Model f o r  
A Sonar  Dome Ht~bber Window 
UNDEFORMED 
F i g u r e  5 .  Deformed Shape  of  The Window F i l l e d  w i t h  Sea Water 
UNDEFORMED 
Figure 6 .  Deformed Shaps a f  T h e  Window F i l l e d  w i t h  A i r  


Static analysis of a sonar dome rubber window

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