Test-finite element correlations for non-woven fibre-reinforced composites and sandwich panels

Marine Structures 7 (1994) 345-363

Test-Finite Element Correlations for Non-woven Fibre-Reinforced Composites and Sandwich Panels

P. Davies, D. Choqueuse & B. Bigourdan Institut Fran~ais pour la Recherche sur l'Exploitation de la Met (IFREMER), Centre de Brest, 29280 Plouzan+, France

ABSTRACT The use of non-woven fabric reinforcement can offer significant advantages in many marine applications. This paper describes tests performed on quadriaxial glass-reinforced epoxy composites in order to validate finite element modelling of these materials. Tests on tensile coupons, circular plates, sandwich beams and large stiffened panels are described, and deflections and strains are compared with finite element predictions. Linear and non-linear finite elements are employed. While good correlation is generally found between measured and predicted deflections, calculated strains are less reliable. Key words." Composite, multiaxial, glass fibre, panels, sandwich, finite element, stiffener, deflection.

INTRODUCTION Traditionally the preferred form of fibre reinforcement for marine applications has been woven fabric, often combined with layers of chopped strand mat. 1 However, the use of more expensive non-woven reinforcement may offer advantages in some applications for two reasons. First, higher fibre contents may be achieved with easier lay-up, thus reducing fabrication time, cost and weight. Second, the use of non-crimped fibres reduces stress concentrations and results in higher strength. Fabrics of various surface weights and orientations are now commercially available. 345 Marine Structures 0951 8339/94/$07.00 ~" 1994 Elsevier Science Limited, England. Printed in Great Britain.

346

P. Davies, D. Choqueuse, B. Bigourdan

Their selection for fast vessels such as surface effect ships is quite advanced, 2 and for these applications weight savings are critical and structural optimisation is essential. 3 The fibre geometry of multiaxial fabrics is simpler than that found in woven materials and this should allow more precise property prediction, but on account of their relatively recent introduction, few independent results are available. This paper presents results from a programme in which an epoxy resin reinforced with quadriaxially oriented glass fibres was tested in the following forms: (i) (ii) (iii) (iv)

standard tensile coupons simply supported circular panels skins on a PVC foam core tested in four-point bending skins on 2 m by 1 m PVC sandwich panels with transverse and longitudinal stiffeners

The first of these forms is of considerable importance as it represents the standard method for determination of properties of monolithic composites and sandwich skins to be used as input data for calculations. The second is a test developed to characterise the behaviour of circular composite panels under more realistic loading conditions and to verify the finite element tools. The forms (iii) and (iv) are sandwich materials. Such materials are the subject of considerable interest at present, as illustrated both in the regulations for naval construction 4"5 and in recent conferences. 6'7 Their analysis has been described in some detail by Allen, 8 while optimisation of sandwich structures has been discussed by Gibson and Ashby. 9 Several references deal more specifically with the problems encountered in modelling of the stiffened panels frequently used in marine structures, and a useful overview is presented by Smith. ~While the application of stiffened composite panels for mine detection vessels has resulted in several published studies, less work has appeared on stiffened sandwich panels. The present paper concentrates on the prediction of stiffness, as regulations for high-speed vessels include requirements for allowable deflections. 5 Further studies are examining aspects of stability and failure.

MATERIALS AND METHODS All the materials tested were produced in-house using contact moulding, followed by a post-cure at 40°C for 4 h. Sandwich panels were made by laminating directly onto a cross-linked PVC core (density 80 kg/m3). The 'omega' stiffeners were produced by laminating two layers of quadriaxial fabric onto a lighter core (35 kg/m3). The reinforcement was in the form of a quadriaxial stitched non-crimp

Test-finite element correlations Jbr fibre-reinforced composites

347

fabric of surface weight 1034 g/m 2, in which the E glass fibres are oriented in the 0 ° (27.4%), 45 ° (22.6%), 90 ° (27.4%) and - 4 5 ° (22.6%) directions. For both monolithic panels and sandwich skins, the lay-up consisted of three quadriaxial layers. These were laid up in the sequence (-45/90/45/0) (-45/90/45/0) (0/45/90/-45). Overall fibre volume fraction was measured by density and burn-off tests on both laminates and sandwich skins to be 37% (+ 1%). The specimen forms, loading arrangements and dimensions are shown in Table 1. Finite element calculations were performed using the material homogenisation modules (CACOUN, CACOTI, CACOMC) developed with the M O D U L E F library of INRIA, 1° and A D I N A version 6.0 for the three-dimensional structural modelling.

RESULTS A N D DISCUSSION (a) Tensile test coupons Twenty tensile tests performed on coupons cut with the 0 ° fibres along the specimen axis produced load-displacement curves such as that shown in Fig. 1. A biaxial extensometer was used to allow determination of a Poisson's ratio and tests were performed under displacement control at 2 mm/ min. The standard test methods suggest testing a minimum of five specimens, ~ but twenty were tested here as part of a statistical study of scatter in properties so that subsequent differences between tests and predictions might be evaluated. Twenty specimens were also tested at 45 °, in order to allow the determination of an in-plane shear modulus. Table 2 shows the results for the modulus values. Interestingly, the variations in measured moduli values between specimens are very low, with coefficients of variation of 5% or less for all values. Nevertheless, the table and Fig. 1 also show clearly the first problem to be overcome in modelling structural behaviour, namely the determination of appropriate input data. The nonlinear response of the material is reflected in apparent moduli values, which decrease significantly as strain increases. This non-linearity is related to damage around the off-axis fibres and acoustic emission recordings have indicated that damage starts to appear at stresses around 25% of the failure stress, at strains of 0.3 to 0.4%. ~2 This strain level should be borne in mind when considering the examples to follow. Moduli values were also determined using the homogenisation technique for periodic media with M O D U L E F . 13 An advantage of this approach is that all the elastic constants, both in-plane and in the thick-

P. Davies, D. Choqueuse, B. Bigourdan

348

TABLE

!

Test Specimen Geometries and Dimensions (All Dimensions in mm)

Geometry

Materials, Dimensions

I ",,"11~-

Monolithic, rectangular coupons 250 x 25 × 4

T E N S I L E COUPON

Lz2x

Monolithic Circular panels. Diameter 300 mm Thickness 4 mm

z~'

C I R C U L A R PANEL

L

F

O

I

cD

Sandwich beams. 120 mm wide Distance between supports: Inner: 475 mm Outer: 950 mm Skins 3 QX layers (approx. 3.5 mm thick) Core 40 mm thick

FOUR P O I N T FLEXURE

/-5

Stiffened sandwich panels 2000 z 1000 Two types (see results) Skins 3 QX layers (approx. 3.5 mm thick)

ST]:FFENED SANDWICH PANEL

Test-finite element correlations for fibre-reinforced composites

300

349

/

i Ir2°° 250

r/

/

/

x x,a, o-100mm

t-5o/

/ / ~" [

-20000

-10000

0

[]

I

10000 Microstrain

Loo2 n

O Tranlverse 20000

I

30000

Fig. 1. Stress-strain plot from test on tensile coupon. Two longitudinal extensometers were used for comparison, with gauge lengths of 25 and 100 mm.

ness direction, can be calculated once the periodicity and component (fibre and matrix) properties are known. Homogenisation also allows the computation of the microstresses in the fibre, resin or at the interface. The elastic constants may also be determined for very low strains using vibration or ultrasonic wave propagation techniques. 14'15 These techniques are currently being developed at I F R E M E R , in order to reduce the number of destructive tests required, and have given promising results. ~° However, destructive tests will remain necessary to evaluate non-linear behaviour and to determine failure characteristics.

(b) Circular plates Tests were next performed on 300-ram diameter circular plates cut from the same panels as the tensile coupons. These plates were simply supported and subjected to uniformly distributed water pressure loading to failure, using a test set-up which has been described elsewhere. 16 This experimental arrangement allows the loading of panels under more realistic conditions than the tensile test and is proposed as an inexpensive intermediate step between coupon and large-scale testing. The response of the thin panels examined here involves large displacements and the press u r e - m a x i m u m deflection responses of four panels cut from the same composite sheet are shown in Fig. 2. The tests are reasonably reproducible. This behaviour was then modelled by a non-linear large-displa-

P. Davies, D. Choqueuse, B. Bigourdan

350

TABLE 2 Input Data for Calculations

Type

E.~ (0) (GPa)

E, (90':) (GPa)

G,.~ (GPa)

v,.,.

Initial tangent

l 5.51 (0-53)

15.5

5.5

0.309 (0.021)

Secant, 10-50% of maximum stress

11.6 (0.45)

11.6

4.1

0.302 (0-02)

H omogenisation

13.84

13.84

5.4

0-287

Measured values, tangent and secant, and values obtained by homogenisation. Values in brackets are standard deviations from tests on 20 specimens.

cement finite element calculation. A quarter panel was meshed and the predicted values of maximum deflection are also shown in Fig. 2. On this plot are shown predictions using three sets of values of moduli, presented in Table 2 as secant, tangent and homogenisation. The latter two agree quite closely with the measured values, to within 10% for all points. Strains were measured on the lower panel face by placing a (0/45/90") strain gauge rosette at the centre during the tests and Fig. 3 shows measured and predicted values. The strain values in all three directions determined by calculation (using initial tangent modulus) were very simi20

[]

D g~

~

~ l0

[0

Homog.

A

Tangent

rl

Secant

~ Exp.1 ~ Exp.2 ~ Exp.3 Exp.4

0

1 Pressure, bars

Fig. 2. Circular panel under pressure loading; measured and predicted central deflection as a function of applied pressure.

Test-finite element correlationsfor fibre-reinforced composites

351

4000

o

[] % 3000

[]

A

00~ • A

[]

0 •e ••

t_

%Q

2000

i] 0

A Exp. 0 ° O Exp. 45°

t_

[] Exp. 9 0 ° oO

1000"

0

-0.5

•

i

0.0

0.5

1.0

1.5

FEM (0, 45 & 90°)

2.0

Applied Pressure (bars) Fig. 3. Circular panel under pressure loading; measured and predicted strains at panel centre as a function of applied pressure. lar to each other (though not identical). Again, reasonable correlation is found between experiment and calculation. The strain values are below 0.4%, so the material non-linearity does not need to be considered. These tests indicate that the prediction of properties of these multiaxially reinforced laminates under uniaxial and uniform pressure loading does not pose significant problems, and that large displacements can be modelled satisfactorily. A number of other materials, with different resins and reinforcements, have also been tested and modelled in this way without major difficulty. The next question was whether the behaviour of this composite as a sandwich beam skin could be modelled. (c) Flexure o f sandwich b e a m s

The testing of sandwich beams under four-point flexural loading is a standard test method, described by ASTM '7 and DIN documents. ~s The latter was used here, as it involves the measurement of deflections at two points, the specimen mid point and the inner load points, so that shear and flexural rigidities can be obtained from a single specimen. Strain gauges were also bonded to the upper and lower sandwich skins at mid-length to give additional information on moduli values. Such tests are frequently used to produce input data on sandwich rigidity for structural calculations,

352

P. Davies, D. Choqueuse, B. Bigourdan

although several authors have expressed doubts over the relevance of applying data obtained on beams to the case of panels of similar materials, for which the membrane stress state leads to lower deflections.~9-2° A preliminary series of tests was performed on the PVC core to determine its properties in shear using a standard shear test. 2~ Accurate knowledge of this value is essential, as will be shown below. These tests yielded a value of 33 MPa for the tangent shear modulus at the origin, and this value is used in calculations for both the beam and stiffened panels. Tests were performed on five one-metre long beams. Some were tested with the skin fabricated first uppermost and others with the beam reversed. This was to check whether the asymmetry, which is always present in such beams, affected the values measured, but no influence on the results was detected. Typical load deflection and load-strain plots (showing the first part of the curves only) are presented in Fig. 4. (The deflections shown are those at the inner load points and the additional deflection in the centre with respect to that deflection, so the total mid-point deflection is the sum of these two curves). Table 3 shows test results, which indicate very little scatter. The beam deflections and strains were also determined by finite element modelling. A linear model was used, and the skin modulus was taken as that obtained by homogenisation. For a given load (1680 N) the predicted total central deflection was 5-0 mm and the corresponding microstrains on upper and lower faces were - 8 6 0 and +890. The measured values at this load were approximately 4.2 m m and 670 microstrain, so the finite element model is about 20% less rigid than the measured values. Several other interesting results emerged from this exercise. The beam response was elastic up to deflections of over 10 ram. The strain gauges on the top and lower faces indicated similar values, so initial tangent moduli values in tension and compression determined by beam theory are similar. This is not always the case when composite materials are tested, but difficulties are often encountered in performing valid compression tests~ and the sandwich beam has been proposed as a compression test specimen. 22 However, the tension modulus values measured in this way here were some 12% higher than those determined on the tensile coupons. There are clearly problems in reconciling the experimental conditions and the modelling of this test. One important factor is the virtual impossibility of accurately measuring skin thickness. A graduated hand-held microscope was used in this work but the variability of thickness of hand laid-up composites can easily result in variations of ±0.2 mm. This can cause variations in the measured modulus of 10%. Another factor may be that indentation occurs at the load points so that locally stresses are altered and the core may deform permanently even at quite low applied loads. Beyond the elastic range the beams fail in the core in shear at loads

Test-finite element correlations for fibre-reinforced composites

353

12000 A A A A

10000

A A A

8000

• •

_o 6000 A

gl.

A

•

•

•

4000'

Inner load point

]

Beam mid-point

I

< 2000

0 -10

0

10

20

Deflection,

30

mm

12000 0 0 0

10000

z

[] 0 n [] [] [] [] [] [] []

0 0 0

8000

0 0 0

_=

0

6000

0 []

0

oO e,~

<

[][]

I [] I

• face Tension

4000 2000

b

0

.

°V

i

•

i

-6000-4000-2000

[ o Compression face

•

•

0

i

2000

.

i

4000

•

6000

Mierostrain Fig. 4. Four-point flexure test. Load-deflection and load-strain plots.

corresponding to relatively low skin stresses (70-90 MPa) and shear stresses of 1 MPa. Even after cracks appeared in the core they did not propagate at the skin/core interface. (d) Stiffened panels under uniform loading

In order to examine the correlation between the measured and predicted response for a structural element, a loading arrangement was designed. This has been described elsewhere16 and is similar to that proposed and used recently by Reichard. 19 Other authors have also described pressure

6502 (114)

Mean (SD)

152.7 (7.7)

147.1 145-8 152-1 153.2 165.2

Shear stif/hess (kN)

17.51 (0-33)

17.85 17.02 17-33 17-64 17-69

Tensile modulus (GPa)

17-58 (0.43)

18-23 17.02 17.48 17.64 17.51

Compressionmodulus ( GPa)

26-7 (1.3)

25.8 25.5 26.6 26.8 28.9

Core shear modulus ( MPa)

Flexural stiffness, shear stiffness and core shear modulus values were obtained by least squares linear regression between 10 and 90% of the maximum force measured during the tests. Tensile and compression moduli are initial tangent values.

6543 6542 6522 6598 6305

Flexural st~ffhess (Nm 2)

1 2 3 4 5

Specimen

TABLE 3 Results from 4-point Flexure Tests

~z

4~

Test finite element correlationsfor fibre-reinforced composites

355

loading tests for sandwich panels 23'24 as they provide a more realistic indication of panel performance in boat hull applications. In those previous studies the panels were restrained either by frames 19'23 or edge clamping. 24 By suitable design, cyclic, creep or high rate loading may be applied. In the set-up used here, the lower face of a stiffened panel is subjected to uniformly distributed pressure loading through elastomeric pressure pads, which are expanded by air at pressures up to 0.5 MPa. The panel is restrained on the top face by adjustable load points applied to the panel stiffeners. These load points include a clamping arrangement to minimise stiffener rotation (Fig. 5). Two types of panel were tested in the current work, as shown in Fig. 6. One is only reinforced with two transverse stiffeners (Panel 1), while the second also has a longitudinal stiffener (Panel 2). These panels were tested and the deflections and surface strains were measured at several points as shown in Fig. 6. These values were then compared with finite element predictions. This exercise also involved a comparison of different finite element codes, which will be described elsewhere, 25 but here only the results obtained using A D I N A are presented. For Panel 1 a linear calculation was performed first. This calculation involved a mesh of 324 twenty-node solid elements to model the core material and stiffeners and 300 height node MITC (Mixed Interpolation of Tensorial Components) shell elements to model the composite skins of panel and stiffeners. (This mesh is very detailed. A model with 57 solid elements and 108 shell elements leads to deflections only 1% lower). The results are shown in Table 4, together with experimental results from two loading cycles on a panel. Agreement between measured and predicted values at the panel centre is reasonably good, but closer to the stiffeners

t I ltll

t

Fig. 5. Pressure loading arrangement for panel 1. The stiffeners are loaded via profiled steel channels.

P. Davies, D. Choqueuse, B. Bigourdan

356

PANELI

I I

M I I 1000

mm

---4)--

-F- -G+-

-

-Im m

I

A

m

B I I 2000

PANEL2

A

mm

I

@

B

¢

=

Fig. 6. Panels tested, showing transverse and longitudinal stiffeners (shaded regions), and positions of displacement transducers and strain gauge rosettes (see Tables 4 and 5).

the predicted deflections are low, (e.g. point F, x = 600, y = 500). The influence of core shear modulus was examined by running the calculation with two additional values, 15 and 25 MPa. These values were examined as the tests on the beams in flexure, section (c)) has indicated lower shear moduli values. The importance of this parameter on the overall deflection values is clearly shown in Fig. 7, but it does not account for the differences noted in Table 4. Although the linear calculated gives reasonable results for deflection it does not model closely either the change in shape of the panel around the stiffener, nor bending effects observed in the side walls of the stiffeners. A second calculation was run using large displacements (non-linear analysis), with 87 solid and 102 shell elements. Other authors have recently shown the importance of non-linear modelling for sandwich panels. 26 In the present case this increases the deflection values slightly as shown in Fig. 7. More importantly, it gives a more realistic indication of the stiffener wall deformation (Fig. 8). The deformation of the stiffener wall will be extremely sensitive to exact laminate thickness, local fibre

Test-finite element correlations for fibre-reinforced composites

357

40

Test mean

A

30

E E

d ° ~

..... -A ....

FEM, G : I 5 MPa

. . . . <~. . . .

FEM. G : 2 5 MPa

---n--

FEM, G : 3 3 MPa

20 Non linear FEM

i

tO

•

m

2000

I000

Position

along

x-axis,

mm

Fig. 7. Measured and predicted deflections along x-axis at y = 500 m m for Panel 1, showing influence of core shear modulus on linear F E M predictions, for an applied pressure of 0.1 M Pa.

content and the properties of the foam used to support the stiffener lamination. The uncertainty concerning these parameters is such that the rotation of the stiffeners and the change in effective length of the panel between them cannot be determined exactly. TABLE

4

Panel 1, Measured and Calculated Deflections for an Applied Pressure of 0.l M P a

Point A B

C D F G H I

K L M N

x

y

FEM linear

FEM non-linear

Test 1

Test 2

220 600 1000 220 600 800 1000 1400 1780 220 600 1000

150 150 150 500 500 500 500 500 500 850 850 850

2.95 7.91 21.69 3.10 7.63 17.12 20.82 7.63 3.10 2.95 7.91 21.69

2.41 9.53 24.70 2.56 9-17 19-7 23.80 9.17 2.56 2-41 9-53 24.70

2.02 7-68 21.73 2.34 10.53 17.97 19.91 10.91 3.87 2.38 10.97 21-59

3.26 10.67 20.52 3.27 10.29 17-30 18-72 10.64 4.09 2.69 10-47 20.44

358

P. Davies, D. Choqueuse, B. Bigourdan

"..~. S J

(a)

'l

IJ

X fi (b) Fig. 8. Linear finite element representation of a quarter of Panel l, showing influence of (a) linear and (b) non-linear modelling on stiffener form, for an applied pressure of 0-1 MPa. Figures show deformed (darker) and undeformed (lighter) shapes.

The calculated strains were in general higher than those measured. Table 5 shows these strains. The maximum strain level was still close to the elastic region in the tensile test for a pressure of 0.1 MPa. There could be a number of reasons for this difference in strains. The skin modelling is performed to represent the stiffness of the ply and not its micromechanical behaviour, so the thickness of the ply entered in the finite element analysis is not exactly that which is measured. As the strain gauges are positioned on the external face of the skin the strains will be quite sensitive to the thickness and this can lead to large errors even if the overall panel stiffness is reasonably well represented. The effect is much more important in

Test finite element correlations Jot fibre-reinforced composites

359

TABLE 5 Panel 1: Measured and Calculated Strains (Linear FEM), for an Applied Pressure of 0.1 M P a

Location (mm)

Strains

Finite eh'ment

Test 1

Test 2

x

)'

,7

1000

150

Top Skin

80 89o 845

3276 -729 1335

2165 -421 964

2020 374 844

220

500

Top Skin

8o 890 845

-- 1001 68 -457

-421 52 -205

-407 31 -158

410

500

Bottom

80 ~90 E:45

3455 - 103 1641

1805 43 900

1851 40 965

Top Skin

e0 890 P45

2115 -235 960

1747 -416 670

-397 565

Bottom

~0 890 845

--3243 354 --1433

-2083 1088 -521

-1719 921 -458

Skin

800

1000

500

500

Skin

1000

500

Top Skin

e0 eg0 845

3068 -338 1376

1655 -841 406

1465 -834 276

1590

500

Bottom

8o 890 E45

3455 103 1641

1880 222 986

2095 - 133 854

Skin

sandwich panels than in the monolithic laminates (section (b)) on account of the large distance from the neutral axis. This is clearly a problem if a failure criterion is to be applied and is being addressed in the second part of this study. For Panel 2, with the longitudinal stiffener, the deflection values predicted from the linear model are all lower than measured values (Table 6). Values away from the stiffeners (such as x = 1000, y = 150 and x = 1000, y = 850) are reasonably close to measured values (within 15%), but deflections measured along the central stiffener (y = 500) are much higher than predictions (Fig. 9). This linear calculation involved a mesh of 120 solid elements to model the core material and stiffeners and 274 shell elements to model the composite skins of panel and stiffeners. The use of a non-linear model (93 solid and 167 shell elements) does not significantly improve the correlation, and the reason for this appears to be related to

360

P. Davies, D. Choqueuse, B. Bigourdan

TABLE 6 Panel 2: Measured and Calculated Deflections, for an Applied Pressure of 0.1 MPa Point

A B C D F G H I K k M N O

x

),

F E M linear

Test 1

Test 2

220 600 1000 220 600 800 1000 1400 1780 220 600 1000 1000

150 150 150 50(1 500 500 500 500 500 850 850 850 300

2.78 5.23 13.78 1.38 3.30 7.54 9.54 3.30 1.38 2-78 5-23 13.78 11.50

5.77 9-12 15.26 4.94 7-79 10.90 11.93 7.25 4-03 5.73 9.14 15.49 13.79

4.85 8-56 15.23 3.73 6.75 10.28 tl.81 7.72 4.57 4.96 8-68 15.83 13.73

the loading conditions. The transverse stiffeners are partially clamped u s i n g a n a r r a n g e m e n t s i m i l a r t o t h a t s h o w n in F i g . 5, b u t t h e c e n t r a l s e c t i o n s w h e r e t h e t r a n s v e r s e a n d l o n g i t u d i n a l s t i f f e n e r s m e e t a r e left free. The non-linear analysis indicates that there may be considerable distortion in t h e f r e e a r e a ( F i g . 10). M o r e i m p o r t a n t l y , it w a s f o u n d t h a t t h e i n t r o -

20"

E ff

.o

10

:: ..................... 112

""O*-' Test,x=600

0.,..

!i!!i!!!! Test,x=1000 FEMx=600

..o0

FEMx=1000

"..~Q~oo°°

2;0

i

i

400

600

800

1000

Position along y-axis Fig. 9. Measured and predicted values of deflection for Panel 2 near stiffeners (x = 600 ram) and at mid-panel position (x = 1000 ram), for an applied pressure of 0.1 MPa.

Test-finite element correlationsfor fibre-rein#orced composites

361

~

j~

--<<-...

z./

Fig. 10. Non-linear finite element analysis for Panel 2, showing undeformed (darker) and deformed (lighter) mesh for an applied pressure of 0-1 MPa.

duction of small changes in the position of the clamped area close to the transverse/longitudinal stiffener intersection into the model resulted in large changes in deflections. While the 'appropriate' choice of the boundary conditions in the model would allow improved correlation with measured values, further study of the response of such crossover points is needed to justify such a choice.

CONCLUSIONS The results presented indicate that deflections and strains in monolithic quadriaxially reinforced composite coupons and panels are well represented by the finite element models employed here. The success of the extension of these models to the deflection of sandwich panel structures is dependent upon two factors: - - accurate knowledge of the skin and core properties appropriate to the strain levels to which panels are subjected. In particular, the skin thickness is not easy to determine, but may strongly influence results. The homogenisation technique for periodic media has proved useful in determination of elastic constants not easily accessible by testing. - - a correct description of the loading conditions, and in particular of the evolution of these conditions during the loading of panels. In such cases non-linear large-displacement modelling may be necessary. Further extension of these models to include failure predictions is now being studied. This is not a trivial task. It first requires the refinement of the models to improve strain predictions. The non-linear material beha-

362

P. Davies. D. ('hoqueuse, B. Biq,our~km

viour at strains above 0.3 0-4% t\)r this material will also need to be included, together with stability, core, skin and interface failure criteria.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the helpful comments of L. Lemoine, P. Chauchot and J. F. Rolin during the preparation of this paper, Part of the work was performed within the B R I T E / C O M A S T programme. The contributions of J. Croquette, E. Griffon, L. Potin, D. Petton and H. Loaec are also appreciated.

REFERENCES 1. Smith, C. S., Design o[" Marine Structures in Composite MateriaLs', eds K. O. Holden, O. Faltinsen & T. Moan. Elsevier Applied Science. London, UK, 1990. 2. Rolin, J. E., Design and manufacturing of the NES24 structure. Proc. 1st Fast Sea Tran.sportation Conference, Norway 1991. Tapir Publishers, Trondhelm, Norway, 1991. 3. Gullberg, O. & Romell, O.. Structural optimization of a high performance GRP-sandwich ship hull. Proc. lsl Fast Sea Tra,sportatian ('ot~[~,rence. Norway 1991. Tapir Publishers, Trondheim, Norway, 1991. 4. Bureau Veritas, Reglementation pour la classification des navires de longueurs infdrieures fi 65 m. In Navires en Mat~;riaux Uomposites, Jan. 1989, Ch. 11. 5. Det Norske Veritas, Rules for classification of high speed and light craft. Norway, January 1991. 6. Olsson, K.-A. & Reichard, R. P. (eds), Sandwich Construc:io,s I. EMAS Publishers, Warley, UK, 1989. 7. Sandwich Constructio,s 2. Conference proceedings, Gainsville, Florida, USA, 9-12 March 1992. 8. Allen, H. G., Analysis and Design ~/ Structural Sandwich panels. Pergamon Press, Oxford, 1969. 9. Gibson, I. J., Ashby, M. F., Celhdar Solids. Pergamon Press, Oxford, 1988. 10. Bigourdan, B., Chauchot, P., Hassim, A. & Lene, F., Homogenisation for the design of cylindrical containers made of composite materials. In Mechanics and Mechanisms o[ Damace #1 Composites and MultimateriaLv, ed. D. Baptiste. MEP Publications, London, UK, 1991. 11. European Standard EN61, Determination of tensile properties of textile glass-reinforced plastics, CEN, Brussels, Belgium, 1977. 12. Report of BRITE "COMAST" contract, 15 Dec. 1991, Ref. 21/07/C/12/0012/ O/R, issued by IFREMER, Brest, France. 13. Begis, D., Duvaut, G. & Hassim, A., Homog6n6isation par 616merits finis des modules de comportements +lastiques de matariaux composites. Rapport de recherche 101, IN RIA, Paris, France, 1981.

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