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An experimental investigation into the buckling and post-buckling

An experimental investigation into the buckling and post-buckling
An experimental investigation into the buckling and post-buckling

An experimental investigation into the buckling and post-buckling

of CFRP shells under combined axial and torsion loading

Chiara Bisagni *,Potito Cordisco

Dipartimento di Ingegneria Aerospaziale,Politecnico di Milano,Via La Masa 34,20156Milano,Italy

Abstract

The results of an experimental studyof the buckling and post-buckling behaviour of four unsti?ened thin-walled CFRP cy -lindrical shells are presented.The test equipment allows axial and torsion loading,applied separatelyand in combination,using a position control mode,and includes a laser scanning system for the measurement in situ of the geometric imperfection as well as of the progressive change in deformations.The results identifythe e?ect of laminate orientation,show that the buckling loads are essentiallyindependent of load sequence and demonstrate that the shells are able to sustain load in the post-buckling ?eld without anydamage.The measured data are fundamental for the development and validation of analy tical and numerical models and contribute to the de?nition of applicable strength design criteria of composite cylindrical shells in the post-buckling ?eld,with the ?nal aim of a larger structure weight saving.ó2003Elsevier Science Ltd.All rights reserved.

Keywords:Post-buckling;Composite cylindrical shells;Experimental tests

1.Introduction

A great e?ort is underwayin the aircraft industryto improve the e?ectiveness of current aircraft structures.Advanced composite materials appear extremelyat-tractive due to their high strength-to-weight and high sti?ness-to-weight ratios and are in-depth under inves-tigation.Theyhave been alreadyextensivelyimple-mented in some cases and appear the onlypossible solution in the near future to achieve a signi?cant re-duction of structural weight,without reduction of structural life.Indeed,the lower weight of advanced composite structures compared to conventional metallic structures achieves directlythe weight reduction goal.However,experiments have shown that there is the possibilityfor further weight savings with composite structures byallowing post-buckling to occur during operation.Unfortunatelythe buckling and post-buck-ling strength prediction is extremelycomplex in the case of composite shell structures.

The traditional approach to shell design is to predict the buckling load using a linear bifurcation buckling analysis with the nominal structural dimensions and

material properties of an idealised geometricallyperfect shell.This predicted buckling load is then reduced bya ‘‘knock-down’’factor based on design criteria such as those reported in NASA SP-8007[1].The use of knock-down factors allows to take into account the in?uence of imperfections and of unintended deviation from nomi-nal values,explaining the di?erence between the pre-dicted and the actual buckling load determined from tests [2–4].This approach can sometimes result in overly conservative designs,or it can potentiallyeven result in unconservative designs if the empirical data are not representative of the considered shells.n anycase,the traditional sources of knock-down factors for predicting buckling loads do not include information for shell structures made bycomposite materials.The laminated composite shells exhibit signi?cant buckling sensitivity to geometric shape imperfections similar to that of iso-tropic shells,but also to other parameters,such as thickness variations,local ply-gaps or overlapping as-sociated with the fabrication process ...

In addition,nowadays modern computational facili-ties,with the enormouslyincreased computer capabili-ties,o?er the opportunityto investigate the complex buckling phenomena with robust non-linear numerical analyses [5–10].These analyses can form the basis for an improved shell design procedure that reduces the de-pendencyon the knock-down design philosophyand

*Corresponding author.Tel.:+39-02-2399-8390;fax:+39-02-2399-8334.

E-mail address:chiara@aero.polimi.it (C.Bisagni).

0263-8223/03/$-see front matter ó2003Elsevier Science Ltd.All rights reserved.doi:10.1016/S0263-8223(03)00024-2

Composite Structures 60(2003)

391–402

https://www.wendangku.net/doc/cf9096583.html,/locate/compstruct

can represent the con?guration,the material system and the imperfection of the particular composite shell of interest.

n anycase,a selected number of well-instrumented and carefullyconducted experiments are essential to validate the design and analysis tools.These experi-mental tests are particularlynecessaryfor thin-walled circular cylindrical shells,for their long recognised im-perfection sensitivityand as theyconstitute primary structural parts.Airplane fuselage,helicopter tailboom, missiles and jet engine casings are but a few examples in the aircraft industry,as well as submarine structures, tubing,piping and o?shore platforms.Depending on their use,these cylindrical shells are subjected,during their life,to individual and combined application of external loads and theyare subject to buckling to resist to these loads.

Unfortunately,while it is relatively simple to?nd experimental data about composite cylindrical shells subjected to axial compression[10–14],it is more di?-cult to obtain data regarding tests under combined loading.And,anyway,the larger part of published data deals with combined compression and external or in-ternal pressure[14,15].Onlyfew experimental results are available for composite cylindrical shells subjected to combined axial and torsion loading[14,16,17]and most of them do not consider the post-buckling?eld,while the shell post-buckling strength capacityhas signi?cant

potential for weight saving.

The present paper describes the results of an experi-

mental investigation regarding thin-walled carbon?ber

reinforced plastics(CFRP)cylindrical shells subjected to

axial compression and torsion,applied individuallyand

in combination.The study,part of a larger research

project including also the development of analytical and

numerical models[7],is aimed to the determination of

the buckling loads of cylindrical shells of di?erent lam-

inate orientations and to the investigation of the

strength capacityof these structures to be able to work

in the post-buckling?eld without anydamage.

2.Test specimens

The specimens were fabricated byAgusta from

CFRP unidirectional tape material and from CFRP

fabric tape material.The material was laid up on a

mandrel and cured in an autoclave to form four shells

with di?erent laminates,including a unidirectional[45°/ )45°]2S shell,a unidirectional[90°/0°]2S shell,a fabric [45°/)45°]S shell and a fabric[0°/45°/)45°/0°]shell.The

nominal lamina material properties are reported in

Table1.

The specimens(Fig.1)are characterised byan in-

ternal diameter and an overall length of700mm,in-

cluding two tabs provided at the top and at the bottom surfaces for attaching them to the loading equipment. The actual length is therefore limited to the central part and is equal to540mm.The two unidirectional shells present a thickness of 1.20mm and consequentlya radius-to-thickness ratio of292,while the two fabric shells present a thickness of 1.32mm and a radius-to-thickness ratio of265.

3.Test equipment

The experimental buckling tests are performed on the cylindrical shells under axial compression,torsion and combined axial compression and torsion,bya loading rig using a position control mode(Fig.2).

To applyaxial compression,the loading platform is pushed bya hy draulic ram against four ball screw sup-ports placed at the four corners of the platform.At the beginning,the load given bythe ram is completely supported bythe four screws,which distribute the real applied load on the specimen during the test.Indeed,the screws motion is computer-controlled,producing ex-actlythe desired displacement to the loading platform, using four stepping motors through four reduction gears.Thus,the load level,which is transferred smoothlyto the cy linder,depends onlyon the platform displacement and on the cylinder elastic response and it Table1

CFRP laminae material properties

CFRP unidirectional CFRP fabric Young?s modulus

(longitudinal)[N/mm2]

11300052000

Young?s modulus

(transverse)[N/mm2]

900052000

Shear modulus[N/mm2]38202350

Major Poisson ratio0.730.302 Plythickness[mm]0.15

0.33

Fig.1.Typical specimen.

392 C.Bisagni,P.Cordisco/Composite Structures60(2003)391–402

does not substantiallydepend on the load magnitude due to the hydraulic ram acting on the platform.

To applytorsion,the rotation is given to the speci-men bottom bya torsion lever.The lever motion is computer-controlled,producing the desired displace-ment of a screw bya stepping motor through a reduc-tion gear,like in the case of axial compression.

All the ?ve stepping motors can be computer-con-trolled separatelyor simultaneously .I n this wayit is possible,from one side,to applyaxial compression and torsion in anyliked sequence,in order to perform combined tests,and,from the other side,to constrain the two ends of the specimens to remain parallel during the tests.

Three LVDT transducers give directlythe axial dis-placement of the specimen at three equallyspaced points,measuring the distance between the inner surface of the upper clamp and of the lower clamp.Other three LVDT transducers measure the tangential displacement of the specimen bottom respect to the top,at the same three points used during axial compression.The load

cell,situated under the lower clamp,allows measuring both the compression load in three points and the tor-sion moment.

An ad-hoc equipment was designed and built to measure the specimens inner surfaces in terms of initial geometric imperfections,pre-buckling shape and pro-gressive change of post-buckling deformations (Fig.3).The equipment is placed inside the specimen during the tests and employs ?ve laser displacement sensors to measure the specimens inner surface,avoiding any contact with the specimen and consequentlywithout in?uencing the buckling behaviour.The ?ve laser dis-placement sensors are ?xed on a slide,capable of ro-tating and translating vertically.The combination of the two movements allows measuring the whole inner sur-face of the specimens.These movements are generated bytwo stepping motors and the vertical position of the slide is determined byan incremental encoder.The laser displacement sensors are placed at the distance of 40mm from the specimen inner surface and guarantee a measurement range of ?10mm with a resolution of 15l m,for recording both the geometric imperfections (some tens of micrometers)and the post-buckling de-formations (about 10–20mm).

4.Imperfection measurements

The measurement of the inner surfaces of the speci-mens is carried out,using the laser scanning system,after each specimen is mounted in the test rig and before anyload is applied,allowing to measure the geometric imperfections in situ and not in a separate rig.Mea-surements are taken over a uniform grid with steps of 10mm in the axial direction and 10mm (approximately 0.03°of arc)in the circumferential direction.

The inner surface measurement is used to determine the initial imperfections,that consist in the deviations from an imaginarycy lindrical reference surface

de?ned

Fig.2.Equipment for the buckling

tests.

Fig.3.Equipment for the measurement of the imperfections and of the post-buckling deformations.

C.Bisagni,P.Cordisco /Composite Structures 60(2003)391–402393

as the best-?t cylinder to the measured data,computed bya least-squares method [4,14,18].The recorded dis-placements are,therefore,recalculated with respect to this best-?t reference surface.n this manner anyrigid bodydisplacement of the shell with respect to the scanning system is removed.

The advantage of this widelyused data processing technique is that it allows comparative studies on the e?ect of the manufacturing process on the magnitude and spatial distribution of the initial imperfections,collected in the International Imperfection Data Bank [4,19,20].Furthermore,in this way,the measured im-perfections can be easilyintroduced into the analy tical and numerical models.

The initial geometric imperfections measured on two cylindrical shells at three di?erent height (one quarter,half and three quarter of the height)are presented in Fig.4in a polar diagram with an ampli?cation factor equal to 70.

5.Test procedure

Each specimen is ?rstlytested under pure axial compression and under pure torsion,individually.Axial displacement is applied bysteps of 0.005mm,while angular rotation bysteps of about 0.0005°,imposed via software.After everystep,the e?ective axial displace-ment and compression load or the rotation angle and torsion moment are measured.The curve of axial load versus displacement as well as the curve of torsion ver-sus rotation are recorded in real-time,during the tests.Then the shells are tested under combined axial and torsion loading.To perform combined tests,three dif-ferent procedures can be investigated.The ?rst proce-

dure consists in twisting the specimen into one direction (clockwise or counter-clockwise)to a pre-set torsion torque level and then in axiallyloading it until buckling.The second one consists in axiallyloading the specimen to a pre-set axial load level and then twisting it into one or the opposite direction until buckling.The third pro-cedure consists in applying ?xed steps of axial load and torsion torque with di?erent ratio of axial load and torsion torque levels.During all the three procedures,the axial and tangential displacements are recorded using the LVDT transducers throughout the whole test,as well as the axial compression load and the torsion torque using the load cell.

The tests are performed using always the same spec-imen and not using di?erent but nominallyidentical specimens.The reason is that past studies performed by Singer [21]and Abramovich et al.[22]on aluminium-alloycy lindrical shells demonstrated that the di?erences in data produced bydamages,due to repeated buckling in carefullyconducted tests,is much less than those re-sulting from the initial di?erences in shape and proper-ties of separate specimens,even if theyare manufactured rather accurately.So,it is reasonable to think that these considerations are true also for composite shells,whose manufacturing process is much more important.In any case,the shells are continuouslymonitored bythe im-perfections measurement,to be sure that the repeated buckling does not induce anydamage.

All the tests are performed to reach the buckling phenomenon,are continued in the post-buckling ?eld and then the specimens are unloaded always using the position control mode.The inner surface of the cylin-drical shells is measured 15–20times during each test using the lasers system,so to be able to measure the pre-buckling surface and to follow the development of

the

Fig.4.Typical polar diagrams of measured inner-surface imperfections:(a)[45°/)45°]2S unidirectional cylindrical shell;(b)[0°/45°/)45°/0°]fabric cylindrical shell.

394 C.Bisagni,P.Cordisco /Composite Structures 60(2003)391–402

post-buckling deformations.This is possible as the time required to measure a complete specimen surface is limited to4min.

6.Tests results

n this paper onlythe results of some tests are pre-sented,in terms of diagrams of axial load versus dis-placement,diagrams of torsion torque versus rotation, of interaction curves for combined tests and of post-buckling deformations.

6.1.Unidirectional shells

Firstlythe shells are tested under pure axial com-pression and under pure torsion,individually.

The values of the measured buckling loads are re-ported in Table2,together to the post-buckling modes. In particular,the post-buckling axial mode reports the circumferential and axial number of half-waves,while the post-buckling torsion mode reports the diagonal number of half-waves.

The two diagrams of axial load versus displacement, obtained during the pure axial compression tests,are presented in Fig.5,together to the diagrams of torsion torque versus rotation,obtained during the pure torsion tests.In these diagrams,both loading and unloading sequences are reported.As expected,the axial sti?ness of the[45°/)45°]2S cylinder is considerably lower than that of the[0°/90°]2S cylinder.This is a direct consequence of the relativelylow material sti?ness for the+45°/)45°laminate in the direction of the cylinder axis.

It is possible to see that,while the buckling phe-nomenon under axial compression appears suddenlyfor the unidirectional[45°/)45°]2S shell,there is a gradually reduction of the sti?ness after the buckling in the case of the unidirectional[0°/90°]2S shell.Under torsion loading the buckling is verysmooth for both shells.

Then the shells are tested under combined axial and torsion loading and the results are reported in Table3. The buckling loads are obtained according to the?rst procedure,that means twisting the specimen into counter-clockwise direction to a pre-set torsion torque level and then axiallyloading it until buckling.n the case of the[0°/90°]2S shell,three combined tests are performed,where the pre-set torsion torque level is equal to a fourth,half and three-fourths respectivelyof the buckling torque obtained during the pure torsion test.In the case of the[45°/)45°]2S shell,?ve combined tests are performed to be able to follow better the in-teraction curve,and so the pre-set torsion torque level is equal to one,two,three,four and?ve sixth of the buckling torque obtained during the pure torsion test.

Fig.6shows the interaction curves under combined loads for the two unidirectional specimens.The inter-action curve of the[45°/)45°]2S shell starts with a low slope near the compression axis and increases the gra-dient at about one half of the buckling moment of the pure torsion test,while the interaction curve of the[0°/ 90°]2S shell presents a quasi-constant slope.From the post-buckling patterns it is possible to recognise that a variation in the slope of the interaction curves corre-sponds to a change in the shell deformations.

Fig.7shows the post-buckling modes recorded dur-ing the pure axial compression test,a combined com-pression–torsion test and the pure torsion test,for the [45°/)45°]2S shell and the[0°/90°]2S shell,respectively.

In the case of the[45°/)45°]2S shell,the axial com-pression post-buckling mode is diamond-shaped,well de?ned and perfectlyregular,with8half-waves around the circumference and1half-waves along the length. The displacements normal to the surface reach,in the post-buckling?eld,13.7mm inward and7.3mm out-ward.The?ve combined compression–torsion tests show that,in correspondence of the change in the slope of the interaction curve,the single row of8?1 diamond-shaped half-waves that distinguishes the post-buckling mode of the pure compression test is substi-tuted bya partial9?2half-waves in the forth combined test and bya partial10?2diamond-shaped half-waves in the?fth test,to reach the12diagonal-shaped half-waves that characterise the pure torsion test,where the displacements normal to the surface reach6.6mm in-ward and2.6mm outward.

The[0°/90°]2S shell,under pure axial compression, collapses into a diamond-shaped post-buckling mode with10half-waves around the circumference and2half-waves along the length,disposed in the lower part of the specimen.The displacements normal to the surface reach,in the post-buckling?eld,7.9mm inward and3.8 mm outward.The three combined compression–torsion tests present inclined waves on three di?erent lines axi-ally,not completely regular.The post-buckling mode of

Table2

Buckling loads for axial compression and torsion tests and stable post-buckling modes

Specimen Unidirectional[45°/)45°]2S Unidirectional[0°/45°/)45°/0°]2S Fabric[45°/)45°]S Fabric[0°/45°/)45°/0°] Buckling axial load[kN]74.9383.6697.95140.20

Post-buckling axial mode8?110?28?110?2

Buckling torsion torque[kNm]11.7411.8913.5813.19

Post-buckling torsion mode12101112

C.Bisagni,P.Cordisco/Composite Structures60(2003)391–402395

the torsion test consists of 10diagonal-shaped half-waves with displacements normal to the surface that reach 7.4mm inward and 3.5mm outward.6.2.Fabric shells

Firstlythe shells are tested under pure axial com-pression and under pure torsion,individually.The values of the measured buckling loads are re-ported in Table 2,together to the post-buckling modes.In particular the post-buckling axial mode reports the circumferential and axial number of half-waves,while the post-buckling torsion mode reports the diagonal number of half-waves.

The two diagrams of axial load versus displacement,obtained during the pure axial compression tests,are

Table 3

Buckling loads for combined compression and torsion loading Unidirectional [45°/)45°]2S Unidirectional [0°/90°]2S Fabric [45°/)45°]S Fabric [0°/45°/)45°/0°]M t [kNm]P ax [kN]M t [kNm]P ax [kN]M t [kNm]P ax [kN]M t [kNm]P ax [kN]3.1671.18 3.0570.20 3.3094.35 3.24114.705.6664.62 5.9250.34 6.5488.23 6.6278.047.4254.128.90

22.91

9.77

46.67

9.86

41.92

8.6139.069.79

25.75

396

C.Bisagni,P.Cordisco /Composite Structures 60(2003)391–402

presented in Fig.8,together to the diagrams of torsion torque versus rotation,obtained during the pure torsion tests.Also for these shells,in the diagrams,both loading and unloading sequences are reported and,as expected, the axial sti?ness of the[45°/)45°]S cylinder is consid-erablylower than that of the[0°/45°/)45°/0°].

Under pure axial compression,the buckling of the [45°/)45°]S shell occurred at a load of98kN,suddenly, with a low noise and with the load dropping at about62 kN,while for the[0°/45°/)45°/0°]shell it occurred at a load of140kN,suddenly,intensively audibly and with the load dropping drasticallyat about50kN.Under pure torsion,the buckling is verysmooth and happened at a load of about13kNm for both shells.

Then the shells are tested under combined axial and torsion loading and the results are reported in Table3. The reported buckling loads are obtained according to the?rst procedure,that means twisting the specimen into counter-clockwise direction to a pre-set torsion torque level and then axiallyloading it until buckling. For both shells,three combined tests are performed, where the pre-set torsion torque level is equal to a fourth,half and three-fourths respectivelyof the buck-ling torque obtained during the pure torsion test.

Fig.9shows the interaction curves under combined loads for the two fabric specimens.The interaction curve of the[45°/)45°]S shell starts with a low slope near the compression axis and increases gradient at about one half of the buckling moment of the pure torsion test, while the interaction curve of the[0°/45°/)45°/0°]shell presents a quasi-constant slope.

As well as for the unidirectional shells,the buckling loads are stronglya?ected bythe alignment of the car-bon?bers and consequentlybythe sequence of the stacking.The related e?ects result more evident for the case of pure axial compression than for combined compression–torsion loading.Also for the fabric shells,from the post-buckling patterns it is then possible to recognise that a variation in the slope of the interaction curves corresponds to a change in the shell deforma-tions.

For the[45°/)45°]S shell,the buckling values ob-tained during the compression–torsion loading tests according to the three di?erent procedures are pre-sented in Table4.Together to the data obtained from the?rst procedure,alreadyreported in Table3,the results of three combined tests performed according to the second procedure and of three combined tests performed according to the third procedure are re-ported.In the tests according to the second procedure, the specimen is axiallyloaded to a pre-set axial load level,equal to the values of the buckling axial loads obtained during the previous combined tests,and then twist into counter-clockwise direction until buckling. The tests according to the third procedure are per-formed applying?xed steps of axial load and torsion so that the ratio of the axial load and torsion levels ap-plied is equal to the values obtained during the previous combined tests.

Fig.10,that reports the interaction curves of the di?erent combined compression–torsion tests,shows that the three procedures bring essentiallyto the same buckling values.Consequently,the buckling values are independent on the wayto obtain them and depend only on the ratio of axial load and torsion levels.Even if it maysound surprising considering the non-linearityof the curves and of the phenomenon,it is perfectlyin accord to what obtained byAbramovich et al.[22]for metallic cylindrical shells subjected to compression-pressure combined loads and byBooton and Tenny son [15]for glass/epoxycy linders subjected to torsion,ex-ternal hydrostatic pressure and axial compression.

Fig.11shows the post-buckling modes recorded during the pure axial compression test,a combined

C.Bisagni,P.Cordisco/Composite Structures60(2003)391–402397

compression and torsion test and the pure torsion test,for the [45°/)45°]S shell and the [0°/45°/)45°/0°]shell,respectively.

In the case of the [45°/)45°]S shell,the axial com-pression post-buckling mode is diamond-shaped,well de?ned and perfectlyregular,with 8half-waves around the circumference and 1half-waves along the length.The displacements normal to the surface reach,in the post-buckling ?eld,13.5mm inward and 7.6mm out-ward.The post-buckling mode does not change for the ?rst two combined tests,while the third combined test presents diamond waves around the circumference,no more regular and diagonallyinclined.The post-buckling mode of the torsion test consists of 11

diagonal-shaped

Fig.7.Post-buckling modes for the axial compression test,a combined compression–torsion test and the torsion test:(a)[45°/)45°]2S unidirectional cylindrical shell;(b)[0°/90°]2S unidirectional cylindrical shell.

398 C.Bisagni,P.Cordisco /Composite Structures 60(2003)391–402

C.Bisagni,P.Cordisco/Composite Structures60(2003)391–402399

half-waves with displacements normal to the surface that reach11mm inward and3.6mm outward.

In the case of the[0°/45°/)45°/0°]shell,the axial compression post-buckling mode is diamond-shaped, well de?ned and perfectlyregular,with10half-waves around the circumference and2half-waves along the length.The displacements normal to the surface reach, in the post-buckling?eld,10.5mm inward and4.9mm outward.The three combined compression–torsion tests present always diamond-shaped half-waves,even if they get more inclined as the component of torsion torque get higher and theyevolve from2half-waves to1half-wave in the axial direction.The post-buckling mode of the pure torsion test consists of12diagonal-shaped half-waves with displacements normal to the surface that reach about9.5mm inward and3.4mm outward.

Fig.12reports two photos of the post-buckling modes during the pure axial compression test and dur-ing the pure torsion test for the[0°/45°/)45°/0°]shell.It is possible to see the diamond-shaped waves for the axial compression test and the diagonal-shaped waves for the torsion test.

7.Conclusions

The results of an experimental investigation on buckling and post-buckling behaviour of unsti?ened thin-walled cylindrical shells were presented and dis-cussed.

An equipment was designed and built to perform buckling tests under axial compression and torsion, applied separatelyor as combined loading,using a po-sition control mode.The diagrams of axial load versus displacement and of torsion versus rotation,measured using a load cell and LVDT transducers,were recorded in real time during the tests.Moreover,an automated laser scanning system provided an e?cient non-contact technique for measuring the initial geometric imperfec-tions as well as the progressive change in deformations during loading and in the post-buckling?eld.

The imperfections measured in the experiments in situ can be directlyused as inputs of analy tical and numer-ical models as well as inputs to the International Im-perfection Data Bank for future studies on the correlation between the manufacturing method of the shells and their geometric imperfections.

Several tests were performed on four CFRP cylin-drical shells with di?erent laminates,including a unidi-rectional[45°/)45°]2S shell,a unidirectional[90°/0°]2S shell,a fabric[45°/)45°]S shell and a fabric[0°/45°/)45°/ 0°]shell.All the considered shells show a completely linear behaviour until buckling load is reached.Then, under axial compression,theyexhibit a sudden drop in load,except for the unidirectional[0°/90°]2S that exhibits a gradual reduction of the sti?ness after buckling.In-

Table4

Fabric[45°/)45°]S shell:buckling loads for combined axial and torsion loading with three di?erent procedure

First procedure Second procedure Third procedure

M t[kNm]P ax[kN]M t[kNm]P ax[kN]M t[kNm]P ax[kN] 3.3094.35 2.4094.05 3.3694.19 6.5488.23 6.7288.23 6.7089.69 9.7746.6710.1046.7510.4448.83

400 C.Bisagni,P.Cordisco/Composite Structures60(2003)391–402

stead,the buckling phenomenon under torsion appears verysmooth for all the considered shells.

The interaction curves,obtained from the combined tests of the shells composed onlybycarbon ?bers ori-ented to ?45°,both in fabric and in unidirectional,present a signi?cant change in the slope and in corre-spondence a change in the deformation shapes.Instead,the interaction curves of the other shells have a quasi constant slope and the change in the deformation shapes is more regular.The e?ects of the alignment of the carbon ?bers result more evident on the buckling loads of the pure axial compression tests than on those of the combined tests.n anycase,the buckling loads result independent from the loading sequence and de-pend onlyfrom the ratio of axial load and torsion

applied.

Fig.11.Post-buckling modes for the axial compression test,a combined compression–torsion test and the torsion test:(a)[45°/)45°]S fabric cylindrical shell;(b)[0°/45°/)45°/0°]fabric cylindrical shell.

C.Bisagni,P.Cordisco /Composite Structures 60(2003)391–402401

The results of the buckling tests demonstrate also that the shells are able to sustain load in the post-buckling ?eld without anydamage,even after several tests with di?erent combinations of axial and torsion loading.The experimental data are fundamental for the de-velopment and validation of analytical and numerical models.Furthermore,theycontribute to the determi-nation of the buckling loads of composite cylindrical shells and to the de?nition of applicable strength design criteria in the post-buckling ?eld,with the ?nal aim of a larger structure weight saving.

Acknowledgement

The constant advice and encouragement of Prof.Vittorio Giavotto is greatlyappreciated.

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搞笑幽默语句我想当皇帝 本文是关于搞笑幽默语句我想当皇帝,仅供参考,希望对您有所帮助,感谢阅读。 1:不是我不小心,而是我故意的!2:钞票不是万能的,有时还需要信用卡。 3:春天我把玉米埋在土里,到了秋天我就会收获很多玉米。春天我把老婆埋在土里,到了秋天我就会…被枪毙! 4:嗨!收到我的短信没有?还发什么呆,笑一下,好吗?你笑起来很好看。 5:静静的夜里,一个人偷偷想你,已成为我最隐秘的快乐。好几次梦中有你,我便贪恋着不想起床,放纵自己恣意占有你的似水柔情。 6:静静读你的信息,丝丝温情缓缓滋长,弥漫包容着我久久不去。谢谢你让我陪伴谢谢你给我柔柔关爱。 7:砍头算什么,脑袋掉了不过碗大的疤,18年后老子又是一条僵尸。 8:理想的世界=免费电话+免费上网。 9:每个人都应该热爱动物,因为它们很好吃。 10:每天...很想你...有你开心省心,对你真心痴心,为你担心忧心,也曾伤心痛心,不敢变心花心,不要多心疑心,写它我很费心,最怕你是无心。 11:明月几时有,把酒问青天…青天说:滚你妈的,我这么忙,哪有时间理你,自己看天气预报去。 12:某人宗旨:一个臭皮匠,弄死三个诸葛亮。 13:如果这一生我们爱不够,来世必能长久。生存还是死亡,是一个问题;上qq还是bbs,是一个问题;去追一个MM还是等一个MM来追,是一个问题,而且还是一个大问题! 14:天赐你一双翅膀,就应该被红烧。 15:我不会眼睁睁地看着你往火坑里跳,我会闭上眼睛的。 16:我买了一个一英寸的显示器,这样可以使我的错误看起来要小一些! 17:我想当皇帝,怕罗嗦;想当官,怕事多;想吃饭,怕刷锅;真想揍你一顿,怕惹祸。 18:我想未来我一定会天天陪你上市场。

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