Nonlinear Pressurization and Modal Analysis Procedure for Dynamic Modeling of Inflatable Structures

Kurt B. Srnalley*Clarkson University, Potsdam, New York 13699_ .andMichael L. Tinker tNASA Marshall Space Flight Center, Huntsville, Alabama 35812An introduction and set of guidelines for finite element dynamic modeling of nonrJgidized inflatable structur_is provided. A two-step approach is presented, involving 1) nonHncar static pressurization of the structure andupdating of the stiffness matrix and 2) ]incar normal modes analysis using the updated stiffness. Advantagesof this approach are that it provides physical realism in modeling of pressure _iffening, and it maintai_ theanalytical eanveniQce of a standard linear eigemolution once the stiffne_ hm been modified. Demonstration ofthe approach is accomplished through the creation and test verification of an inflated cylinder model using nlargecommercial finite dement code. Good frequency and mode shape eompm_isens are obtained with test data andprevious modeling efforts, verifying the accuracy of the technique. Problems enc_ntered in the npplication of theapproach, as well as their solutions, are discussed in detail.NomenclatureFz, F2 ffi element forces in nonlinear static solution, N/Co, ft = estimates of tangent stiffness, N/mmP, PI, P2 = applied loads, NRi, R2 = unbalanced loads, Nu = displacement, nunAPj, AP2 = applied load increinents, N• AUo, AUI = displacement prediction and correction, nunIntroductionNFLATED cylindrical sl_uts constructed of thin polymer filmshave considerable practical application and potential for use ascomponents of inflatable concentrator assemblies, antenna struc-tures, and space power systems. Because of their importance, it isof great interest to characterize the dynamic behavior of inflatablecylinders both experimentally and analytically. It is very helpful totake a building-block approach to modeling arid understanding in-flatable assemblies by first investigating in detail the behavior ofcomponents such as struts. The film material used for constructionof such cylinders (and the film-pressurized air interaction) is highlynonlinear, with modulus varying as a function of frequency, temper-ature, and level of excitation. Thus, the primary motivation of testsand analytical modeling efforts was to determine and understand theresponse of inflatable cylinders for different pressures and boundaryconditions. In this investigation, it is assumed that the structure hasnot yet been (or will not be) rigidized following its inflation.In recent years, inflatable structures have been the subject of re-newed interest for space applications such as communications an-tennas, solar thermal propulsion, and space solar power.t-s A majoradvantage of using inflatable structures in space is that they areextremely lightweight. Additional obvious advantages include on-orbit deployability and related volume savings in the launch .config-uration. A recent technology demonstrator flight for inflatable struc-tures was the inflatable antenna experiment that was deployed onReceived 18 June 2001; revision received 16 January2002; accepted forpublication 28 May 2002.Copies of this paper may be made for personal or internal use, on condi-tion that the copier pay the $10.00 per-copy fee to the Copyright ClearanceCenter, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code0022-4650/02 $10.00 in correspondence with the CCC.r_L_Atudent °f Mechenical Engineering"er_pace Technologist, Structural Dynamics and Loads Group/ED21.Associate Fellow AIAA.orbit from the Shuttle Orbiter. Although difficulty was encounteredin the inflation/deployment phase, the flight was successful overalland provided valuable experience in the use of such structures.S.2The Solar Orbital Transfer Vehicle 3 is a potential technologydemonstrator for solar thermal propulsion. The basic concept be-hind solar thermal propulsion is to utilize sunlight or solar energyas a means of heating a working fluid (propellant) to provide thrustat increased specific impulse. As described in Ref. 7, thrust is pro-duced by expanding the heated propellant through a nozzle. Nocombustion occurs, and the thrust level is low. For this reason, solarthermal propulsive systems are mainly applicable for orbital transfervehicles.Another technology, demonstration concept for solar thermalpropulsion is the Solar Thermal Upper Stage (STUS), which is de-scribed in Ref. 8. The engine system envisioned for the STUS isdesigned to utilize hydrogen propellant to produce a thrust level ofabout 8.9 N (2 lbf). Two inflatable parabolic collectors could be usedthat would bi_ rotated and gymballed for focusing sunlight into anabsorber cavity. The collectors would be inflated after separation ofthe upper stage from the launch vehicle.In Figs. 1 and 2, a prototype inflatable solar concentrator 9']° isshown that consists of a tutus/lens assembly supported by threestruts. This concentrator is constructed of Kapton W polyirnide film,with epoxy as the primary adhesive for joints. Adhesive tape wasalso utilized in this concentrator to attach the lens to the torus. TheFresnel lens of such a concentrator assembly would focus sunlightinto a collector near the fixed ends of the struts. Solar energy storedin the collector could be utilized to heat a propellant, as describedearlier, or for generation of electrical power. The inflatable struts areattached to a base plate or spacecraft by means of three cylindricalappendages. These hollow appendages also allow inflation of theconcentrator assembly through air hoses connected at each strut.It can be seen that inflatable cylindrical struts (Fig. 3) are criticalcomponents of structural assemblies for practical applications. Inview of their importance, structural dynamic and static behavior oftypical inflated film struts need to be investigated.The purpose of the current paper is to present a practical finiteelement approach, using a commercially available code, that willenable researchers to model the dynamics of nonrigidized inflat-able structuresaccurately.To date,relativelylittlework hasbeenpublishedondynamic modeling ofinflatables,andmost methodspresentedareeitherapproximateandlackingphysicalrealism,orverylaboriousintheirimplementation.First,thepaperwillgiveanoverviewofpreviousmodelingofinflatablecylinders.An intro-ductionisthengivenforthepresentmethod ofmodeling,which