Appl Compos Mater (2006) 13: 217–235 DOI 10.1007/s10443-006-9013-z ORIGINAL PAPER
Geometry and Stacking Sequence Effect on Composite Spinnaker Pole’s Stiffness: Experimental and Numerical Analysis Antonino Valenza & Chiara Borsellino & Luigi Calabrese & Guido Di Bella
Received: 22 September 2005 / Accepted: 4 April 2006 # Springer Science + Business Media, Inc. 2006
Abstract Composite materials are widely employed in sailing sports, a possible application is for the mast pole or other sail poles. In the paper the attention is focused on the spinnaker poles mechanical performances; in particular the focus is on axial and ring compressive properties of three different carbon fibre/epoxy resin spinnaker poles, to investigate both the diameter and stacking sequence effect on the mechanical performance of the structure. Starting from the stacking sequence used in the production of a particular spinnaker pole, the effect of a lamina at 0- in the middle of wall thickness is investigated with the purpose to obtain a more stiff structure. Moreover to test the proposed stacking sequence on different size products, a prototype with lower diameter is realized. To properly evaluate axial and ring stiffness, axial compression test and ring stiffness one are performed. Then a numerical model is developed to support the design of the finished product: A simple and versatile numerical analysis (FEA with software ANSYS), by simulating ring stiffness and pull-direction compression tests, is carried out in elastic regime. Such model should be suitable for designing and/or verifying the mechanical
A. Valenza Dipartimento di Ingegneria Chimica dei Processi e dei Materiali, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy e-mail:
[email protected] C. Borsellino : L. Calabrese (*) : G. Di Bella Dipartimento di Chimica Industriale e Ingegneria dei Materiali, University of Messina, Salita Sperone 31, 98166 S. Agata di Messina, Italy e-mail:
[email protected] C. Borsellino e-mail:
[email protected] G. Di Bella e-mail:
[email protected]
218
Appl Compos Mater (2006) 13: 217–235
performance of pole structures, even though differing from those above described, for materials, geometry and stacking sequence. Key words spinnaker pole . stacking sequence . composite material . FEM
1. Introduction In the last decades the use of composite materials has been gaining ground in marine and offshore industries as they present several advantages over products constructed with other traditional materials. Particularly these objects exploit dearly the properties of high rigidity and reduction of the vibration of the composite materials to improve their performances, and to reduce weights, winning the challenge with traditional products as wood, steel and aluminum [1]. Due to the limited availability of design criteria for composite structures, the product characteristics, in terms of mechanical performances, are still left to the experience of the manufacturers, and their reliability is tested on board ship [2]. One of the possible applications of composite materials in sailing sports is for the mast pole or other sail poles. In this paper the attention is focused on the spinnaker poles mechanical performances. The pole is connected at the tips with the mast and the spinnaker tack by means of pole ends fittings that realize hinge constraints. The pole’s purpose is to keep the sail as far from the boat as possible. In Figure 1 the most employed spinnaker pole jibing method (end-for-end) is shown. It’s possible to observe the pole topping lift, the pole downhaul (or foreguy) and guy (or afterguy) actions on the spinnaker pole. The pole topping lift is used to adjust the height of the outboard end of the pole to suit the sailing angle and wind velocity. The pole downhaul holds the spinnaker pole down; when the lift is raised, the foreguy is eased the same amount, so that the pole is always held in a controlled position. Finally the guy is attached to the tack of the spinnaker, is run through the end of the spinnaker pole and controls the fore and aft angle of the pole in relation to the pole and centerline of the boat [3]. Figure 2 shows a typical assembly system at the spinnaker pole end. Due to this particular tack/guy connection, the wind action on the spinnaker will never induce flexural loads but only a potential axial component can act on the pole. Moreover the coupled action of the topping lift and the downhaul generate a significant axial load on the spinnaker pole. So the spinnaker pole experiences strictly compressive forces. This consideration brings to the necessity to study the buckling phenomena in these structures under compressive load [4]. In fact when the compressive load reaches a critical value the buckling inevitably occurs [5] due to infinitesimal lateral disturbance [6]. In addition under these load conditions the delamination is a frequent cause of failure due to the geometric discontinuities that can induce stresses concentration [4–7]. The buckling phenomenon is well studied by various authors for composite cylinders subjected to several load conditions, as axial compression, lateral pressure and torsion applied individually or in combination [8–12]. Furthermore also the ring stiffness is an important characteristic to avoid damaging due to the stresses induced during transportation or storage on board ship; in fact it can fortuitously receive
Appl Compos Mater (2006) 13: 217–235
219
Figure 1 Spinnaker pole jibing method (end-for-end)
solicitation along a no specific direction. During this operations the spinnaker pole can undergo accidental damages (i.e., crushing). In this paper the focus is on axial and ring compressive properties of three different carbon fibre/epoxy resin spinnaker poles, to investigate both the diameter
Figure 2 Spinnaker pole end fitting
220
Appl Compos Mater (2006) 13: 217–235
and stacking sequence effect on the mechanical performance of the structure. In fact the buckling behaviour of laminated cylinders depends on the position of the differently oriented layers within the shell [13]. In particular, starting from the stacking sequence used in the production of a particular spinnaker pole, the effect of a lamina at 0- in the middle of wall thickness is investigated with the purpose to obtain a more stiff structure. Moreover to test the proposed stacking sequence on different size products, a prototype with lower diameter is realized. To properly evaluate axial and ring stiffness, axial compression test and ring stiffness one are performed. Then a simplified Finite Element Model of the compressive tests is developed; the proposed model is verified by comparing experimental and numerical data obtained by simulating the compressive tests on the spinnaker poles.
2. Experimental Setup 2.1. Materials and Fabrication Processes Spinnaker poles prototypes are manufactured by ComProd – Composite Products S.a.s (Italy) with a standard 6 tons pultrusion machine equipped with eight spools, double-head pull-winder. The Pull-winding machine provides a combination of conventional pultrusion and continuous filament winding. This allows high volume production of thin-walled tubes and profiles, creating the optimised properties, e.g., high hoop strength. A prototype of thin walled pole is created by employing a couple of die and mandrel; with diameters of 80/76 mm (in the following called PROT80 – see Table I). Then a second one is proposed to evaluate how the position of the lamina at 76- affects the resistance, the prototype is realised with a different lamination sequence (in the following called MOD80): The presence of the central lamina at 0- is used to increase the distance of the lamina at 76- from the neutral axis and obtain a stiffer structure. Finally a third prototype (MOD60) is created to verify the geometry effect on the spinnaker pole performances. This last has the same characteristics (layers thickness, volume fraction ...) that has been defined in design and manufacturing phases of the MOD80, it differs from the MOD80 just for the diameter value (it is produced with die/mandrel diameters of 60/56 mm – see Table I).
Table I Geometry of a pole’s section and volume fraction for all prototypes – production data. Layer
1 2 3 4 5
Prototype 80 mm (PROT80)
Prototype 80 mm (MOD80)
Prototype 60 mm (MOD80)
Angle [-] 0 76 j j76 0
Thickness [mm]
Volume fraction
Angle [-]
Thickness [mm]
Volume fraction
Angle [-]
Thickness [mm]
Volume fraction
0.62 0.25 j 0.25 0.75
0.52 0.41 j 0.43 0.59
0 76 0 j76 0
0.37 0.25 0.75 0.25 0.25
0.52 0.41 0.58 0.43 0.59
0 76 0 j76 0
0.37 0.25 0.75 0.25 0.25
0.52 0.41 0.58 0.43 0.59
Appl Compos Mater (2006) 13: 217–235
221
Moreover a very thin finishing fabric, specific for pultrusion use, is present in every sample. For all prototypes the tow angles, the nominal thicknesses and the volume fractions of each layer are reported in the same table. The mechanical properties (tensile and shear) of the employed materials (fibres and resins) are in the follow summarized (Table II) [14]; as reinforcement material only carbon fibre roving is employed. The resin is a low viscosity, high reactivity epoxy-anhydride formulation, with small quantities of filler and other additives.
2.2. Mechanical Testing
&
&
Axial Compression Test, according to ISO/DIS 8513 and to [15] (Figure 3(a)). This mechanical test is realised by employing a Universal Mechanical Testing by Instron equipped with a 200 kN load cell. The prototypes of 80 and 60 mm diameter have, respectively, an overall length of 160 and 120 mm, these lengths are in according to the standard. These ones, supported on a rigid plate, are subjected to top loading by a mobile plate that has a constant rate (1 mm/min). On the diametrically opposites generatrices of the sample two strain gauges, connected on the opposite lines of the Weathstone bridge and interfaced with a PC, are pasted to survey the possible out axis load. The samples ends are not blocked by steel rings, to investigate the failure modes that occur when the pole undergoes axial loads: The typical assembly system at the pole end is shown in Figure 2; namely there are almost two failure modes in competition (delamination/buckling) for this kind of configuration. For each prototype six samples are tested. Ring Stiffness Test, according to UNI EN 1228 (Figure 3(b)). For testing is used an Universal Testing Machine model LR 10 K by Lloyd Instruments is used equipped with a 500 N load cell (0.025 N accuracy) and with a couple of parallel steel plates. The prototypes have a length of 20 mm. The load is applied with constant rate (1 mm/min) on the side of the specimens, for each prototype again six samples are tested.
Table II Mechanical properties of the fibres and resin [14].
Fibres Properties Longitudinal tensile modulus Exf [GPa] Transverse tensile modulus Eyf [GPa] Shear modulus Gxyf [GPa] Shear modulus Gyzf [GPa] Poisson’s ratio nxyf Poisson’s ratio n yzf
234 15 24 5 0.29 0.49
Resin Properties Longitudinal modulus Em [GPa] Shear modulus Gm [GPa] Poisson’s ratio nm
3 1.1 0.36
222
Appl Compos Mater (2006) 13: 217–235
Figure 3 (a) Axial Compression Test (b) Ring Stiffness Test – Experimental Set-Up
3. Results and Discussion 3.1. Axial Compression Test Figure 4 shows a typical load/displacement curve for an axial compression test. In this last, three regions can be identified: At the beginning a nonlinearity is shown, due to the variation of plate/sample contact’s conditions. In the second Figure 4 Load/Displacement trend for a prototype MOD80 in an axial compression test
Appl Compos Mater (2006) 13: 217–235 Table III Experimental results of mechanical testing.
Prototype
PROT80 MOD80 MOD60
223
Axial Compression Test
Ring Stiffness Test
Pmax [kN]
Range [kN]
Pmax [N]
Range [N]
71 136 86
16.40 9.36 2.55
102 226 319
7.39 12.65 17.63
region the sample behaviour is linear. Then, in proximity of the peak, corresponding to the maximum load, the curve exhibits a small nonlinearity until the sample fracture occurs on the sample bottom or top; producing, in general, a delamination. This one can be accompanied by a buckling failure. The obtained results for the tested prototypes are reported in Table III. –
Lamination sequence effect The comparison between the prototype PROT80 and MOD80 is shown in Figure 5(a). The slope of the load/displacement curves and then the axial stiffness of both samples are similar since the total thickness of the lamina at 0- in both samples does not change. Instead the reached maximum loads are different; in particular the first one is higher. For the PROT80 at the first
Figure 5 Load/displacement trends: (a) Lamination sequence effect (b) Diameter effect
224
Appl Compos Mater (2006) 13: 217–235
Figure 6 Buckling failure in prototype (a) MOD60 (b) PROT80
–
peak of the curve a localised crack appears on the external lamina. Then the load slowly drops due to buckling damage propagation until the interlaminar failure takes place (Figure 6(a)). The cylinder PROT80 is less stable than the other one because the lamina at 0- in the wall thickness is external. This affects the failure mode because the external laminas at 0- are separated by the laminas at 76- that do not contribute to the structure resistance in the axial compression test. Then the failure is induced by the transversal and localised cracks on the external surface. Diameter effect The comparison between the prototypes MOD80 and MOD60 is shown in Figure 5(b). The first one presents a higher maximum load than the second one due to the bigger cross-section area. The different diameter induces a different failure mode in the samples. For the prototype with lower diameter the first peak, corresponding to the maximum load, is observed when a localised failure of the external lamina of the cylinder occurs. This behaviour is due to a local skin buckling failure mode. The load drops and then the full fracture occurs due to the delamination at the sample edge, near the damaged zone. This phenomenon does not imply a catastrophic fracture that instead occurs for higher displacements for effect of the global buckling [16]. This failure mode is showed in Figure 6(b). Instead the prototype MOD80 shows only the delamination phenomenon that interests the top or the bottom of the samples. This failure mode is mainly
Appl Compos Mater (2006) 13: 217–235
225
Figure 7 Load/Displacement trend for a prototype MOD80 in a ring stiffness test
due to the contact between the plate and the sample, in this critical area a stress concentration is present, the buckling is not reached and then the delamination is a premature fracture. This behaviour can be explained because the sample with higher diameter is much stable: The buckling resistance of the cylinder increases with increasing the sample diameter. Moreover the axial stiffness, defined by the curve slope, is similar for both prototypes; this because besides the used material quantity varies, the fibres volume fraction and the thickness of the lamina at 0-, that mainly carry the axial load, are constant for both samples.
3.2. Ring Stiffness Test Figure 7 shows a typical load/displacement curve for a ring stiffness test. The trend is initially linear until the curve gradually achieves a nonlinearity. Then the external lamina at 0- breaks and the load collapse. Then it increases again, after a local delamination between the lamina at 0- and 76- nearly the crack, for effect of the lamina at 76- that strongly contribute to the sample resistance; after that it achieves another peak, usually lower than previous one. Then the load drops and the sample is completely delaminated as shows Figure 8. The cracks interest the contact surfaces between the lamina at 76- and the external lamina at 0- and these
Figure 8 Delaminated sample
226
Appl Compos Mater (2006) 13: 217–235
Figure 9 Load/displacement trends: (a) Lamination sequence effect (b) Diameter effect
ones propagate along the fibres at 0- causing the sample damage. The central lamina resists until the final fracture. The obtained results for the tested prototypes are reported in Table III. The observed trends are similar for all prototypes. –
–
Lamination sequence effect The comparison between the prototype PROT80 and MOD80 is shown in Figure 9(a). The first one shows a lower curve slope and the obtained results are very poor. This behaviour is influenced from the different lamination sequence that involves lower specific ring stiffness as reported in Table IV. Diameter effect The comparison between the prototype MOD80 and MOD60 is shown in Figure 9(b). The slope of the linear trend is bigger for the second one, due to its lower diameter that strongly influences the ring stiffness, as shows the relationship of the specific ring stiffness FS_ from UNI EN 1228: S ¼ ð1860 þ 2500 y=dm Þ 105 F=ðL yÞ
ð1Þ
where y and F are, respectively, the displacement and the load corresponding to the value of strain 0.03 as defined in the standard, L is the sample length and dm
Appl Compos Mater (2006) 13: 217–235 Table IV Specific ring stiffness values.
227
Prototype
y [m]
F [kN]
S [kN/m2]
PROT80 MOD80 MOD60
0.00234 0.00234 0.00174
0.010 0.048 0.084
4.00 19.72 46.84
is the mean diameter of the cylinder. The results for all prototypes, reported in Table IV, confirm the better behaviour of the sample MOD60.
4. Finite Element Analysis The experimental tests are simulated employing the geometrical and mechanical characteristics of all prototypes. The numerical simulation is conducted using the ANSYS 7 finite element software and the prototypes are realised using a shell element type (Shell99). The lamina properties data are obtained via the Hahn theory [18] starting from the constituent’s data, reported in Table II. The finite element modeling parameters are reported in Table V where the lamina are numbered starting from the external (#1) to the internal one (#5). The composite structure behaviour is simulated by a numerical procedure performed in elastic regime and the post-elastic behaviour is intentionally neglected to obtain a simple and versatile numerical simulation as is required in designing. 4.1. Axial Compression Test Figure 10 shows the comparison between experimental and numerical results in the axial compression test for prototype MOD80. The prototypes MOD60 and PROT80 confirm similar results. The model well matches the linear elastic trend of the load/ displacement curves for all the tested prototypes, showing a good prediction of their axial stiffness. The stress, in the middle lamina, along the sample axis is reported in Figure 11.
Table V Finite element modelling parameters.
Lamina
1
2– 4
3–5
Young Modulus Ex [GPa] Young Modulus Ey [GPa] Young Modulus Ez [GPa] Poisson Coefficient nxy Poisson Coefficient nyz Poisson Coefficient nxz Shear Modulus Gxy [GPa] Shear Modulus Gyz [GPa] Shear Modulus Gxz [GPa]
115.84 6.24 6.24 0.32 0.47 0.32 3.09 2.2 3.09
94.14 5.32 5.32 0.33 0.44 0.33 2.47 1.91 2.47
129.95 6.98 6.98 0.32 0.48 0.32 3.62 2.42 3.62
228
Appl Compos Mater (2006) 13: 217–235
Figure 10 Experimental and numerical results in the axial compression test for prototype MOD80
This one is uniformly distributed; this behavior is observed for all sample lamina, although the values in the lamina at 0- and in the lamina at 76- are very different (Table VI). –
–
Lamination sequence effect The axial stresses are higher in the prototype MOD80 than the prototype PROT80. For the second one the higher stress is observed in the external lamina according with the transversal and localized cracks that start on these laminas. Examining the interlaminar stress, the boundary effect is absent in this prototype and the stress is constant on the whole surface. The evaluated values are so low to prevent delamination, according to the experimental results. Diameter effect For the prototype MOD80 the axial stresses are higher than the prototype MOD60 in each lamina. Moreover for each sample the stress in the lamina at 0is higher due to its fibres orientation in the load direction; these one are the
Figure 11 Axial Stress for prototype MOD80 in the middle lamina
Appl Compos Mater (2006) 13: 217–235 Table VI Axial Stresses on the lamina surface.
Lamina
1 2 3 4 5
Figure 12 Interlaminar Stress for the prototype (a) MOD80 (b) MOD60 (c) PROT80
229
0 76 0 j76 0
PROT80 s [MPa]
MOD80 s [MPa]
MOD60 s [MPa]
j200.8 j9.6 j j9.4 j218.1
j412.3 j23.6 j390.1 j23.0 j417.0
j396.3 j25.5 j313.3 j29.3 j366.1
230
Appl Compos Mater (2006) 13: 217–235
most solicited carrying widely the axial compression. Particularly in the prototype MOD60 the higher stress is observed in the most external layer. This is in according with the experimental behavior, the sample MOD60 that is less stiff, reaches the fracture for buckling in the external lamina. The interlaminar stress (Figure 12) can determine the possible delamination at the layer interface. For the samples MOD80 and MOD60 an accentuate boundary effect is observed and this one explains why the fracture can occur on the sample top or bottom. Moreover, for the prototype MOD80 the values are higher than the other prototype and these ones are constant inside every lamina according to the failure mode, which is delamination. Instead the prototype MOD60 shows different behavior, in fact the interlaminar stress between lamina 1 and 2 is higher than the other lamina one, confirmed from the fact that the delamination do not occur randomly but it is localized; although at the end the global failure is due to local buckling interesting the external surface.
4.2. Ring Stiffness Test Figure 13 shows the comparison between experimental and numerical results in the ring stiffness test for prototype MOD80. The prototypes MOD60 and PROT80 confirm similar results. The experimental curves are non-linear and the model well matches only the first linear elastic trend of the load/displacement curves (zoomed in the same Figure 13). Although the non-linearity is strongly evidenced, this numerical analysis is able to evaluate the ring stiffness from the maximum slope of the first trend, as defined in Equation (1). Then with a simple geometrically linear model it is possible to find out the ring stiffness of the prototypes. In Figure 14 the stresses in load direction (s y) for the prototype MOD80 are reported. The study of the stresses trend on the single lamina allows us to understand the behaviour of the whole structure in this particular load condition. The lamina 1 and
Figure 13 Experimental and numerical results in the ring stiffness test for prototype MOD80
Appl Compos Mater (2006) 13: 217–235
231
2, as well the lamina 4 and 5, show the same distribution, so only the lamina 2 and 4 at 76- are reported. In the lamina 2 (Figure 14(a)) the load induces a maximum tensile stress on the external parts. The lamina 3 (Figure 14(b)) is almost unloaded and this explains how this lamina works, only by separating the laminas at 76-. On Figure 14 Stress distribution in the load direction for prototype MOD80 (a) lamina 2 (b) lamina 3 (c) lamina 4
232
Appl Compos Mater (2006) 13: 217–235
the other lamina (4 and 5) a trend inversion is observed due to the load conditions; in fact the lamina 4 has a maximum compression stress on the external parts. In Figure 15 the stress in transversal direction (s z) for the prototype MOD80 is reported. Also in this case a trend inversion in the stress is observed. In the lamina 2 Figure 15 Stress distribution in the transversal direction for prototype MOD80 (a) lamina 2 (b) lamina 3 (c) lamina 4
Appl Compos Mater (2006) 13: 217–235 Table VII Maximum stresses for each lamina.
Lamina
1 2 3 4 5
0 76 0 j76 0
233
PROT80
MOD80
MOD60
sy [MPa]
sz [MPa]
sy [MPa]
sz [MPa]
sy [MPa]
sz [MPa]
56.6 126.6 j j153.0 j59.0
j101.3 j231.6 j 260.3 104.3
37.5 234.9 õ0 j258.4 j42.8
j68.1 j434.1 õ0 439.9 74.0
34.8 270.1 õ0 j302.0 j31.5
j63.6 j507.1 õ0 499.4 53.3
(Figure 15(a)) a maximum compression stress on the sample top, where the load acts, is attained. The lamina 3 (Figure 15(b)) is unloaded and the lamina 4 (Figure 15(c)) is subject to a maximum tensile stress. The prototypes MOD60 and PROT80 present similar trends for both stresses. In Table VII, for all prototypes, the maximum stress values for each lamina are reported. The lamina at 76-, which mainly carries the applied load, shows higher stress values than the external lamina at 0-. Moreover the stress is higher on the sample top (s z). The numerical results are in according to the experimental failure mode that is the insurgence of cracks in the external lamina in the top position. The observed delamination is only a consequence of the cracks propagation. The prototype MOD60 has the higher stress value than the other prototypes while the prototype PROT80 the lowest.
5. Conclusions On the basis of the experimental and numerical tests performed on the three prototypes of spinnaker pole it is possible to draw out the following considerations:
&
&
&
In axial compression test the sample behaviour is mainly elastic. The load increases linearly until the sample fracture. The analysed prototypes have similar axial stiffness but the reached maximum loads are very different. An increased cross-section area and the presence of a central lamina at 0- confer higher mechanical resistance. In the ring stiffness test the sample behaviour is initially elastic until the curve gradually reaches a nonlinearity and then the collapse of the lamina at 0- is observed. The load changes for effect of the lamina at 76- position. The presence of smaller diameter, as the presence of the central lamina, increases the specific ring stiffness. From the FEM analysis, performed by employing the commercial ANSYS code, the static-mechanical behaviour of the composite structure is well approximated in elastic zone. For the axial compression test the effect of the interlaminar stresses is important to allow the understanding of the fracture insurgence. In the ring stiffness, the s y and s z trends show that the central lamina is unloaded being only a gap between the lamina at 76-. Moreover the stress is higher on the sample top where the failure occurs interesting mainly the external lamina. The evaluated stresses are the highest for the
234
&
Appl Compos Mater (2006) 13: 217–235
prototype MOD60 and the lowest for the prototype PROT80. Such results allow confirming that the model is suitable for designing and/or verifying the mechanical performances of pole structures, even though different from those above described, for materials, geometry and stacking sequence. The effect of introducing a lamina at 0- in the centre of the lay up is: The increase of axial resistance (independently from the lamina position) and the increase of the ring stiffness of the spinnaker pole. In the higher diameter’s prototypes an increase of about 91% and about 393%, respectively, in axial resistance and in specific ring stiffness was found. At the same time the diameter reduction with respect to the better stacking sequence causes a decay of about 37% in axial resistance and an increase of about 138% in ring specific stiffness. Therefore for the higher diameter’s spinnaker pole the choice of introducing the lamina at 0- determines a relevant increase in its global performances while the production of a lower diameter’s one still allows good mechanical properties for a slender structure.
Acknowledgements Particular thanks are addressed to the ComProd – Composite Products S.a.s (Italy) to have supplied the spinnaker poles prototypes and the production data on the used materials.
References 1. Tsouvalis, N.G., Zafeiratou, A.A., Papazoglou, V.J., Gabrielides, N.C., Kaklis, P.D.: Numerical modeling of composite laminated cylinders in compression using a novel imperfections modeling method. Compos., Part B Eng. 32, 387–399 (2001) 2. Spagnoli, A., Elghazouli, A.Y., Chryssanthopoulos, M.K.: Numerical simulation of glassreinforced plastic cylinders under axial compression. Mar. Struct. 14, 353–374 (2001) 3. Whidden, T.: Sailing with a Spinnaker. Boston Harbor Sailing Club, Racer’s Information (2004) 4. Tafreshi, A.: Buckling and post-buckling analysis of composite cylindrical shells with cutouts subjected to internal pressure and axial compression loads. Int. J. Press. Vessels Piping 79, 351– 359 (2002) 5. Kim, T.D.: Fabrication and testing of composite isogrid stiffened cylinder. Compos. Struct. 45, 1–6 (1999) 6. Mao, R., Williams, F.W.: Post-critical behaviour of orthotropic circular cylindrical shells under time dependent axial compression. J. Sound Vib. 210(3), 307–327 (1998) 7. Tafreshi, A.: Efficient modelling of delamination buckling in composite cylindrical shells under axial compression. Compos. Struct. 64, 511–520 (2004) 8. Simitses, G.J.: Buckling of moderately thick laminated cylindrical shells: a review. Compos., Part B Eng. 27, 581–587 (1996) 9. Messager, T.: Buckling of imperfect laminated cylinders under hydrostatic pressure. Compos. Struct. 53(3), 301–307 (2001) 10. Tafreshi, A.: Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure. Compos. Struct. 72(4), 401– 418 (2006) 11. Meyer-Piening, H.R., Farshad, M., Geier, B., Zimmermann, R.: Buckling loads of CFRP composite cylinders under combined axial and torsion loading – experiments and computations. Compos. Struct. 53(4), 427– 435 (2001) 12. Ye, J., Soldatos, K.P.: Three-dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels. Int. J. Solids Struct. 32(13), 1949–1962 (1995) 13. Geier, B., Meyer-Piening, H.R., Zimmermann, R.: On the influence of laminate stacking on buckling of composite cylindrical shells subjected to axial compression. Compos. Struct. 55, 467– 474 (2002) 14. Dispenza, C., Fuschi, P., Pisano, A.A.: Mechanical testing and numerical modelling of pullwound carbon-epoxy spinnaker poles. Compos. Sci. Technol. 62, 1161–1170 (2002)
Appl Compos Mater (2006) 13: 217–235
235
15. Elghazouli, A.Y., Chryssanthopoulos, M.K., Spagnoli, A.: Experimental response of glassreinforced plastic cylinders under axial compression. Mar. Struct. 11, 347–371 (1998) 16. Kidane, S.: Buckling analysis of grid stiffened composite structures. PhD thesis, Louisiana State University (2002) 17. Valenza, A., Borsellino, C., Calabrese, L.: Experimental and numerical evaluation of sandwich composite structures. Compos. Sci. Technol. 64(10–11), 1709–1715 (2004) 18. Tsai, S.W., Hahn, H.T.: Introduction to Composite Materials. Technomic. Hardcover (1980)
