Mobile and Rapidly Assembled Structures III, C.A. Brebbia ... · If concrete, however, is prestressed in compression, tensile stress due to the applied load has to compensate compression

Behaviour of inflated structures at medium

pressures

C. Wielgosz, E. Leflaive, J.C. Thomas

Laboratoire de Genie Civil de Nantes S* Nazaire,Nantes, France.

Abstract

Inflated structures present many interesting properties : they are light, easilyfolding and present reversible behaviour after failure (they come back to theirinitial position after unloading). The development of modern textile materialsenlarge the possibilities of these objects. Inflation cause tension prestressing inthe walls and in the yarns of the structures. This prestressing is proportional tothe pressure, and ensure important and quite surprising mechanical strength.Although inflated structures are not recent, no studies have been conducted onthis subject at medium or high pressure. The aim of the paper is to presentexperimental and numerical studies on inflated panels and tubes. They behave astensioned yarns or wires, but a yarn model gives unacceptable results at mediumand high pressure. A beam model cannot be used to calculate the deflectionbecause one cannot link the bending momentum to the curvature , but givescorrect results for the limit load. The only way to predict the deflection of aninflated structure is to use numerical modelling. The results obtained by thefinite element method are close to the experimental ones.

1 Introduction

This paper presents results from research conducted at University of Nantes(France) on the mechanics of inflated structures. Such structures are not new andresults are available when the pressure is lower than one bar ; however, theory oftheir behaviour is not presently available when the pressure equals several barsand, consequently, development of new types of structures making full use ofperformance characteristics of modern textile materials is impaired. The purposeof present research is to be able to calculate stresses and strains in inflated panelsand tubes when subjected to external forces ; more complex structures will then

Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1

42 Mobile and Rapidly Assembled Structures III

be studied and it will become possible to develop codes of practice for thedesign of inflatable structures and thus, to provide engineering guidance todesigners.

Experimental work has shown that inflated panels or tubes cannot be viewedas ordinary plates or beams, because their deformation pattern is quite different:they behave like yarns. Such objects must be calculated as structures made oftension prestressed walls and internal link members. The problem is twofold :modelize the structure and obtain adequate values of mechanical characteristicsof outer walls and inner members materials. Numerical modelling is done by thefinite element method with hypothesis of large displacements and with followingforces applied normally to the fabric. Cloths are replaced by orthotropicmembrane finite elements and the constitutive law is obtained from experimentaldata on polyester. Numerical results are close to experimental ones. Strengthabilities of these inflatable structures are given by local buckling conditions ofthe fabric.

2 Aim of the study

Before going into detail over the experimental and numerical researchdevelopments and commenting on their interesting and somewhat unexpectedresults, it would seem useful to explain briefly why inflated structures are ofinterest and why the study of their mechanics appears necessary.

Inflated structures may be considered from two different viewpoints. The firstoutlines their practical advantages, the awareness of which leading to variousapplications already widely known. The second concentrates on the capacities ofnew materials that have only recently become available and raises the question:how can we make full use of these capacities ? Polymers are very versatilematerials and have found innumerable applications ; among them polymericfibers and textiles, which both have exceptional properties. One answer to theabove question is that inflated structures are a means of multiplying thepossibilities of application of modern textile materials. These two approaches aredeveloped below.

Inflated structures have specific advantages that are more or less importantaccording to their use, such as : temporary buildings, space antennas, lifejackets, boats, medical instruments, pools, etc... It must be noted here thatpneumatic tires for vehicles, by far the most common inflated structures inpractical use, are not included in this study. They have to satisfy a number ofspecific requirements and have been extensively studied by tire manufacturers.For the purposes of this paper we simply have to note that the basic advantage ofpneumatics for vehicles is their relatively extensive shape adjustment propertiesnecessary for their function of interface between the road and the vehicle, therequired adaptation depending upon road or terrain roughness. We have thusidentified a first characteristic of inflated objects, which is their ability to adaptto and to resist local or dynamic forces through local shape adjustment withoutany permanent consequence.Consider another application such as an inflated vertical wall (acoustic or

visual protection for example). The extensive capacity for local shape adaptation


Mobile and Rapidly Assembled Structures III 43

results in the ability of the wall to lean over (bend down) under the effect, forinstance, of strong gusts of wind and to come back to its initial position once thegust is over. If such exceptional leaning is functionally acceptable, the safetycoefficient with respect to wind load may be much smaller than withconventional materials. This behaviour may be called "reversible failure",because even though the strength of the structure has been temporarilyovercome, the system subsequently returns to its initial status.

As far as temporary structures such as shelters for exhibitions or other eventsare concerned, it is well known that inflated constructions are convenient interms of ease of erection and dismantling, transport and storage (resulting fromtheir light weight and folding ability). This is particularly true when weight is acrucial factor, as for space components (antennas, reflecting panels,instrumentation shelters), but is also the case for more conventional uses wherelightweightedness often represents a significant edge over other materials.

A comparison has been made between the strength of steel, aluminium,wood and inflated beams. For the same length and the same bearing capacity (2meters between supports with a one ton load), the weight of the abovementioned beams are respectively 12, 6, 18 and 3 kilograms. It must be statedthat displacements under load are very different, the deflection of the inflatedbeam being much larger than that of the other materials. In a number ofsituations, however, this is not a drawback. If load bearing capacity is not acriterion, as for stage settings or the decoration of structures inside exhibitionhalls, incredibly light inflated architectures can be created.

In architectural and urban design terms, two specific additional features ofinflated structures are their daylight transmission ability and thermal isolationproperties. Taking into account the possibility of creating new shapes anddesigns and considering the growing need to control climatic conditions inspaces of ever larger size, inflated textile structures have a great future.

At the same time, it must be noted that these structures also have a large fieldof application in industry and technique. For example, scaffoldings, temporaryor permanent pylons or towers, water pipes or mains for fluid transport,cofferdams, bridges, etc..., may use inflated components either for their lightweight, shape adaptation capabilities, reversible failure or possibility of remotecontrol.

As stated above, the second viewpoint on inflated structures is to considermaterial properties. Inflation is a means of greatly enlarging the possibilities ofpolymer textile fiber use. Polymer fibers are high performance materials. It isproven that a polyester yarn, with the same length and weight, has a strengthwhich is more than twice that of a steel wire. Polymers exhibiting a sufficientlyhigh glass transition temperature (Tg), such as polyester or polyamide, are notsubject to creep up to fairly high stress conditions. At the same time resistance toenvironment is excellent.

However, yarn strength is high only under tension and, given that fibers havevery small diameters, yarn is perfectly flexible. Consequently it can be used onlywhen tensile strength is required and structures resisting compression, flexion ortorsion cannot be built with yarn. It is therefore apparent that these highperformance materials cannot be exploited for most practical needs.


44 Mobile and Rapidly Assembled Structures HI

There would appear to be a way to circumvent this situation, and that is touse prestressing. For yarn, tension prestressing, to be more exact. Inconstruction, prestressing is more widely known as compression prestressing forconcrete. As concrete has a low tensile strength, a beam, for example, exhibitslow flexion resistance. If concrete, however, is prestressed in compression,tensile stress due to the applied load has to compensate compression stress dueto prestressing before the material is physically put under tension. Prestressing iswidely used in concrete structures and has considerably widened its technicalusability.

For yarn, the situation is reversed. It is the compression strength that isinsufficient, being not only low, but actually nil. Here, tension prestressing maybe employed to artificially induce a compressive strength into yarn; this being sobecause a yarn under tension can sustain an external compression force as longas such compression force is lower than the prestressing tension. But how toinduce tension prestressing into yarn ?

The easiest way is through air pressure. Coating the textile fabric to make itairtight, manufacturing enclosed chambers, and inflating the obtained structuresgenerates tensile stresses in the fabric and makes it resistant to externalcompressive efforts. One may raise the question as to whether the above conceptis simply an abstract idea or whether it is really applicable and useful. As amatter of fact, the strength of inflated objects is due to nothing more than theprestressing of the envelope. This, for example, is the only way to explain whyone can sit down on an inflated armchair without sinking to the floor. Thequestion nonetheless remains: can significant resistance be obtained frominflated structures built with currently available fabrics ?

Take the example of a vertical cylinder under a vertical load. Using alOOOg/m* coated polyester yarn fabric, a cylinder 0.5m in diameter with aninflation pressure of 2 bars (200kPa) has a compressive strength near 4 tons. Thestrength of this cylinder is wholly due to the tension of the fabric walls, whichcan sustain compression as long as the compressive stress due to load does notovercome the tensile stress due to inflation pressure. This example shows thatvery strong structures can be built with polymer yarn fabrics. There is no otherway to produce a four ton resistant, collapsible column, weighing 1.5kg permeter of length.

The concept of tension prestressing also shows that for inflated structures,inflation pressure is not simply an auxiliary expedient to generate the shape ofthe structure, but that it is the actual source of its mechanical strength.Keeping in mind the above ideas, one can imagine the construction of strongand/or large structures using inflated coated textiles and relatively high inflationpressures. At this stage, the question is : can the behaviour of such products bereasonably predicted ?

A preliminary calculation shows that a bridge, made of parallel tubes of a20m span and weighing 35kg per meter, has a load limit of ten tons. But,considering how little is known about textile materials performance by engineersoutside the textile community, could anyone be convinced to drive a vehicleover such a bridge simply on the basis of this estimate ? If a 2 or 3 ton vehicle



was used, what would be the deflection of the bridge and the resulting slope toovercome, once the middle of the bridge has been reached?

Other examples could be presented. The development of inflated structuresrequires the understanding of their mechanics in order to be able to both designsuch structures intelligently and to be able to predict their behaviour withreasonable accuracy. Only then will this technology advance and designers beprovided with engineering guidance.

Actually, inflated structures are by no means recent. One could thereforethink that their mechanics has been understood for a long time. A firstunexpected result of the work presented in this paper is that the literature surveyundertaken in the early stages of the research unveiled very few publications onthe subject. Almost no experimental work has been performed and nocalculation model has been found (the case of pneumatic tires may again bementioned here: tire manufacturers have carried out extensive research, but thisdeals with a very specific type of structure and, at any rate, remains essentiallyconfidential).

Experimental and theoretical approaches have therefore been developeddealing with two types of inflated elements: panels and tubes.

3 Behaviour of inflated panels

The panels are made of two parallel coated woven fabrics connected by yarnsand a cross section of these panels is shown figure 1.

Figure 1 : Cross section of the panels

The yarns density is enough to ensure the flatness of the fabric structure. Itsbehaviour depends on the inflation pressure which leads the fabrics and theyarns to be prestressed and then to support local compression loads.The panels are simply supported "beams" loaded by a concentrated force. Theshapes of the deformed panel are shown figure 2 for two values of the inflationpressure (0.5 and 2 bars).



Figure 2 : Deformed shape of inflated panels

One can see that the bending shape is quasi linear between points of loadingand that light curvatures appear near loading areas (supports and loading point).This will be called local effects. The free ends of the panel remain almoststraight when the pressure is low, and the rotation angle with respect to thehorizontal is proportional to the applied pressure. The panel has therefore abehaviour similar to that of a tensioned yarn and by no means that of a beam.

The main results are relative to the limit load and the maximum values of thedeflection for a given load. The limit load of the panels can be easily calculatedwith limit analysis because the shape is similar to the yield mechanisms ofbeams [1] . One can prove that this limit load is proportional to the appliedpressure and to if (h is the height of the beam). Deflection values can't be easilyobtained; a yarn theory gives correct values of the deflection when the pressureis low (and because the free ends of the inflated panels remain straight), but verybad values when the pressure is greater than one bar. A beam theory isn'taccurate because of the less of curvature and also the fact that in a beam theorythe pressure can't be taken into account. Moreover it's impossible to relate thebending momentum to the curvature of the beam : the first is linear betweenpoints of loading and the second is zero ! We can't therefore define a flexuralrigidity.

The only way to obtain correct values on the deflection is to use numericalmodelling. The panels were studied with the finite element method, and with avery fine meshing near the loading point and the supports in order to reproducethe local effects. Computations were done with the hypothesis of largedisplacements and with following forces applied normally to the fabrics (to takeinto account the pressure). Fabrics are membranes in tension and the connectingyarns are non linear bars. The constitutive law is obtained from experimentaldata on polyester.



Figure 3 : theoretical and experimental values of the deflection

All computations have been done with Castem 2000 [2] . A comparison betweentheoretical and experimental values of the deflection is shown figure 3 for twopoints of the structure. Numerical results are very close to experimental ones.

Figure 4 : theoretical deformed shape of the panels at 0.5 bar

Figure 5 : theoretical deformed shape of the panels at 2 bar

The theoretical deformed shapes (figure 4 and 5) given for two values of thepressure (0.5 and 2 bar) show linear parts and also local curvatures near the



loading point and the support and prove that we are able to take into account thelocal effects.

4 Behaviour of inflated tubes

Inflated tubes are also simply supported "beams" loaded by a concentrated force.The inflation pressure will vary up to 5 bars. The bending shape of a tube withradius equals to 7.8 cm and a pressure of 2 bars is shown figure 6.

Figure 6 : deformed shape of an inflated tube

One can see that the bending shape is once again quasi linear between points ofloading. The free ends are here straight. Local great curvatures appear near theloading point. The tubes have also a tensioned yarn behaviour between points ofloading and not a beam behaviour. But once again, the yarn model givesvaluable results on the deflection when the pressure is low, but the results arevery bad for higher values of this pressure [3].

A beam model has been developed by Main [4] which has shown that inflatedtubes behave like beams ; this is true because their study has been done withtubes submitted to 0.3 and 0.7 bar. This beam model can't be used here, for thesame reasons that those given for the panels.

For the tubes, we can define the wrinkling load, when local wrinkles appearnear the loading point, and the limit load which appear when the beam collapses.It is interesting to see that this second load is twice the first, and that they areproportional to RA These results can be found in Comer [5]. We have shown [3]



that theoretical values of these loads are close to experimental results and areobtained within 20% error.

Here again, the only way to obtain correct results on the deflection is to solvethe problem by the finite element method. We have now to use shell elements,and if we want to obtain accurate results, we must use a very fine meshing toreproduce the local effects. The numerical modelling is therefore possible, but itleads to extremely long computation times. A comparison between theoreticaland experimental values of the deflection is given figure 7. Numerical results areclose to experimental ones.

40 50 80 100 130 150 200 250

load(N)

Figure 7 : theoretical and experimental values of the deflection

5 Conclusion

These first experimental and numerical results on the modelling of the behaviourof fabric panels and tubes show that it is now possible to compute this kind ofinflated structures and therefore to foresee the building of light, easilytransportable and extremely strong fabric structures. Their industrial applicationcan be very numerous: crossing and temporary structures, light roofs,.... Onehave now to work on the reliability of such structures in order to prove that theycan be used by industry.


gQ Mobile and Rapidly Assembled Structures III

References

[1] Wielgosz, C., Leflaive, E., Dube, J.F. Experimental study and numericalmodelling of inflated fabric panels, Computer Methods in Composite MaterialsVI S.V. Hoa, W. P. De Wilde, W. R. Blain, Eds, Computational MechanicsPublications, 1998, pp. 137-145.

[2] Guide d'utilisation de Castem 2000, version 96[3] Wielgosz, C., Leflaive, E., Dube, J.F., Thomas, J. C. "Behaviour of inflated

fabric beams at medium pressures", Proceedings of the Twelve InternationalConference on Composite Materials, I.C.C.M. 12, Paris, 1999, paper 334.

[4] Main, A., Peterson, S. W., Strauss, A. M., "Load - deflection behaviour of space -based inflatable fabric beams", A.I.A.A. Journal, 1994, Vol 7, N° 2, pp 225-238.

[5] Comer, R. L., Levy, S., "Deflections of an inflated circular cylindrical cantileverbeam", A.LA.A. Journal, 1963, Vol 1, N° 7, pp 1652-1655.


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Mobile and Rapidly Assembled Structures III, C.A. Brebbia ... · If concrete, however, is prestressed in compression, tensile stress due to the applied load has to compensate compression