- Email: [email protected]
Computerized multilevel analysis for multilayered fiber composites
Computm & Stwctwe~,
Vol. 3, pp. 467-482.
Pergamon Pm%
1973. Printed in Great Britain
COMPUTERIZED MULTILEVEL ANALYSIS FOR MULTILAYERED FIBER COMPOSITESt CHRISTOSC. CHAMIS National Aeronautics
and Space Administration, Cleveland, Ohio, U.S.A.
Lewis Research Center,
Abstract-A FORTRAN IV computer code for the micromechanics. macromechanics, and laminate analysis of multilayered fiber composite structural components is described. The code can be used either individually or as a subroutine within a complex structural analysis/synthesis program. The inputs to the code are constituent materials properties, composite geometry, and loading conditions. The outputs are various properties for ply and composite; composite structural response, including bending-stretching coupling; and composite stress analysis, including comparisons with failure criteria for combined stress. The code was used successfully in the analysis and structural synthesis of flat panels, in the buckling analysis of flat panels, in multilayered composite material failure studies, and lamination residual stresses analysis.
INTRODUCTION filamentary composites are structural materials which have evolved in recent years. These composites are constructed by laminating several plies (layers). The plies, in turn, consist of high strength filaments which are embedded in a low strength, low density (for nonmetallic matrices) matrix material while the matrix is in its molten state. Subsequently, the system is processed at specified pressures and temperatures. The result is a very light (for nonmetallic matrix composites), high strength material. Its strength depends on the orientation of the filaments with respect to the direction of the maximum anticipated stress. Coincidence of the filaments with the direction of maximum stress utilizes this material most efficiently and gives it its most attractive features, stiffness and strength to weight ratio. Multilayered filamentary composites as structural materials have exhibited great potential in space vehicles, deep submergence vessels, radomes, and other structures where the stiffness and strength to weight ratio, nonmagnetic, structural damping, elevated temperature, and environmental resistant properties are important. The underlying structural strength principle for these materials is that the filaments are the primary load carrying members while the matrix provides the structural integrity by serving as a load transferring medium, providing rigidity (keeping the filaments fixed in their position), and protecting the filaments from exposure to unfavourable environment. Though multilayered filamentary composites have many desirable design features, as a structural material they are at the dawn of their great potential. One of the factors that keeps these composite materials at the dawn of their great potential is the designer’s lack of proven and readily available mathematical formalisms which could be used to select constituent materials when the structural application of the composite is specified. These types of mathematical formalisms constitute a multilevel analysis encompassing the following levels : micromechanics, macromechanics, combined-stress strength functions, laminate MULTILAYERED
TPresentedat the National Symposium on Computerized Structural Analysis and Design at the School of Engineering and Applied Science, George Washington University, Washington, D.C., 27-29 March, 1972. 467
CHRISTOSC. CHAWS
468
analysis, and delamination criteria. This type of multilevel analysis is quite extensive and cumbersome. It needs to be transformed into an efficient computer code to be effective and practical. A FORTRAN IV computerized multilevel analysis for multilayered fiber composites which has grown to maturity over the past several years is the subject of this paper. This multilevel analysis includes all the levels mentioned previously. It has been extensively used for analyzing several fiber composite systems. The computer code is described herein from the engineer’s/analyst’s usage viewpoint. Therefore, the description is limited to input-otrtput, results produced and application versatility. The complete documentation of the code is given in [l]. Several of the mathematical functions programmed are described briefly as part of the code output. OBTAINING
AND USING THE CODE
The mechanics required to use this code for the analysis of multilayered fiber composites are described in some detail. Here, it is assumed that the user is interested in using the code as a tool only and that he has available to him a FORTRAN IV manual. The physical representation of the code is illustrated in Fig. 1. The geometry of the constituents, the ply, and the composite are defined in this figure. The required input
(1) Fiber, Properties needed: Efll, a 33: wlf 23,~ GII& 23,~ ~11, n 3~ Ktll, 22 33; Yfn PL Nf; 4; sft
tb) Matrix. Properties needed: Emil, 22 33; vml& ~$13; Gtl& Z$IE omtl, 22 3% Krnll,22,33; km, pm0 Smc. empt empc. empw ‘mpTOR. PlY orientation angle, 90-x deu
(cl Ply. Input Fiber and matrix properties: & &1, & Al. Properties computed: Eni, 22 33; vuz 23.13; ‘4.t~ 211% au, n, 33; Ku 22,33; 4% PI, tL 64
SUIT, 11~. m, m, 125,235; Km. stress aMWs: ‘~122 18 anl, 22 13 1.0 - F(a.SJW
FIG. 1. Typical multilayered fiber composite and some basic definitions.
ZI
Computerized
Multilevel Analysis for Multilayered Fiber Composites
469
properties, correlation coefficients, and computed properties are summarized in Fig. 1 in symbolic form. The physical arrangement of the code is illustrated in Fig. 2. The numbers given in each block of cards are for subsequent discussion and do not appear on the code. Four steps are required to use the code in the user’s computer facility: (1) Obtain the code. (2) Make it operational in the user’s computer facility. (3) Supply the input data. (4) Interpret the code output results.
Matrix inverter (INVAI
FIG. 2. Code physical arrangement.
470
ChRISTOS c.
CMMIS
Obtain the Code The code can be obtained in cards or tape from [2]. If this is not convenient or possible, then the cards can be punched from the compiled listing appended in [l]. Make it operational Making the program operational requires the availablity of a FORTRAN compiler in the user’s computer facility, certain control cards at the beginning of the code, and the card that preceeds each subroutine. Consult your computer group about these items. The control cards present in the code are only for the Lewis IBM 7044/7094 direct couple system. Once the deck of cards has been assembled as is shown in Fig. 2 (except Input Data) with the proper control cards, the user is ready to compile the code in his facility. The compilation will indicate whether any additional modifications are needed. Most modifications will be minor and will usually deal with certain logical and subroutine call statements peculiar to each compiler. Consult your computer group for these modifications. Suppl_vthe input datu The physical arrangement of the input data cards is illustrated in Fig. 3. The numbers in the group of cards are for identification purposes in this description and do not appear on the cards. A sample input data sheet is illustrated in Table 1 for the Thornel-SO/epoxy composite system.
TABLE1. Input data for Thornel-SO/epoxy composite THORNEL-50/EPOXY 54 8 71 .5UOOOE.U8 .ZOOOUE.UO .5700UE.U6 .UUU00E.00 .4UOOCE.U1 .00000E.00 .00000E.00 .lCOOCE.Cl -.55000E-u6 .42800E-u4 .5BOOUE.U3 .12500E.L~1 ,Ou000E.00 .10000E.01 .31416E.01
1420
1
.lOOOOE.O7 .13000E.07 .57000E.06 .OCUUOE.CO .20000E.O1 .OOuOOE.OO .COOOCE.OO .lOOOOE.Ol .56000E-05 .428006-04 .5800OE*02
.12500t.01 .22500E*OO .10000E.01
P F F .0000uE.uO .OOOOUE.CU O.OUOOUE.00 0.5000CE.00 0.5UCOl’E.W .00000E.U0 -.4500UE.UZ .UU805E.UC .OO&l05E.U0 -0.3uCOUE.U3 -0.30UOUE.03 .83COuE.UU .1650l~E.C2 .51)00CE.UU [email protected] [email protected] .0450CE.00 .5COOUE.U4 .lUU00E.U3 [email protected] 0.00000E.00
.05900E.00 .uUOOOE.OU O.OOOOOE.OO 0.5000DE.00 0.50U00E.00 .450UOE.02 r4500CE.02 .UUt)U5E.00 .00805E.00 -0.30000E.03 -0.300UOE.03 .1UOUOE.O1 .10000E.01 .13300E.02 .21000E.05 .0U000E.00 .00000E.00 O.OOOOCE.OO
.lOOOOE.07 .70000E.O6 .36000E.00 .OOOOOE.OO .40000E.01 .23560E.01 .UOOOOE.OO .OOOOOE.OO .56000E-05 .42800E-04 .58000t.02 .25000E.00
.20000E.00 .13OUUrz.O7 .36OUUi.O0
.25000E.00 .57000E.06 .36000E.00
.ZoOUUE.Ol .00000t.00 .OoOUUE.OO .OoOUUE.OU
.00000t.00 .OOOOoE.OO .10000E.01 .OOOOOE.OO
.170uUt.00 .ooouo~.oo
.12500E.01 .oOOOoE.OO
.10500E.01
.10500E.01
.04430E.00 .00000E.00 O.OOOOOE.OO 0.50000E.00 0.50000E.00 -.45000E.OL .00000t.00 .00000E.00 .00800E.O0 -0.30000E.03 -0.30000E.03 .26000E.00 .lOOOOE.Ol .31900E.05 .UZOOOE.OO .UOOOOE.OO .UOOOOE.OO 0.00000E.00
.U0026E.00 .uoUuUE.OO 0.50000E.00 .90UUUE.02 .UOMdJE.OO -0.30000t.03
.00000E.00 0.50000E.00 .90UOOE.02 ~00800E.00 -0.30000E.03
.27UUUE.00 .04650E.O0 .10000E.01
.17000E.00 .lOOOOE.Ol
.lJ50rrUE.00
.04500E.00
o.UOOUOE.00
.lOOOOE.Ol
0r00000E*00
COmPuteriN Multilevel Analysis for Multilayered Fiber Composites
Thickness boolean: one card, one entry
four car& 16 entries
one card, three entries
Constituent materials four cards, LBentries
CompositeSystemcard: one card, 55 characters
FIG.
3. Physical arrangement of input data cards.
Listings of input data for several composite systems are appended in [l]. These systems are shown graphically in Fig. 4. The input data for these systems can be punched from the
472
CHRISTDS C. CHAWS
listings, and the cards that need alterations for the specific problem can be modified accordingly. Input data for additional composite systems may be easily prepared. This is done by selecting a related system from those available and modifying those entries that need modification.
FIG. 4. Composite systemsfoe which input data are supplied.
After the input data have been properly assembled (as is shown in Fig. 3), it is placed in its physical position (Fig. 2), and the code is ready to be run for results.
Input ply properties
There could be cases when the user would prefer to supply some of his own ply properties instead of using the code to compute them. The user has to provide his own formats for these cases. The physical location for these statements is described in the section MAIN PROGRAM. A flow chart of the MAIN PROGRAM is shown in Fig. 5. The functions of the subroutines are listed in Table 2.
Computerized
473
Multilevel Analysis for Multilayered Fiber Composites
a
Start
Kvlj- pUi Krq - Plzj ‘2, - Pnj %s-
Pu21
9 - Pu3j P114j’PUZ, + Pn31 P113j’ Pll3j d180 L
PUP, ’ Pu4, ?a0 1 End j - LOOP I Call CECL
I
IS 1Subrouti:e CUSC pibroutife
1
GACD3l
kubroutine GPCFDii LSubroutIne CPH kbroutine
1
GECL 1
1 Subroutine COMPSA 1
FIG. 5. Code MAIN PROGRAM TABLE
Subroutine INVA GLLSC GACD 3 GPCFD 2 GPH GECL GSMF COMPSA
flow chart,
2. Subroutine description Function
Matrix inverse Simple limit stresses (strengths) ply (unidirectional composite) Three.-dimensional laminate thermoelastic properties Two-dimensional laminate thermoelastic properties Ply heat conductivities Ply thermoelastic properties Strain magnification factors Laminate analysis, ply stress-strain, ply margin of safety
cHRIsTos c. CHAMIS
474
OUTPUT
AND ~T~~~C~
RELATIONS
The program output consists of printing out, (1) the input data, (2) the composite threedimension strain-stress and stress-strain relations about the structural axes (see Fig. 6), (3) the composite properties generated in array PC, (4) the composite constitutive equations about the structural axes, (5) the reduced bending and axial stiffness, (6) displacement-force relations, (7) the current load or displacement condition, and (8) the ply properties, stresses, and margin of safety generated in array PI,.
Fiber directbn
Fio. 6. Ply orientation geometry. Composite structura1 axes, x, Y, t; composite material axes; 1,2,3; ply material axes (coincides with fiber direction, lg. 2t, 3s).
The printout of the input data is preceded by its code name. For example, the first and second lines of printout are: THORNEG5O/EPOXY NL, NPL, NPC, NFPE, NLC 8
71
54
1420
1.
The output of code generated data is preceded by title headings. The output of the composite three-dimensional strain-stress temperature relations and composite stress-strain relations about the structural axes are printed under the headings 3-D COMPOSITE
STRAIN-STRESS
The matrices [EJ;’
and {a& in the equation
are printed out.
RELATIONS-STRUCTURAL
AXES
475
Computerized Multilevel Analysis for Multilayered Fiber Composites
3-D STRESS-STRAIN
RELATIONS-STRUCTURAL
AXES
The matrix [E,], in
is printed out. The subscript s in the preceding equations indicates that the relations are written about the structural axes. It is noted that these properties are only local to subroutine GACD 3. They can be made global if needed. The output of the composite properties, generated in array PC are printed under the heading COMPOSITE PROPERTIES-VALID THROUGH THICKNESS
ONLY FOR CONSTANT
LINES 1 TO 31 3-D COMPOSITE PROPERTIES LINES 33 TO 54 2-D COMPOSITE
TEMPERATURE
ABOUT MATERIAL
PROPERTIES
AXES
ABOUT STRUCTURAL
AXES
Fifty-four entries are printed under this heading as follows :
PC(l) PW) PC(3) to PC(I 1) PC(12) to PC(14) PC(15) to PC(18) PC(19) to PC(30) PC(31) PC(32) PC(33) to PC(38)
El
PC(39) to PC(47)
E cl19 Gcl29
PC(48) to PC(54)
{4,
vc12
KC, HC
weight density thickness three-dimensional stress-strain relations about material axes three-dimensional coefficients of expansion about material axes three-dimensional heat conductivities and heat capacity along material axes three-dimensional constants about material axes distance to reference plane from bottom of composite blank two-dimensional stress-strain relations about structural axes two-dimensional elastic constants along structural axes two-dimensional coefficients of thermal expansion, heat conductivities, and heat capacity along structural axes.
The output for the composite constitutive equations are printed under the heading FORCES
FORCE-DISPLACEMENT
RELATIONS
DISPL
THERMAL
FORCES
CHRISTOS C. CHAMIS
416
The elements of matrices A,,, C,,, NchTx, and McATxare printed out. The output for the reduced bending rigidities is printed under the heading REDUCED
BENDING
RIGIDITIES
The elements of O,“, are printed out in one line. The output for the reduced axial stiffness AFxis printed out under the heading REDUCED
STIFFNESS
MATRIX
The inverse of the constitutive equations is printed out under the heading DISP
DISPLACEMENT
FORCE RELATIONS
FORCES
The elements of this inverse are printed out. The output for the current load condition is printed next to the headings FOR THIS CASE NBS (X’, Y, XY-M) IS
FOR THIS CASE MBS (X, Y, XY-M) IS The current values of N,,, m,,, mcxy, B,,, Mcy, and Me,.. are printed out under these headings. The output for the current displacement conditions is printed under the heading FOR THIS CASE THE DISPLACEMENTS WCBYY, WCBXY) ARE:
DZSI’(ECSXX, ECS Y Y, ECSX Y, WCBXX,
The output of the ply properties generated in array PL are printed out under the heading LAYER PROPERTIES,
ROWS-PROPERTY,
COLUMNS-LAYER
Seventy-one entries are printed out under this heading as follows:
pw, 1) fw, 1) PL(3, PL(4, PL(5, PY6, PL(7, PL(g, PL(9,
I) I) I) I) I) I) I)
ply void content ply apparent fiber content ply actual fiber content ply apparent matrix content ply actual matrix content ply weight density ply layer thickness ply and interply layer thickness interply layer distortion energy coefficient
Computerized Multilevel Analysis for Multilayered Fiber Composites
PL(10, I)
z
PUll, I) PYl2, I)
ZC# 8 es
PL(l3, I)
01
PL(l4, I)
8lx
PL(15, PY24, PL(27, PU30, PY31, PL(43,
I) I) I) I) I) I)
Pw4
I)
to PL(23, I) [EJ to PL(26, I) {QI} to PL(29, I) {K,} HC, to ~~(32, I) &I, v112, G,,, to PL(48, 0 &I229 4pi29413 d pd.?1
AT PY50, I) PL(5 1, I) to PL(60, I) SI1i T, etc. K 112crg PL(61, I) PL(62, I) PL(63, I) P.W& ;; to PL(69, I) $;I, 1~11 i PL(71: I)
477
distance from bottom of composite to ply centroid distance from reference plane to ply centroid angle from structural axes to composite material axes (same for all plies), Fig. 6 angle from ply material axes to composite material axes, Fig. 6 angle from ply material axes to composite structural axes, Fig. 6 ply stress-strain relations ply thermal coefficients of expansion ply heat conductivities ply heat capacity ply elastic constants ply strain magn%cation factors interply delamination factor ply temperature ply limiting stresses coefficient in combined-stress-strength criterion ply margin of safety-from distortion energy interply delamination margin of safety ply strains and stresses adjacent ply relative rotation margin of safety from Hoffman’s failure criterion.
The failure criterion may be determined by either of the following methods. (1) Modified distortion energy
(2) Hoffman’s criterion F-l-
dli C
F>O F=O F< 0
-~u14122
&llCSlllT
no failure incipient failure failure
where o denotes stress and S the limit stress always taken positive. The subscripts denote direction and sense.
478
cHRL9TOs c. CAAMIS
The interply delamination criterion for the ith interply layer at the mth load condition is governed by +PL(63, I) when i > 1 H%l A4j=*(e,ly
-&,&in
2e1- sin 20,_ I) -~Ecxy(COS 281+COS 28i_ 1)
{&,}+[A,,l-l({m,}+(N,*,,)+[C,,l{w,,)) or as given by the displacement force equation described previously. The inputs to the subroutines to generate the PL array are the ply angle measured from the structural axes (0, from PL(14, I)), the distance from the reference plane to centroid of the ply Grl from PL(11, I)), the ply temperature (AT,, from PL(50, I)), the interply delamination limit (A~a,rj from PL(60, I)), and the ply thermoelastic properties stored in PL(24to 26, I) and PL(31 to 42, I). The ply extensional and coupling rigidities A,,=ACX and C,, = CPC; the local curvatures W&x=WXX; the adjustment constants K;iZTT=BET(l, 7), I&--=BET1(2, 7), K’,,,,,=BET(l, 8), and K’11ZCC=BE7’(2, 8); and the load condions N,,=NBS(m). All other adjustment constants are input data. A sample output for a Thornel-SO/epoxy angle ply composite is given in Table 3.
Computerized Multilevel Analysh for Multilayered Fiber Compoaitea
TABLB3. Sample case output (cont’d)
-0.2449E46
D.l43Ut-04
-U.Z*WE-J* O.WTlE-07
0.93S3E-09
o*
0.
0.
ML
0.
0.2937E-DS
0.
0.
-0.
0.
0.
0.
0.
0.2917e01
0.
-0.
0.
0.
0.
0.
0.
O.?0W-09
4.
WWJCTUAL
0.+779$
07
0.4ZIYL
06
-D.
-0.
07
D.49ZOE
01
-0.
-0.
0.42ISE
01
D.W2OE
Ob
D.llbOa
07
-0.
-0*
.D.
-0.
-0.
-0.
4.
-0.
-0.
-D.
-0.
0”: 01
:
::
z: CC33 CCII CCSS eCb6
:*:::z . O.llbOE c.3+OsE D.3IOY C.SODlI
:: or 06 Ob DT
-O.>l3lE-OS 0.11999~F-al 0.1.,X-M 0.2199E 01 0.75*4e 02 0.371% 01 O..?UIn? DD
19
Et
:: ::
EC22 K33 z::
p;w~ O.lOCK . 0.3405f C.wDOY
“0; 07 06 0.
::
UC12
ECl?.
C.50011
ii_
czi
Dt 01 00 DO 00
0.24DlC
32 3s
WDEC ccl1
o.JIWt-01 0. U.149K
00
ZCDC
ii::
Yaw
O’
% :;
2:: :::
O’ 07 :;
2 ::
K22 K12 UC12
::*99’e O.SODlE ty~
4‘ .I
z: CY,,
D:YOOlR 0.17121 0.3OwE -C. -0.
01 01 00
::
-
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z%: c:mz
“sic”::
ILLNIDIIS
01
is: ccl3
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SIRAIW
07
: S
I9
SIRSSS
D.4779E
O.S16W-01 D.WOCGOl
D.l712E 0.309br -D.d:ZY -O.*?K+DL D.2lJ(t
COIPOSITE
O.lSD+E
ffUfELTIcS - VALID I 13 31 .3-O CUWOSItE 3, 7” s4 24 ConPUstTE
ClLl L c7cz2 CTCSJ tail )*a m33
O.E*BSI49
0.
rc
12 1s 14 19 16 ::
01!19m-D@
-9.
-0.
Dd
:
:
-0.
-0.3tBlC-09
0.
0.
-0.2L96E-04
0.
LIWS LINLS
0.
-O.&?~bL-JL
P-D
CDwOlllt
0.4kIIPDT
&1*09E-Ob
DI
Da
0.340011
WV fm Cc~SlLhl l(LRfeRATUAR TwI(uOR PROIMTtfS AlpUT RAtIIIhL U‘S lnOISRllts LdOUl SrRucruIuL ARCS
01
0. 01 -0.
-0. o.upr -Dd
rn:u9rss
AXES
-0. 06
-0. 0.S0011
01
CHBISTOS c. CHAMIS
TABLE 3. POWiS
FDlCE
Sample case output (cont’d)
o,sPL.CE*‘*l
RELATllYtS
DI SPL
,tlE”“.L
FOIICES
nr
0.952Y
06
0.1949E
06
0.
0.1*21c-01
0.4518E-O,
O.lOleE-0,
“I
-O.,6,bE
a1
IlY
0.2949E
Q6
O.lltZE
01
0.
O.C5,8E-OS
0.1209E-04
o.,l**E-o4
“I
-0.342TE
03
WY
0.
0.
0.,041t-0,
O.l(l,lE-0.
0. U)IZE-04
VW””
111
O.LZZIE-03
O..516E-04
O.,O61C-03
O.325LL
03
O.lOOlE
03
0.6,POE
01
“XI
-IJ.Z23SE-OT
NY
0.451*-o4
O.ZZOPE-04
O.,ll5L-04
O.,OO7E
03
0.11796
02
0.22601
02
““I
-0.29WE-01
WV
O.IObaE-oi
O.,U%-0.
0*3052E-04
0.6WE
02
0.226OE
02
O.LO9X
II,
*I*
KEcuCEn
amOIYG
0.52513E
aicucED 0.96bZE
OS
0.12OOE
06
03
0.419OCf
02
OISP.
O*LO06,E
0,
O.,II,P,E 02
0.29494E
06
0.,7225~
0.223x-05
-O.,PIE-05
-0,3127E-01 O.L‘32E-2,
VKPW YXK
-0.34,6K-12
WV
O.M09E-12
YKV
-0,1792E-12
O.,IIPE-2,
0.,5592-l,
O.llP%-05
0.62251-12
-0.1006E-I*
-O.Z2?3E*Ol -0.4003E-*O
0.L83JE-02
-O.L92OE-L2
-C.l,,ZE-02
-O.,PR-OS O.l13ZE-21
0.34ISE
00
-0.3454X-12
00
O.b4OpE-12 -0,7792E-12
0.22IPIF
02
-o.,q281E-Lo
O.LO924E
0)
0.3200~
04
-0.7792E-12
“K
-0.2716E-L,
-0.36101-12
NV
-0.14436-12
-0.292oL-,2
NKV
-O.L7l2c-02
YK
12
-0.,,046-01
-0.3*,OE-12
-O.SSlOE
-O.#,6lE-01
-O.“ooLE-,I
-O.LIOIE-OL
0.223SE-05
OI
-0.49231-10
0.6409E-
-0.%4X-12
O,SPL.CE)(ENI
O.lZlIE-01
0.6300W
PORCEI
O.t.ZZSE-I2
-0.2716E-Ll
DIP.
02
-0.H2816-LO
-O.,,%E-,2
O.L,12E-21
O.L2%E-04
06
O.zll*,E
FORCE LELAl*ONS
oIsPLACE*EHr
VK
0.29~0E-o7
*EttOlr*P, O.LoObVE
sliPPM,, mmtx 06 0.29491E 06 -0,49233E-10
UK
3.
0.34316-0,
-O.L05,E-02
-O.IOS,E-C2
NV
0.103VE-OL
wxv
POACE KCLU IONS
FDKCLS
-0.5121E-0,
O.,,,ZC2I
-O.,4,6E-12
O.L409E-12
-0*779IE-I2
0.12,4E~4
0.,,,9~21
0.622,E-12
-O.I7,4E-Ll
-0.349dC-12
O*IS59E-21
0.,,2,E-O,
-0.,.4*-12
-0.29*(N-12
-0.9OOIE-LL
0.483X
34
-O.,rZTE
0
0.
0.622,E-12
-0.,006E-12
0.6,lJE~02
-O.I104E-01
-O.LIl*E-02
-0.21,6E-11
-O.,,43E-,2
-O.,lO4E-01
0.39,lE-01
-O.lo,,E-02
-0.*9,OE-O,
-O.,b,OE-12
4.2920E-12
-0*1Tl2E-02
0.1031-01
0.29SOE4V
-O.lOSR-C2
0.5310E
02
LIVER PKoPER11E 5. ROWS-PROPER I(” : 3
::.
0. O.SOOOE 00 0.9now 00 0.5n0oE on o.son3t 00 o.s**si-0, o.,ooOC-02 0.6slleS-OI -o.oooof-LP o.*ooaS-02 -0.2,OOE-0, 9. 0.5136E 00 0.52,bS 00 0.25‘9f 011 0.4LII 06 O..LL,L Ob .p:;"(",: g
0. 0.503nt JO 0.50,UE 30 O.S,,JE 30 o.soocE 30 0,516~E4L O.IOEOE-02 n.*slbL-01
::soocE O.JOOW ~.,00oE O.SOPcE 0.516*~01 0.5008-01 O.bSlY-Ol
00 00 “0 00
0.
-De:sz,bE on -3.5236E 00 0.25‘9L O.+,lBE 0.4ll8E O.L,605 3 .r.oi
01 $6 0. 0, 06
0.44nC-s-01 O.L2OOF-"L ::,z,bS 00
o.,*,SE 0*2,49E O..llC O.~LLSS O.LLwE o.*f,B
00 "8 06 Ob 01 06
0. 0.5000E o.soonE O.,POOE 0.5090E 0.,165E-0, 0. “D”lE-02 O.bS~bE4,
0. 0, 37 03 00
Loo,-01 0,2noo,-B, n. -0,,2,6E ,') -0.,*,01 ,o 0.25.9E OS ".4LLOE 06 O..LI,F es O.LI,JE "1 0,+79x OS
O.EYYOC ,,
o.,mni
0, O.,,99C ,, 0.5?00E 11 9.,1,,9-51 0.,,"JP-,2 O.,,,bE-5. 0. O.S1ODE-3, 0.2IOJI-9, 0. O.,2,b, ,, o*,*,~, 5, 0.2S6.5 3, D..,lIE o* O.,,l"E 01 O.IlIOP 37 0.6lKlC 01
ComputerizedMultilevelAnalysisfor MultilayeredFiber Composites
481
TABS 3. Samplecase output (eont’d)
CODE APPLICATIONS This computerized multilevel analysis has been applied extensively to various aspects of fiber composite analysis, design, and optimization. Typical cases include: nonmetallic [3-5] and metallic [6] fiber composite characterization, random composite characterization [7], lamination residual stresses [&lo], buckling of fiber composite anisotropic plates [11, 121, exploratory designs of fiber composite turbine blades (unpublished notes), feasibility studies of high-tip-speed compressor blades made from advanced fiber composites [lo], failure analysis of flat and tubular members [3, 41, gross and local impact studies [13, 141, structural synthesis, and sensitivity studies of flat plates [3], and other important factors in designing with fiber composites [15]. IMMEDIATE
EXTENSIONS
The code can be readily modified and supplemented to handle nonlinear material response, temperatures dependent properties, inter, and intraply hybrid fiber composites. The details of these modifications become apparent once the user has some experience in using the code. REFERENCES 111C. C. CHAW,Computercode for the analysisof multilayeredfiber Composites-Usersmanual. NASA TN D-7013 (1971). [2] ANON., Analysis of multilayered fiber composites(M71-10112), from COSMIC (Computer Software Management and Information Center), Barrow Hall, Univ. Georgia, Athens, Ga. 30601.
481
cEIamns c. clwuls
[3] C. C. (Zmnas, Design oriented analysis and synthasis of multilayered filametary structural panels.
Ph.D. This, Case Wc&ern Reserve Univ. (1967). [4] C. C. CHAMI~, IWurc criteriafor tilamentary compositea. NASA TN -5367 (1969). [Sl C: C. CHAHELI, Thermoektic properties of unidirectional filamentary comp&es by a semiempirical wca theory. Science of AdwmcsdMoterlals md Procem &gineering Procee&g~, 14,
WMcrQ Fbiodicols Co., paper 145 (1?68). [s] C.&Cmm, Cbaractmtion and design mechanics for fiber ruinforced metals. NASA TN D-5784
[7] C. C. &rum, Dadgo propertie of randomly reinforced fiber/r&~ composites. Proc. 27th Sot. Pkastfcs Ind, AnnnolTuch.Co& paper 9-D (1972). [8] C. C. Cmm, Design and anab& of fiber composite structural components. Aerospace Structural Materials,NAM SP-227.217-218 (1970). t91 C. C. Cn&aa, Lamination residual stxcwu in muhilayered fiber composites. NASA TN D-6146 (1971). [lo] C. C. CHAMIS, Lamination residual atresses in cross-plied fiber composites. Proc. 261 Sot. Plastics Znd. ANI& Td. Cot& 17-Dl to 17-D12 (1971). [ll] C. C. tBi&m, Buckbg of anisotropiccomposite plates. L Strucr. Div. AXE%, 2119-2139 (1969). [12] C. C. C%IAMIS, Budding of boron/abninium and graphite/resin fiber composite anisotropic panels. Sod&y of Amwpac8 A4aterialandProms Engineers Space ShuttleMaterial,r3,137-147 (1971). [13] C. C. fhma, M. P. HANSON and T. T. SEMFINI,Designing for impact resistance with unidirectional fikp cwmpo&a. NASA TN D-6463 (1971). [14] ~gT,.jMoo~, Wave rurfacea due to impact on anisotropic fiber composite plate& NASA TN D-6357 1151C. C. ‘bum, Important factors in fiber composite design. Proc. 24th Sot. PlasticsZnd.Amuol Tech. Cord. 18-E-l to 18-W3 (1969). (Received22 Febtwwy1972)
Vol. 3, pp. 467-482.
Pergamon Pm%
1973. Printed in Great Britain
COMPUTERIZED MULTILEVEL ANALYSIS FOR MULTILAYERED FIBER COMPOSITESt CHRISTOSC. CHAMIS National Aeronautics
and Space Administration, Cleveland, Ohio, U.S.A.
Lewis Research Center,
Abstract-A FORTRAN IV computer code for the micromechanics. macromechanics, and laminate analysis of multilayered fiber composite structural components is described. The code can be used either individually or as a subroutine within a complex structural analysis/synthesis program. The inputs to the code are constituent materials properties, composite geometry, and loading conditions. The outputs are various properties for ply and composite; composite structural response, including bending-stretching coupling; and composite stress analysis, including comparisons with failure criteria for combined stress. The code was used successfully in the analysis and structural synthesis of flat panels, in the buckling analysis of flat panels, in multilayered composite material failure studies, and lamination residual stresses analysis.
INTRODUCTION filamentary composites are structural materials which have evolved in recent years. These composites are constructed by laminating several plies (layers). The plies, in turn, consist of high strength filaments which are embedded in a low strength, low density (for nonmetallic matrices) matrix material while the matrix is in its molten state. Subsequently, the system is processed at specified pressures and temperatures. The result is a very light (for nonmetallic matrix composites), high strength material. Its strength depends on the orientation of the filaments with respect to the direction of the maximum anticipated stress. Coincidence of the filaments with the direction of maximum stress utilizes this material most efficiently and gives it its most attractive features, stiffness and strength to weight ratio. Multilayered filamentary composites as structural materials have exhibited great potential in space vehicles, deep submergence vessels, radomes, and other structures where the stiffness and strength to weight ratio, nonmagnetic, structural damping, elevated temperature, and environmental resistant properties are important. The underlying structural strength principle for these materials is that the filaments are the primary load carrying members while the matrix provides the structural integrity by serving as a load transferring medium, providing rigidity (keeping the filaments fixed in their position), and protecting the filaments from exposure to unfavourable environment. Though multilayered filamentary composites have many desirable design features, as a structural material they are at the dawn of their great potential. One of the factors that keeps these composite materials at the dawn of their great potential is the designer’s lack of proven and readily available mathematical formalisms which could be used to select constituent materials when the structural application of the composite is specified. These types of mathematical formalisms constitute a multilevel analysis encompassing the following levels : micromechanics, macromechanics, combined-stress strength functions, laminate MULTILAYERED
TPresentedat the National Symposium on Computerized Structural Analysis and Design at the School of Engineering and Applied Science, George Washington University, Washington, D.C., 27-29 March, 1972. 467
CHRISTOSC. CHAWS
468
analysis, and delamination criteria. This type of multilevel analysis is quite extensive and cumbersome. It needs to be transformed into an efficient computer code to be effective and practical. A FORTRAN IV computerized multilevel analysis for multilayered fiber composites which has grown to maturity over the past several years is the subject of this paper. This multilevel analysis includes all the levels mentioned previously. It has been extensively used for analyzing several fiber composite systems. The computer code is described herein from the engineer’s/analyst’s usage viewpoint. Therefore, the description is limited to input-otrtput, results produced and application versatility. The complete documentation of the code is given in [l]. Several of the mathematical functions programmed are described briefly as part of the code output. OBTAINING
AND USING THE CODE
The mechanics required to use this code for the analysis of multilayered fiber composites are described in some detail. Here, it is assumed that the user is interested in using the code as a tool only and that he has available to him a FORTRAN IV manual. The physical representation of the code is illustrated in Fig. 1. The geometry of the constituents, the ply, and the composite are defined in this figure. The required input
(1) Fiber, Properties needed: Efll, a 33: wlf 23,~ GII& 23,~ ~11, n 3~ Ktll, 22 33; Yfn PL Nf; 4; sft
tb) Matrix. Properties needed: Emil, 22 33; vml& ~$13; Gtl& Z$IE omtl, 22 3% Krnll,22,33; km, pm0 Smc. empt empc. empw ‘mpTOR. PlY orientation angle, 90-x deu
(cl Ply. Input Fiber and matrix properties: & &1, & Al. Properties computed: Eni, 22 33; vuz 23.13; ‘4.t~ 211% au, n, 33; Ku 22,33; 4% PI, tL 64
SUIT, 11~. m, m, 125,235; Km. stress aMWs: ‘~122 18 anl, 22 13 1.0 - F(a.SJW
FIG. 1. Typical multilayered fiber composite and some basic definitions.
ZI
Computerized
Multilevel Analysis for Multilayered Fiber Composites
469
properties, correlation coefficients, and computed properties are summarized in Fig. 1 in symbolic form. The physical arrangement of the code is illustrated in Fig. 2. The numbers given in each block of cards are for subsequent discussion and do not appear on the code. Four steps are required to use the code in the user’s computer facility: (1) Obtain the code. (2) Make it operational in the user’s computer facility. (3) Supply the input data. (4) Interpret the code output results.
Matrix inverter (INVAI
FIG. 2. Code physical arrangement.
470
ChRISTOS c.
CMMIS
Obtain the Code The code can be obtained in cards or tape from [2]. If this is not convenient or possible, then the cards can be punched from the compiled listing appended in [l]. Make it operational Making the program operational requires the availablity of a FORTRAN compiler in the user’s computer facility, certain control cards at the beginning of the code, and the card that preceeds each subroutine. Consult your computer group about these items. The control cards present in the code are only for the Lewis IBM 7044/7094 direct couple system. Once the deck of cards has been assembled as is shown in Fig. 2 (except Input Data) with the proper control cards, the user is ready to compile the code in his facility. The compilation will indicate whether any additional modifications are needed. Most modifications will be minor and will usually deal with certain logical and subroutine call statements peculiar to each compiler. Consult your computer group for these modifications. Suppl_vthe input datu The physical arrangement of the input data cards is illustrated in Fig. 3. The numbers in the group of cards are for identification purposes in this description and do not appear on the cards. A sample input data sheet is illustrated in Table 1 for the Thornel-SO/epoxy composite system.
TABLE1. Input data for Thornel-SO/epoxy composite THORNEL-50/EPOXY 54 8 71 .5UOOOE.U8 .ZOOOUE.UO .5700UE.U6 .UUU00E.00 .4UOOCE.U1 .00000E.00 .00000E.00 .lCOOCE.Cl -.55000E-u6 .42800E-u4 .5BOOUE.U3 .12500E.L~1 ,Ou000E.00 .10000E.01 .31416E.01
1420
1
.lOOOOE.O7 .13000E.07 .57000E.06 .OCUUOE.CO .20000E.O1 .OOuOOE.OO .COOOCE.OO .lOOOOE.Ol .56000E-05 .428006-04 .5800OE*02
.12500t.01 .22500E*OO .10000E.01
P F F .0000uE.uO .OOOOUE.CU O.OUOOUE.00 0.5000CE.00 0.5UCOl’E.W .00000E.U0 -.4500UE.UZ .UU805E.UC .OO&l05E.U0 -0.3uCOUE.U3 -0.30UOUE.03 .83COuE.UU .1650l~E.C2 .51)00CE.UU [email protected] [email protected] .0450CE.00 .5COOUE.U4 .lUU00E.U3 [email protected] 0.00000E.00
.05900E.00 .uUOOOE.OU O.OOOOOE.OO 0.5000DE.00 0.50U00E.00 .450UOE.02 r4500CE.02 .UUt)U5E.00 .00805E.00 -0.30000E.03 -0.300UOE.03 .1UOUOE.O1 .10000E.01 .13300E.02 .21000E.05 .0U000E.00 .00000E.00 O.OOOOCE.OO
.lOOOOE.07 .70000E.O6 .36000E.00 .OOOOOE.OO .40000E.01 .23560E.01 .UOOOOE.OO .OOOOOE.OO .56000E-05 .42800E-04 .58000t.02 .25000E.00
.20000E.00 .13OUUrz.O7 .36OUUi.O0
.25000E.00 .57000E.06 .36000E.00
.ZoOUUE.Ol .00000t.00 .OoOUUE.OO .OoOUUE.OU
.00000t.00 .OOOOoE.OO .10000E.01 .OOOOOE.OO
.170uUt.00 .ooouo~.oo
.12500E.01 .oOOOoE.OO
.10500E.01
.10500E.01
.04430E.00 .00000E.00 O.OOOOOE.OO 0.50000E.00 0.50000E.00 -.45000E.OL .00000t.00 .00000E.00 .00800E.O0 -0.30000E.03 -0.30000E.03 .26000E.00 .lOOOOE.Ol .31900E.05 .UZOOOE.OO .UOOOOE.OO .UOOOOE.OO 0.00000E.00
.U0026E.00 .uoUuUE.OO 0.50000E.00 .90UUUE.02 .UOMdJE.OO -0.30000t.03
.00000E.00 0.50000E.00 .90UOOE.02 ~00800E.00 -0.30000E.03
.27UUUE.00 .04650E.O0 .10000E.01
.17000E.00 .lOOOOE.Ol
.lJ50rrUE.00
.04500E.00
o.UOOUOE.00
.lOOOOE.Ol
0r00000E*00
COmPuteriN Multilevel Analysis for Multilayered Fiber Composites
Thickness boolean: one card, one entry
four car& 16 entries
one card, three entries
Constituent materials four cards, LBentries
CompositeSystemcard: one card, 55 characters
FIG.
3. Physical arrangement of input data cards.
Listings of input data for several composite systems are appended in [l]. These systems are shown graphically in Fig. 4. The input data for these systems can be punched from the
472
CHRISTDS C. CHAWS
listings, and the cards that need alterations for the specific problem can be modified accordingly. Input data for additional composite systems may be easily prepared. This is done by selecting a related system from those available and modifying those entries that need modification.
FIG. 4. Composite systemsfoe which input data are supplied.
After the input data have been properly assembled (as is shown in Fig. 3), it is placed in its physical position (Fig. 2), and the code is ready to be run for results.
Input ply properties
There could be cases when the user would prefer to supply some of his own ply properties instead of using the code to compute them. The user has to provide his own formats for these cases. The physical location for these statements is described in the section MAIN PROGRAM. A flow chart of the MAIN PROGRAM is shown in Fig. 5. The functions of the subroutines are listed in Table 2.
Computerized
473
Multilevel Analysis for Multilayered Fiber Composites
a
Start
Kvlj- pUi Krq - Plzj ‘2, - Pnj %s-
Pu21
9 - Pu3j P114j’PUZ, + Pn31 P113j’ Pll3j d180 L
PUP, ’ Pu4, ?a0 1 End j - LOOP I Call CECL
I
IS 1Subrouti:e CUSC pibroutife
1
GACD3l
kubroutine GPCFDii LSubroutIne CPH kbroutine
1
GECL 1
1 Subroutine COMPSA 1
FIG. 5. Code MAIN PROGRAM TABLE
Subroutine INVA GLLSC GACD 3 GPCFD 2 GPH GECL GSMF COMPSA
flow chart,
2. Subroutine description Function
Matrix inverse Simple limit stresses (strengths) ply (unidirectional composite) Three.-dimensional laminate thermoelastic properties Two-dimensional laminate thermoelastic properties Ply heat conductivities Ply thermoelastic properties Strain magnification factors Laminate analysis, ply stress-strain, ply margin of safety
cHRIsTos c. CHAMIS
474
OUTPUT
AND ~T~~~C~
RELATIONS
The program output consists of printing out, (1) the input data, (2) the composite threedimension strain-stress and stress-strain relations about the structural axes (see Fig. 6), (3) the composite properties generated in array PC, (4) the composite constitutive equations about the structural axes, (5) the reduced bending and axial stiffness, (6) displacement-force relations, (7) the current load or displacement condition, and (8) the ply properties, stresses, and margin of safety generated in array PI,.
Fiber directbn
Fio. 6. Ply orientation geometry. Composite structura1 axes, x, Y, t; composite material axes; 1,2,3; ply material axes (coincides with fiber direction, lg. 2t, 3s).
The printout of the input data is preceded by its code name. For example, the first and second lines of printout are: THORNEG5O/EPOXY NL, NPL, NPC, NFPE, NLC 8
71
54
1420
1.
The output of code generated data is preceded by title headings. The output of the composite three-dimensional strain-stress temperature relations and composite stress-strain relations about the structural axes are printed under the headings 3-D COMPOSITE
STRAIN-STRESS
The matrices [EJ;’
and {a& in the equation
are printed out.
RELATIONS-STRUCTURAL
AXES
475
Computerized Multilevel Analysis for Multilayered Fiber Composites
3-D STRESS-STRAIN
RELATIONS-STRUCTURAL
AXES
The matrix [E,], in
is printed out. The subscript s in the preceding equations indicates that the relations are written about the structural axes. It is noted that these properties are only local to subroutine GACD 3. They can be made global if needed. The output of the composite properties, generated in array PC are printed under the heading COMPOSITE PROPERTIES-VALID THROUGH THICKNESS
ONLY FOR CONSTANT
LINES 1 TO 31 3-D COMPOSITE PROPERTIES LINES 33 TO 54 2-D COMPOSITE
TEMPERATURE
ABOUT MATERIAL
PROPERTIES
AXES
ABOUT STRUCTURAL
AXES
Fifty-four entries are printed under this heading as follows :
PC(l) PW) PC(3) to PC(I 1) PC(12) to PC(14) PC(15) to PC(18) PC(19) to PC(30) PC(31) PC(32) PC(33) to PC(38)
El
PC(39) to PC(47)
E cl19 Gcl29
PC(48) to PC(54)
{4,
vc12
KC, HC
weight density thickness three-dimensional stress-strain relations about material axes three-dimensional coefficients of expansion about material axes three-dimensional heat conductivities and heat capacity along material axes three-dimensional constants about material axes distance to reference plane from bottom of composite blank two-dimensional stress-strain relations about structural axes two-dimensional elastic constants along structural axes two-dimensional coefficients of thermal expansion, heat conductivities, and heat capacity along structural axes.
The output for the composite constitutive equations are printed under the heading FORCES
FORCE-DISPLACEMENT
RELATIONS
DISPL
THERMAL
FORCES
CHRISTOS C. CHAMIS
416
The elements of matrices A,,, C,,, NchTx, and McATxare printed out. The output for the reduced bending rigidities is printed under the heading REDUCED
BENDING
RIGIDITIES
The elements of O,“, are printed out in one line. The output for the reduced axial stiffness AFxis printed out under the heading REDUCED
STIFFNESS
MATRIX
The inverse of the constitutive equations is printed out under the heading DISP
DISPLACEMENT
FORCE RELATIONS
FORCES
The elements of this inverse are printed out. The output for the current load condition is printed next to the headings FOR THIS CASE NBS (X’, Y, XY-M) IS
FOR THIS CASE MBS (X, Y, XY-M) IS The current values of N,,, m,,, mcxy, B,,, Mcy, and Me,.. are printed out under these headings. The output for the current displacement conditions is printed under the heading FOR THIS CASE THE DISPLACEMENTS WCBYY, WCBXY) ARE:
DZSI’(ECSXX, ECS Y Y, ECSX Y, WCBXX,
The output of the ply properties generated in array PL are printed out under the heading LAYER PROPERTIES,
ROWS-PROPERTY,
COLUMNS-LAYER
Seventy-one entries are printed out under this heading as follows:
pw, 1) fw, 1) PL(3, PL(4, PL(5, PY6, PL(7, PL(g, PL(9,
I) I) I) I) I) I) I)
ply void content ply apparent fiber content ply actual fiber content ply apparent matrix content ply actual matrix content ply weight density ply layer thickness ply and interply layer thickness interply layer distortion energy coefficient
Computerized Multilevel Analysis for Multilayered Fiber Composites
PL(10, I)
z
PUll, I) PYl2, I)
ZC# 8 es
PL(l3, I)
01
PL(l4, I)
8lx
PL(15, PY24, PL(27, PU30, PY31, PL(43,
I) I) I) I) I) I)
Pw4
I)
to PL(23, I) [EJ to PL(26, I) {QI} to PL(29, I) {K,} HC, to ~~(32, I) &I, v112, G,,, to PL(48, 0 &I229 4pi29413 d pd.?1
AT PY50, I) PL(5 1, I) to PL(60, I) SI1i T, etc. K 112crg PL(61, I) PL(62, I) PL(63, I) P.W& ;; to PL(69, I) $;I, 1~11 i PL(71: I)
477
distance from bottom of composite to ply centroid distance from reference plane to ply centroid angle from structural axes to composite material axes (same for all plies), Fig. 6 angle from ply material axes to composite material axes, Fig. 6 angle from ply material axes to composite structural axes, Fig. 6 ply stress-strain relations ply thermal coefficients of expansion ply heat conductivities ply heat capacity ply elastic constants ply strain magn%cation factors interply delamination factor ply temperature ply limiting stresses coefficient in combined-stress-strength criterion ply margin of safety-from distortion energy interply delamination margin of safety ply strains and stresses adjacent ply relative rotation margin of safety from Hoffman’s failure criterion.
The failure criterion may be determined by either of the following methods. (1) Modified distortion energy
(2) Hoffman’s criterion F-l-
dli C
F>O F=O F< 0
-~u14122
&llCSlllT
no failure incipient failure failure
where o denotes stress and S the limit stress always taken positive. The subscripts denote direction and sense.
478
cHRL9TOs c. CAAMIS
The interply delamination criterion for the ith interply layer at the mth load condition is governed by +PL(63, I) when i > 1 H%l A4j=*(e,ly
-&,&in
2e1- sin 20,_ I) -~Ecxy(COS 281+COS 28i_ 1)
{&,}+[A,,l-l({m,}+(N,*,,)+[C,,l{w,,)) or as given by the displacement force equation described previously. The inputs to the subroutines to generate the PL array are the ply angle measured from the structural axes (0, from PL(14, I)), the distance from the reference plane to centroid of the ply Grl from PL(11, I)), the ply temperature (AT,, from PL(50, I)), the interply delamination limit (A~a,rj from PL(60, I)), and the ply thermoelastic properties stored in PL(24to 26, I) and PL(31 to 42, I). The ply extensional and coupling rigidities A,,=ACX and C,, = CPC; the local curvatures W&x=WXX; the adjustment constants K;iZTT=BET(l, 7), I&--=BET1(2, 7), K’,,,,,=BET(l, 8), and K’11ZCC=BE7’(2, 8); and the load condions N,,=NBS(m). All other adjustment constants are input data. A sample output for a Thornel-SO/epoxy angle ply composite is given in Table 3.
Computerized Multilevel Analysh for Multilayered Fiber Compoaitea
TABLB3. Sample case output (cont’d)
-0.2449E46
D.l43Ut-04
-U.Z*WE-J* O.WTlE-07
0.93S3E-09
o*
0.
0.
ML
0.
0.2937E-DS
0.
0.
-0.
0.
0.
0.
0.
0.2917e01
0.
-0.
0.
0.
0.
0.
0.
O.?0W-09
4.
WWJCTUAL
0.+779$
07
0.4ZIYL
06
-D.
-0.
07
D.49ZOE
01
-0.
-0.
0.42ISE
01
D.W2OE
Ob
D.llbOa
07
-0.
-0*
.D.
-0.
-0.
-0.
4.
-0.
-0.
-D.
-0.
0”: 01
:
::
z: CC33 CCII CCSS eCb6
:*:::z . O.llbOE c.3+OsE D.3IOY C.SODlI
:: or 06 Ob DT
-O.>l3lE-OS 0.11999~F-al 0.1.,X-M 0.2199E 01 0.75*4e 02 0.371% 01 O..?UIn? DD
19
Et
:: ::
EC22 K33 z::
p;w~ O.lOCK . 0.3405f C.wDOY
“0; 07 06 0.
::
UC12
ECl?.
C.50011
ii_
czi
Dt 01 00 DO 00
0.24DlC
32 3s
WDEC ccl1
o.JIWt-01 0. U.149K
00
ZCDC
ii::
Yaw
O’
% :;
2:: :::
O’ 07 :;
2 ::
K22 K12 UC12
::*99’e O.SODlE ty~
4‘ .I
z: CY,,
D:YOOlR 0.17121 0.3OwE -C. -0.
01 01 00
::
-
U.isTIE
z%: c:mz
“sic”::
ILLNIDIIS
01
is: ccl3
::
SIRAIW
07
: S
I9
SIRSSS
D.4779E
O.S16W-01 D.WOCGOl
D.l712E 0.309br -D.d:ZY -O.*?K+DL D.2lJ(t
COIPOSITE
O.lSD+E
ffUfELTIcS - VALID I 13 31 .3-O CUWOSItE 3, 7” s4 24 ConPUstTE
ClLl L c7cz2 CTCSJ tail )*a m33
O.E*BSI49
0.
rc
12 1s 14 19 16 ::
01!19m-D@
-9.
-0.
Dd
:
:
-0.
-0.3tBlC-09
0.
0.
-0.2L96E-04
0.
LIWS LINLS
0.
-O.&?~bL-JL
P-D
CDwOlllt
0.4kIIPDT
&1*09E-Ob
DI
Da
0.340011
WV fm Cc~SlLhl l(LRfeRATUAR TwI(uOR PROIMTtfS AlpUT RAtIIIhL U‘S lnOISRllts LdOUl SrRucruIuL ARCS
01
0. 01 -0.
-0. o.upr -Dd
rn:u9rss
AXES
-0. 06
-0. 0.S0011
01
CHBISTOS c. CHAMIS
TABLE 3. POWiS
FDlCE
Sample case output (cont’d)
o,sPL.CE*‘*l
RELATllYtS
DI SPL
,tlE”“.L
FOIICES
nr
0.952Y
06
0.1949E
06
0.
0.1*21c-01
0.4518E-O,
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ComputerizedMultilevelAnalysisfor MultilayeredFiber Composites
481
TABS 3. Samplecase output (eont’d)
CODE APPLICATIONS This computerized multilevel analysis has been applied extensively to various aspects of fiber composite analysis, design, and optimization. Typical cases include: nonmetallic [3-5] and metallic [6] fiber composite characterization, random composite characterization [7], lamination residual stresses [&lo], buckling of fiber composite anisotropic plates [11, 121, exploratory designs of fiber composite turbine blades (unpublished notes), feasibility studies of high-tip-speed compressor blades made from advanced fiber composites [lo], failure analysis of flat and tubular members [3, 41, gross and local impact studies [13, 141, structural synthesis, and sensitivity studies of flat plates [3], and other important factors in designing with fiber composites [15]. IMMEDIATE
EXTENSIONS
The code can be readily modified and supplemented to handle nonlinear material response, temperatures dependent properties, inter, and intraply hybrid fiber composites. The details of these modifications become apparent once the user has some experience in using the code. REFERENCES 111C. C. CHAW,Computercode for the analysisof multilayeredfiber Composites-Usersmanual. NASA TN D-7013 (1971). [2] ANON., Analysis of multilayered fiber composites(M71-10112), from COSMIC (Computer Software Management and Information Center), Barrow Hall, Univ. Georgia, Athens, Ga. 30601.
481
cEIamns c. clwuls
[3] C. C. (Zmnas, Design oriented analysis and synthasis of multilayered filametary structural panels.
Ph.D. This, Case Wc&ern Reserve Univ. (1967). [4] C. C. CHAMI~, IWurc criteriafor tilamentary compositea. NASA TN -5367 (1969). [Sl C: C. CHAHELI, Thermoektic properties of unidirectional filamentary comp&es by a semiempirical wca theory. Science of AdwmcsdMoterlals md Procem &gineering Procee&g~, 14,
WMcrQ Fbiodicols Co., paper 145 (1?68). [s] C.&Cmm, Cbaractmtion and design mechanics for fiber ruinforced metals. NASA TN D-5784
[7] C. C. &rum, Dadgo propertie of randomly reinforced fiber/r&~ composites. Proc. 27th Sot. Pkastfcs Ind, AnnnolTuch.Co& paper 9-D (1972). [8] C. C. Cmm, Design and anab& of fiber composite structural components. Aerospace Structural Materials,NAM SP-227.217-218 (1970). t91 C. C. Cn&aa, Lamination residual stxcwu in muhilayered fiber composites. NASA TN D-6146 (1971). [lo] C. C. CHAMIS, Lamination residual atresses in cross-plied fiber composites. Proc. 261 Sot. Plastics Znd. ANI& Td. Cot& 17-Dl to 17-D12 (1971). [ll] C. C. tBi&m, Buckbg of anisotropiccomposite plates. L Strucr. Div. AXE%, 2119-2139 (1969). [12] C. C. C%IAMIS, Budding of boron/abninium and graphite/resin fiber composite anisotropic panels. Sod&y of Amwpac8 A4aterialandProms Engineers Space ShuttleMaterial,r3,137-147 (1971). [13] C. C. fhma, M. P. HANSON and T. T. SEMFINI,Designing for impact resistance with unidirectional fikp cwmpo&a. NASA TN D-6463 (1971). [14] ~gT,.jMoo~, Wave rurfacea due to impact on anisotropic fiber composite plate& NASA TN D-6357 1151C. C. ‘bum, Important factors in fiber composite design. Proc. 24th Sot. PlasticsZnd.Amuol Tech. Cord. 18-E-l to 18-W3 (1969). (Received22 Febtwwy1972)