Evaluation of section properties for hollow composite beams

PAPER Nr. : 35

EVALUATION OF SECTION _PF;OJ?EJ:ITIES FOR HOLLOW COMPOSITE SEAMS

by V. GIAVOTTO ( *) M. SORI=ll ( *) L •. J?UCCINELLI ( *) V. CAJ:IAMASCHI (**) F. MUSSI (**)

( *) lstituto di lngegneria Aercspaziale det

Politecnico di Milano, ltalia,

(**) Costruzioni Aercnautiche Giovanni Agusta

_S.p.A.,_Cascina_Costa di Samarate, ltalia. FIFTH EUROPEAN ROTORCRAFT AND POWERED LIFT AIRCRAFT FORUM

Abstract

The paper describes the plan and the first results of a ~oint raeesrch pro-ject, aiming at the development and the validation of design procedures for composite beam-like structures and structural components.

Ana~ytica~ as wel1 as e~erimental results are re~orted; one o~ the moe~

si-gnificant o£ such resuits bas been the development of ~e program HANBA (Sol-low Anisotropic :Beam Analysis) which, based on an original displacement method approach, allows t~e evaluation o~ section atit~eeses and stresses. The ~ro­ grac works on a fini~e aleman~ idealization of uhe beam section·and computes

the stresses f~om the resu2tant forces and ~omen~a ac~~ on the particular section, as the usual e~eer's beam theory.

~erimental results are mainly concerning the iden~ification o~ elastic ~r£

per~ies tor com~osite laminates, at rela~vevely low s~ess levels, end the

validation or the r~gul~s a~ the program ~Ao rbe ~atter has been planned through ~he evalua~ion o~ a large number of ~en~g and torsion tas~a to be ~erformed on blade a~a.-s and on comple~e Olades.

1naljtical ~eeulta com~are very we1l with a~erimen~al ones, the largest di£-ferences in section s~~~enesaee so ~ar e~ua~ed being o~ the order o! 1%. ~e plan is st11l going on and :future ac"t'i7i t:.ias sre also out"l.i.ned 1.n the paJ)er.

1, I:ITRODUCT!Oll

The cont~uous evelution of com~ositea materials is bringing them among the moat interesting and i:he most studied materials for the manufacturing of air-cra:ft, end of course also of helicopter.

Among their most si~~icant featureS, besides having, qui~e obviously, a fa-vourable strength to weight ratio, composites promise a high fatigue resistance

and a good damage -tolerance.

AGUSTA, following this trend, has undertaken a plan for composite application develo11m.ent~ whicb. will lead, i.Il. the near tuture, to the use of comllOBi tes in the manufacturing of ~rimar,y structural components, as rotor hnbs and blades, and in that of secondary cocllonents, as doors, fairings etc ••

Figure 1 shows the potential o:f composite application in the structure o:f a modern Agosta helicopter.

Such development plan brought up the need of reliable analysis procedures for primary structural subassemblies made from composites.

Besides being sufficiently reliable such procedures must also be:

suf:ficiently efficient and simple in use to be employed from the ea~ly de-sign stages, in. interactive modes by the dede-signers as well as integrated in optimizing routines;

sufficiently sophisticated to take into account the presence of di:f:ferent materials in the same section, non-orthotrollio materials and non-l~ear oo~ pling between shear and normal stresses., ee it may be needed in the more a.2_ vaneed designs;

•uf:ficiently flexible to be able to compute the inertia end eti:ftness pro-perties of rotor blades, to be used in dynamics and dynamic instability

-analysis

or

rotors.

For such reasons a coo~eration has been undertaken between AGOSTA and IASP (Istituto di Ingegneria Aerospaziale del Politecnico di Milano) ror the de-velopment and the validation of erperimental and computational procedures pertaining the analysis and design of composite beams, with particular em-phasis on rotor blades.

The cooperation has been a complete success, partly due to good planning and effective management; undoubtedly it has been a new evidence of the tre-mendous potential of the cooperation of different ad complementary competen-cies, as the ones of University and Industry.

It may be enough to note that, the first contract having been signed the 27th sept. 1978, now a significant amount of erperimental work has been com-pleted, and the first version of the program HANBA is being used tor design purposes. Such version, whiah in tact is a medium size code, has already

been validated trough the eva~uation o~ a certain number of theoretical tee~

cases, i.e. cases where exact solutions baaed on monocoqueror semi-~onocoque

schemes were available.

Besides, the first results of EANBA compare very we~ also with the results

ot ad-hoc measurements made on blade s~ars in bending and torsion.

2. TEE RESEARCH PLAN

The main activities ol: the plan are listed beJ.ow, grouped according to me'th£_ dologiee.

A. BASIC THEOro:T!C..U. DEV3LOP!.!ENTS

Al Formulation of a displacement method procedure !or the anal~sis of a beam. saetion

.!.2 Finite element tormulation o'£ the same -procedure '!or linear e'lastic In!. terials; element !ormnlation

A3 Critical statement o~ the problem of ident~ying non-e~ast1c beha~our

ot composite materials at high stress levels

A4 Development of non-elastic material models and of failure criteria A5 Formulation of finite element procedures employing the models

develo-ped by activity A4, based on the general formulation stated in Al B En'ElliME!!T..U. ACTIVITIES

:B1 Eval.uation o'£ techniques for the direc-t measurement of elastic -pro-per-ties of composite laminates, in uniaxia~ stress states, at low stress levels

B2 DeVQlopment and evaluation at techniques for the direct measurement o~ elastic prope~ties of composite laminates in pluriaxial stress states

B3

Observation of failure conditions and failure modes for composite

la-minates in pluriaxial stress states

B4 Deflections and stiffness measurements on blade spars and complete blade sections in various bending and torsion load condi tiona, in the elasti.c range

B5 Observation of strength properties and of failure characteristics of longerona end complete blade sections in various combined load condi-tions

-·c lJEVEIPl'MENT 01' COMFUTER CODES

C1 Drafting o:f the genera~ apeci:fications of the program C2 Detai~ specifications o:f the ~inear version

C3 Coding, test and va~dation of the ~ear version

C4 Detai~ speoi:fications for an extended version o:f the program inc~uding non-elastic material behaviours and strength eva~uations

C5 Coding, test and va~idation of the extended version specified by acti-vity C4.

The ~ogica~ flow o:f the activities of the p~an, showing also depen-dance connections, .is reported in :figore 2.

At the present time the activities Al, A2, B1, B3, C1, C2 and C3 have been comp~ete d.

3. AliALITICAL !PPB.OACR

The approach is based on the hypothesis that the so~id can be considered as a "beam•, i.e. that, with a good approximation, i t has the shape of a 07~

dar o~ any cross section, loaded only an i~a end sections. In o~her words

the basic hypothesis of De Saint Venant are supposed to ho~d, and we seek a aolut:ion which ia cor::oec"t on.ly in a· cer-tain distance t2"om the end sections, where ~oads and/or constraint may be app~ed.

In this case it is we~~ known that the a tress and/ or the strain state can be determ~ed on a cross sec~on o~ the beam, only from the resultant ~orcea and

~aments acting on the same cross section, ignoriDg the situation o! the neigh-)loring sections.

Let us consider a so~id that can be assumed to be a beam, or shortly a beam, and ~st Ox::7" be an orthogonal reference set having the z aXis paralell to the generatrices of the cy~nder; the point 0 is a point of the cross sec-tion that has been choosen as a reference point.

I~ the beam is moderately bent the z axis is only ~oca~y para~•~ ~o the generatrices, or, more precisely, paral~e~ to the straight lines tangent to the generatrices at the cross section considered.

So z can a~so be considered an abscissa measured along the line connecting ths points 0 of the cross sections of the beam.

Let us immag'-ns that the set Oxyz moves during the deformation in such a way that 3 axis remains tangent to the defiectsd axis of the bel!lll and x and y

B.Xis rotates around z axis by and angle

6-

=

&(z) co=esponding to the torsion o~ the section (~).

If 1![

=

~( z) is the disp~acement of the points 0, in the case o~ sma~ de-flections, the rotation ~ •

(i

(z) of the set Oxyz has the components:

{

-'liT'~

~ D 111'' X

9

(1)

(s) In genera~ this definition wou~d require a turthsr specification about torsion: in the case of ho~ow sections the projection of the section on xy plane can be assumed to remain undeformed and torsion is unique-ly specified.

-where the apex means derivation respect to the aPecisaa z.

The displacement a ot eny point P ot the cross section can then bs regar-ded as the sum o~-the rigid displacement of the reference set plus the fol-lows:

.!!. (P,z) =1£'(z)+

fo-

(z) /1 (P-O) + E. (P,z) (2)

The third component gz of the relative displacement E. is generally known as the "warping• ot the points of the cross section.

The decomposition ( 2), within the specification ( 1) ot the rotation

fE.

gives the following formulations tor the significant strain components:

' (3)

d

..,_z = 2

(d

(n)

&·

+ where:

2

0

(n) • (P-O) A

~·1£

=

my- ynx (4)

is ths double of the area dashed in figure 4

L-1_7,

~2_7.

It may be no~ad tha~ the significan~ components of strain, from (3), depend on the 4 globa~ deflec-:ion parameter o'£ the cross section tu~, ur;, UT" and 8'',

and on the warping g . Y

I~ the constitutive !aws a! the materials are s~eci~1ed

₁

stresses, virtual work of deformation, and anything alae usable tor atudy.ing equilibrium, can be erpressed as functions of the 4 gl.obal deflecticn parameters and o! the tonction gz.

In this case the·desplscement method implies that the above global deflection :parameters and the warping function are assumed as the iraknown of the aquila:_ brium equations.

An efficient so~ution ~rocedure can be ob~ained by means of finite element techniques, i.e. by dividing the cross section surface in a certain number ot finite elements, each element being characterized by a certain number of nodes or grid points; the unknown, discrete in number, are then assumed to be the 4 global desplacement parameters, plus the values ri (1

=

1,2, ••• ,m) of the warping function g in the m grid points o~ the cross section. The basic element types tbit can be useful tor idealizing the section of •.!!.

ronautical beams and beamlike structures seem to be the following:

a) ~anal elements, i.e. elements thin enough ~o be re~resentab~e on the cross section by a suitable mean line;

b) flange elements that on the cross section must be considered as surface

elements;

o) •oint elements.

The material model can be any linear material model, and generally anysotro-pic model (i.e. non-orthotroanysotro-pic) must be allowed. So also semi-mono

schemes can be reproduced just specifying tor panel elements a material

ha-ving only the shear modulus G non-sera, and tor flange elements a material

capable only of normal stress (G

=

o).

For the panels it has been convenient to develop isoparametric elements ha-ving 2, 3 end 4 nodes each.

The joint elements are used to represent a longitudinal •oint in the beam: on the cross section a joint element is always connecting 2 grid points and has a stittnees that can be specified independently 'at the shape and the

-siena o~ the joint itself.

?igure 5 shows a1l these types o~ elements with some possible way o~ using them.

To describe brie~ly the ~inite-element approach it is convenient to develop, as an example, the contribution, to the equilibrium o~ the whole c~oss se£ tion, o~ an isoparametric panel having 3 nodes idealizing a piece o~ laminate o~ thickness t.

With re!erenee

p a (

)t

and in accordance with

b-dy-

0

X

we define

q=

fz-x-,.ii

1;

the usual approach ~or hollow beam

j

(:~

dy a 0

t

(5)

we can assume that: • ( 6)

TO shorten the notation it is convenientto denote tha stress !lows with the column {

p]

and the Sig!li~icent strains in the column

[E.} ,

i.e.:

• (7)

?or linear elastic materials, taking into account (5) and (6), the constitution !"elation can be put in the !o1lowi.ng symbolic ~orm:

(8)

where

LC

J

is a symmetrical matrix summarizing the sigili~icant elastic

pre-parties o~ the laminate.

LcJ

wi1l be a diagonal matrix only i~ the unidirectional laminae are so orie!O, ted that the resultant laminate is orthotropic res~ect to the direction of the a axis, or in other words has an orthogona~ symmetry of the elastic properties respect to a direction par~e~ to z axis.

The signi~icant de~ection parameters, i.e. the 4 global parameters plus the 3 values

[r}

o~ the warping at the panel nodes can be denoted by the column:

r1

f2

r3

e·

.

(9)

•

urx

-ur·

_y 'U1' z

Denoting by [X} and { Y] the column

o~

the x and y coordinates of panel nodes, the idea ot isoparametric element comes off into the tsct that the coordinate x y and the warping runction gz o:f any point o~ the panel mean line are expressed in the same way:

-x =

t

N } T_ {X

1

p { N

J

T · [ Y

J ;

g,_ = [ N

J

~

[

r} ,_ (

10) where { N

J

are sui table shape functions.

From (3}, taking into account (4), (9), and (10), the strains can be expres-sed ~s linear functions of displacement parameters, as follows:

{e]•[BJ

.

{

"]

( 11 )

-~

['

0 0 _{0 -:z: -y}

J

[BJ:

dN1

~2

dl'!3 :z:n _{y - yn:z:} 0 0 0 • ( 12)

dX d:z:

di

To derive equilibrium equations we now start writing the virtual work

pertai-n~ to a slice of the beam bound by two cross sections at the vanishing

distance dz ..

The contribution ~e of the-isoparametric panel that we are considering

to the virtual work of "external" forces ( e.xternal for the elementary beam s~ice), with the notations of figure

7

is:

whence, tor (1} and (2):

and;;; _~,.

where Tx , T 7 tion of the pane~

section, and:

to the

{;}

=

s _z

I

_z +P

I

_z ~ s _z + nn • _~

6 •; ) di

_{- z ( 13)}

1 Mx ,

My

and Mz are, regpectively, the contribu-rasultant forces and moments acting on the cross

C£>1 ~ '+'2

~3

ii

j3s

z cpk E P;z d:z: ( 15)

i

1 k y

-ii

_:z:

¥z

Likewise, the contribution of the same pane~ to the virtuu work of de forma- · tion:

( 16)

for (8) end (11) oan be expressed as :

·6-s·ld

T

.. [ cS

u]D<J{li}

dz ( 11) where:

Cr:.J=

j

3

CBJ [cJ [BJ

dx 1 • ( 18) Ele~ents of other type will give contributions to external and internal Vir-tual work fo~lly identical to (14) and (17), even if the nu~ber of nodal unknown

[fJ ,

the shape function and the DUltrix

L-BJ

DUlY be different. In any case the total Virtual work of the beam slice comes from the SUm of the contribution of ell the elements, after having arranged all the unknown parameters in the column:

m being the number The total external

r~

[ u.}

~

e·

1.11" _:r

•

1JJY

'

1J1'

"

of nodes of the whole section.

and int:e:rnaJ. v:t.rtual works come of~ as follows: S'L

--.,...::.e_

a

(~

... !!:')

s

vr'+

(~

-l£0)

Sur' -

T

0

S'

1.1f+

r

.Su.}T

{P}

dz x y z y :r y z z

1

(19) (20)

where the to;cea T, the moments M, [ P} and

["'xJ

come from the summing,or assembling of all element contributions.

The principle of virtual works states that at equilibrium, for any choice of the virtual variation of the parameters, it I!ItiSt be:

S"Ld

_"'

s·L

•

(21)

whence, for (20)' i t must be:

'

•

•

II! =- T II!

_•

T T .. 0

y X X y z (22)

and:

Cr:.J

_{u}

-

[P}

(23)

The equations (22) are the well known equilibrium· equations of the resultant forces acting on the section.

The set of linear equations ( 23), in the unknown displacement parameters { u}

-are the actual equilibrium equations of the f~ite element section scheme.

Yet 1 t must be noticed that not all the terms at the column {

P]

are aCtual-lY" known. As a matter at fact the first C!l terms

¢

are depending on

P;z (15), which at the moment cannot be known.

N~vertheless we may note tnat according to the basic hypothesis, stresses

and strains can only be constant with z or linear function o£ z, while the etifness matrix

L-KJ must be constant

w1 th z.

Then deriving both menbere of (23) with regard to z, the foLlowing set of e-quations is obtained: where 0 0 0 0 0 (24) (25)

So -;he kc.own terms being acfually known, the (25) can be solved for u' EventuaLly deriving equations (8) and ( 11) w1 th regard to z :

{ Pjz}

~

CcJ {

C

/z };

[t:;.,}=['BJ {

u•} (26) the terms

CP ·

oi' the known term of (23) can be evaluated by means' oi' (15). It it is worth noting that the set of equations (23) and (25) have the same coefficient matrix, eo the latter can be factorized once for both solutions. Once the matrix L-KJ has been factorized it wiLl be convenient to compute ae~arately the 6 solutions corresponding to unit values a~ any one of the 6

components o~ resu~tant forces and moments.

I£ a~ the e~ements have orthotro~ic materials norma~ s~sses and shear stresses remain unconp~ed. In this simpler case it is ~ossible to de£ine, in

the usual way, the centroid o£ normal stresses, the pr~cipal axes tor ben-di!lg and the corresponding bending sti:f'i'nessea, the shear center and the CO!:,

responding torsional stiffness.

In the more general caae where normal and shear stresses are COuPled the above usual definitions no longer hold, and the sti~fDass properties of the cross

section mast be expressed by a matri~.

Nevertheless such general cases and the possible ways oi' presenting the cor responding stiffnesses deserve. a further study, due to the interest inherent

in the possibility of using non-orthotropic laminates to improve section pro

parties. ·

-4. THE PROGRAM !L'.Nll..l.

The finite element procedure outlined above has been implemented in the pro-gram HANEA (Eollow Anisotropie Eeam Analysis). ·

Before the first statement of the program had been written, the design of the ·program has been developed, and detailed to the description oi' the

-nee, at data base and test cases.

This allowed different parts of the program to be developed independently by 8 persons, belonging to AGUSTA and IASl', in a prettY short time, and integr.!!.

tion to be performed w1 thout any particular problem.

In particular RANEA has been designed to have an open modular structure, and with the possibility of stop and restart at intermediate points.

The first level structure of the program is done by the following modules: - Input and Preprocessing

- Analysis

Stress computation and output.

The input and preprocessing module reads the data given or specified by the user.

It mak:ee use of a library of [!lStarials, laminae and laminates, with diffe-rent modes o~ operation9 at user's ehoice.

For instance the user may specify a laminate by choosing one of tha lamina-tes of the library, or by seJ.ecting a certain number and s:peci:f'ing a certain arrangement of unidirectional la~ae.

Modules are also provided to un~rove the library.

In addition the preprocessing module performs checks and emits diagnostic messages about input data, prepares the printed and graphic output for data check, and the input for the subseguent analysis.

The analysis modn~e computes the inertia and stirtaess ~ro:perties ot the beam section, and the solutions needed by the possible subsequent compUtations.

The stress module com~utes the stresses in the laminae forming the laminates,

in tlange e~ements and in joint e~emen~s, tor given load conditions. The gross flow diagram of program iiAIGlA is depicted in figure 8. At present the ~o~owing e~ements have been im~lemented:

~,anel elements,isoparame~c, 2, 3 and~ nodes; Gauss numerical integrative at order

2, 3

or

4;

- flange elements capable ot work~ also in normal stresses; - ~oint elements.

Besides the element nodes may be displaced from the grid points by a certain displacement or offset. So the grid points can be fixed on the external pro-fila and the actus~ element nodes are automatically placed, in positions de-pending on the la~ate.

Clearly the Program HAlf.BA can be also a flexible and efficient instrument for the analysis of hollow beams of any material, and then also wings 1 tail plana a etc:.

In particular, as it computes the beam section by section, it is much more ver sa tile and manageable than the usual finite element codes, especially in the -early design stages.

As such it is already being· used at AGUSTA.

5. EXAMPLE OP AN IDEALIZATION

To give an impression of the idealization that can be used with the program RANEA, the scheme adopted for analyzing a rotor blade is reported in figure 9. Figure 9A shows the actual cross section of the blade, while figore 9 E shows the idealization prepared by the user, with the grid points located on the outer profile.

Figure 9C reports the element nodes, computed by the program, whose actual

position de£enda on element ~ess.

-·The scheme has a total o:r 59 degrees o:J: freedom,6 cubic panel elements (4 no-des), 11 parabolic (3 nodes) and 7 linear (2 nodes), plus 5 :!lange elements and 12 joint .elements.

Despite its sempl1city and relatively low cost this model is capable o:J: re-presenting the cross section with a very good accuracy.

6. ELASTIC PROPERTIES O:F L.AMI!L~TES

The elastic moduli o:J: laminates heve been measured directly, employing a techn1

que based on uniaxial tension tests of specimens cut· from the laminate at d.if"--ferent angles. Figcre 10 shows the three types of specimens, denoted as I, II and III: the specimen longitudinal axes x form with the laminate re:J:erence direction X angles o:J: 0°, 90° and 45°, respectively.

:For non-orthotropic laminates the strain y o:J: specimens type III may be non negligible, and then it may be important the~ the end clamps allow this strain without inter~erences. For that reason th~ clamps were hinged in the specimen centerline, at the stations where the specimen emerges from the clamps, as shown in :J:igcre 11.

Each specimen have· been equipped with two strain rosettes, one on each face, to eliminate possib~e bending e~fects from the measurements. So, for each stress level, three strain measures can be extracted from one specimens,and then 9 tor one group of 3 s~ecimens ot the 3 types.

?or an orthotropic laminate these 9 measured values are obvioual7 ~edundant

to determine the 4 inde~endent elastic constants.

In the first teats these 9 strains where used to determine the 9 terms of the elastie matrix, without making any asauption on orthotropy, nor even on symmetry. The first teats were run with 12 specimens, coming f~m the same sheet, 4 tor each o:J: the types in figure 10.

The sheet was done by three ttnidiree~~al layers, material SP250 S2920,placed at Q0-90•-eo.

All the testshave been rnn with a Data Acquisition System, making use o:J: a

small computer, programmed to eval:cata the e.lastic moduli !rom strain measu-rements, on line.

The first tests showed essential symmetry and orthotropy o:J: the elastic

ma-trix, and a rather strong dependence at the tangent mo·dulus G on stress level. To make easier the observation of possible stress-dependence of the moduli, a simpler processing of meassured data was programmed, accepting a priori orth~ tropy and symmetry. Particularly 5 moduli were directly extracted, as :!allows:

E;r

and .:) X :!rom specimens type I and :!rom specimens type II

:!rom specimens type III.

This type o:J: teet was done ~ the same 12 specimens used be:J:ore, with stress levels up to about 6 kg mm- •

Specimens type I and Il shoWed linear stress-strain relations, whi~e specimens type III mani:J:ested remarkable non-linearitias, notably creep and hysteresis. Figure 12 shows the decay in time

at

the secant modulus ~. :!or specimens type III at constant stress: i t was also apparent thet au~ modulus is stron-gly dependent on specimen temperature.

Figure 13 ahows typical stress strain curves tor the three types ot spec~mens; the curve reported for s~ec~men Ill was obtained wi~ a fized loaa an un2oad v~ locity o:r +.02 kg mm-2 8

-l.

Table I gives a summary o:J: the most signi:J:icant :J:eatures and of the moduli mea

sured with the 12 specimens; the moduli G reported for specimens III are se-cant moduli, measured with a stress o~ 5.53 kg mm-2, applied for 5.5 ~utaa.

-I

I

I I i Specimen

,.

Type 245 I 246 I 247 I 248 I 253 I I 254 II 255 II 256 II 249 III 252 III 250

I

III 251 III .ADHESIVE ,1. 1 .ADHESIVE

F

2 TABLE 1 Adhesive Ex Vx

I

E [i!:g mm-2] y

,.

2 3426 .1440 1 3397 .1645 1 : 3462 .1647 1 3473 • 1649

I

1 1 2444 2347 I ₂ 2372 I

I

I

2 2387

I

1 ! 1

i

2

I

I 2 '

MICRO-I>IEASllllEME!lTS type M-:BONil 200 S.:B.M. type Z 70

From tab~e the following observation can be drawn:

vy G _xy [Kg

mm-~

.1076 .0989

I

.0883 .0847 379 382 I 427 I

I

394

-a) Moduli

Ex

and

By

measured from specimens I and II show a very low soat~er, be~ow

2%.

-b) System.ati.c differences appear between the mea'surements comi,ng from strain gages app~ied with the two dif:f'erent adhesives, at least for

Vy•

and even more for GXY' whiah are essentia~:r dependent on resin stiffness. In parti-cular it appears that adhesive

P

2 causes an excessi~e stitfen~ of the

re-sin.

-c) The values of

Ev

J.

are systematically lower than the values of EX

J

Y' even comparing on2j-

th'B

measurements taken from strain gages applled W:1 th the same adnesiva. This QaY appear as a lack of' symmetry of the elastic ~atri:, but most.probably it is simply due to the fact that specimen width is not enough to transfer transverse contraction :!'rom the inner layer to the outer ones7 for specimens II.

Nevertheless the authors think that the methodology so far tested has proved to posses a

higa

potentia~ accuracy; in the fUture larger specimens wi~ be used, end the effect o~ adhesive ~ be care:f'ul~y inVestigated.

7. TEST ON BLADE SECTIONS

Several experimental tests with different beam cross section end construction have been planned. Figure 14 shows typic~ cross sections employed in tests. Xhe test articles have been made from different co~posite materials, dit~erent number of pre-preg layers, and different fiber angle •

.Uso the materl~ employed come from. different manufacturers.

Tests are run with a :f'rame ~lowing the loads to be a:P:Plled in a we~ defined plane, without undesired e:f'fects on other planes, and able to give good eva-luations o~ shear center location.

Loads are applied by weights, and deflection have been measured with dials in the first tests (figure 15), and subsequently with a set of LVDT transducers

'(figure 16).

.11

-I

Strain gages have also been fit, to detect the strains of the outer layars. Figure 17 shows some typical bending and twist measurement obtained from the tests.

Figure 17b contains also results from a metal blade tested for the first eva-luation of the e~uipment and of the results of ~~~BA. In torsion results it appears that the length of the specimen is sufficient to obtain a significant part of the diagram with a linear trend of the twist angle, i.e. outside the iu£1uence of end restraint.

8 • EV AIUATION OF HAlf.EIA RSSUI!S

Four types of beam sections have been so far tested, shown in figure 18. Section A was tested only in bending, in both principal planes; section D, co=esponding to a typical metal blade was tested only in torsion, while the remaining sections were tested both in bending and in torsion.

In each test bending deflection and twist angles were measured at 9 s~ations, in different load levels.

~ these measurements were then used, in an o~timizing procedure, to compute the value of the stif~nessee Snd the values of the slope at the first station

(one for each load), gi~g the best fit af e7perimental points.

Such ezperi~ental ~alues of the stif!nesses were then compared with the corre spending values obtained analytically from the program HAlf.EIA, with the ideal! zations showed in figure 19.

The'tables in Pig.20 report some of these comparison. FUrther tests are needed to draw conclusive evaluations, and p~bably a dee~er insight into reai~ creep may give a bet~ar interpre~ation at some .of torsional results. Nevertheless the agreement between analytical and exper2mental results seems to be ex~e­ mel_y good.

9. FUT!JP.E llEVEI.OJ?ME:!!TS

The main future developments, :related to the completion ot the research plan, are:

- completion at the linear version o! the program HANBA, trough the develop-~ent ot isoparametric flange elements, capable at developing both normal and

shear stresses. Complete development at the stress output module, and of the inter:f'aces for rotor dynam:ics programs.

- Development o~ a non linear version o~ HAN.BA, allowing tor general non l i

-near behsviour:n:l: materials, and including also strength evaluations. As it has been outlined above, this will re~uire some further theoretical work and much experimental activity.

In the mean time another research project is now being planned as a joint ve~ ture between IASP and AGUSTA, concerning the development and validation ot

new codes !or the analysis ot rotor dynamics and instabilities.

10. CONCLUDING llniJJlKS

The resul ta so tar obtained strengthen the opinion of the authors that the a;e plication of finite element techni~ues to the classical problem of De Saint Vlfu.ant, can give, tor many actual :problems, an answer w.b.ich may be more e!~e.£_ tive, more flexible and more usable then the one o~ usual F.E. programs.

1 1 • BIBLIOGRAPHY

- MANTEGAZZA P., Analysis of semimonoco~ue beam sections by displace-ment method, L'Aerotecnica Misaili e Spazio, Journal ot AIDAA, 1977 l! • G.

-2- GIAVOTTO

v.,

Procedimento peril calcolo di travi a guscio in materials anisotropo .:. Studio di base 1978, IASP Research repo"rt -Restricted.

3 CRIVELLI VISCONTI, Materiali compositi tecnologie e progettazione -Tamborini Edi tore - 1975.

4 N.J. PARRAT - Fibre-Reinforced Materials technology - Van Nostrand, New York 1972.

5 BROX~ L.J., KROCK R.R., Composite materials vol. 1-8, Academia Press, New York 1974.

6 -

c.c.

CRAMIS, Computerized multilevel analysis of multilayered composites. Computer & Structures. Jan. 1973 pp. 467-~92.

7

c.c.

CRAMIS, Computer code for the analysis of multilayered fiber composites - Nasa TN D- 7013 -March 1971.

8 - J.J. KI~ NOLIN - A nonlinear laminate analysis program - Nasa Gr. 2410 - Feb. 1975.

9 F.W. WENDT, H. LIEBOWITZ, N. PERRONE- Mechanic of composite ~ate­

ria1s - Pergamon Press 1967.

10 Agard specialist meeting on failure modes of composite materials

-Agard CP-1 63.

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