Modeling of the impact on cylindrical composite shell as continuous patch loading

Transcription

1 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 8 Modeling of the ipct on cylindricl coposite shell s continuous ptch loding * Frzin Firouzbdi, rn yob, M.R.rjndi, Soheil Gohri, Nyeleh Deirr bstrct Due to gret properties, oposite terils re utilized in ny pplictions in dvnce nd ccurte industries such s erospce nd fuel vessel structures. In contrst with ll of the coposite dvntges, susceptibility of these terils to ipct dge bece jor concern recently. The i of this reserch is to study the dynic response of the coposite cylindricl shell subjected to ipct by odeling the ipct loding s continuous ptch loding on the contct surfce of cylinder. Rdil deflection of the cylinder s of the ost iportnt preter in dynic response hs been studied in this reserch using nlyticl pproch nd FEM ethod. In nlyticl pproch proper governing equtions re derived nd represented in Mtlb. In the second pproch we used finite eleent nlysis nd BQUS softwre to deterine the ccurcy of the results obtined nlyticlly. The present study concludes tht, ount of the rdil defortion of cylinder is t its highest vlue in contct point nd it will decrese grdully by getting fr wy fro ipct point on circuferentil pth on the cylinder surfce. Index Ters cylindricl oposite shell, Finite eleent nlysis, Ipct, Rdil Deflection L I. INTRODUTION OOKING for cheper, lighter nd stronger terils, coposites re ttrcting lots of interests []. Gret perfornce of these terils introduced the s one of the ost useful terils in ny ccurte nd dvnce industries such s fuel vessel structures, ircrft, sporting goods nd ny other fields. Vulnerbility of the coposite structure to the ipct loding bece jor proble for the reserchers nd industries []. Since this type of loding (ipct cretes contct surfce with high stress concentrtion which leds to * Frzin Firouzbdi, Fculty of Mechnicl Engineering, Universiti Teknology Mlysi, 80, (UTM, Skudi, Mlysi (firouzbdi.frzin@gil.co rn yob, Fculty of Mechnicl Engineering, Universiti Teknology Mlysi, 80, (UTM Skudi, Mlysi (rn@fk.ut.y Mohd Rez rjndi, Fculty of Mechnicl Engineering, Universiti Teknology Mlysi, 800, (UTM Skudi, Mlysi (Mr.rjndy@gil.co Soheil Gohri, Fculty of Mechnicl Engineering, Universiti Teknology Mlysi, 80, (UTM Skudi, Mlysi (soheil.gohri7@gil.co Nyeleh Deirr, Fculty of cheicl Engineering, Universiti Teknology Mlysi, 80, (UTM Skudi, Mlysi (deyrr@gil.co serious undistinguishble defects on the coposite structure, behvior of coposite structures under such loding is n iportnt cse for studying []. lthough experientl study consider s the best ethod for obtining the coprehensive, first hnd nd detiled results, due to difficulties nd expensiveness of the study few reserches [],[] hve been conducted to investigte the behvior of coposite terils subjected to ipct experientlly. ccording to the literture, ost of the reserches in this field del with the nlyticl pproch nd FEM ethod for their investigtion on the ipct otion on coposite structures []-[]. One of the erliest studies on ipct response of coposite terils ws done in 987 using proper D finite eleent ethod for clcultion the ount of the distributed stress nd strin in FRP coposite linte during trnsverse ipct []. Reserchers considered rectngulr plte with continuous fibers nd they eployed Hertzin contct low, Newrk ethod nd Newton Rphson ethod for their nlyticl pproch nd 8 node brick eleents for their FEM siultion []. To iprove the FEM results reserchers in 99 used prtil ixed D finite eleent ethod for their study [6]. n dvnced coordinte syste hs been used by experts in 998 to investigte the dynic response of the fully clped FRP linte coposite plte subjected to the low velocity [7]. They defined the generl coordinte syste using the displceent of the hitter nd the totl displceent of coposite [7]. Recently nother study hs been conducted to investigte the filures hppens in coposite due to ipct [8]. Reserchers used two fous criteri, criticl trix crcking nd delintion t the interfce, for their filure nlysis. They did the filure nlysis for two different types of ipct, (point loding nd line loding [8]. II. METHODOLOGY The i of this project is to investigte the dynic response of the cylindricl coposite shell subjected to ipct. For this purpose, two fous ethod (nlyticl nd FEM hve been eployed. In the first step, the ipct otion on the coposite cylinder will be odeled through the BQUS softwre. Since the properties of striker nd cylinder nd condition of ipct otion hve been chosen nd odeled exctly the se s [0], their results will be used s the benchrk to vlidte the obtined dt in BQUS softwre. In the second step, the contct force history which hs been chieved by BQUS nd vlidted by the published dt IJMME-IJENS June 0 IJENS

2 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 9 will be pplied s ptch loding on the coposite cylinder surfce nlyticlly. For this prt the proper Fourier series ter for the chieved ptch loding nd other essentil governing equtions will be derived nd represented in Mtlb to deterine the rdil deflection of the cylinder. By the end the obtined results for both ethods will be copred with ech other to deterine the ccurcy of the reserch results. Fig. shows schetic of ipct otion on cylinder nd it corresponding ptch loding odeling. Fig.. ( Schetic of ipct otion on cylinder. (b Ptch loding odel of ipct on cylinder III. FEM PPROH s entioned erlier, ipct otion on cylinder is odeled the se s [0] in BQUS softwre. Tble illustrtes the coposite cylinder nd striker s properties. fter odeling the cylinder nd ipctor the contct force history of ipct otion is recorded for contct point on cylinder. Furtherore, finl rdil deflection of coposite cylinder due to ipct is investigted nd plotted. TBLE MTERIL ND STRUTURL PROPERTY DT FOR THE OMPOSITE LMINTES ND IMPTOR [0] IV. NLYTIL PPROH oposite ylinder Rdius of ylinder 0. Length of ylinder 0. Thickness of ylinder. Fiber Orienttion [0/90/0/90] s E 8.0 GP E 9.00 GP G 7.0 GP G 7.0 GP G. GP υ 0. Density 0 Kg/ Ipctor Dieter of Ipctor Density 7800 Kg/ Initil Velocity /s Elsticity Modulus 00 GP The contct force history which hs been chieved by FEM ethod nd BQUS softwre nd vlidted with published dt in previous section will be used s the ptch loding which is cting on cylinder. To obtin the rdil deflection of cylinder subjected to the prbolic contct force history (ipct nlyticlly we will drive proper Fourier series ter to odel the ipct otion s ptch loding. ccording to the literture [],[6] the pplied force which is cting on the surfce of cylinder ( Px, P r, P θ nd their corresponding displceent (U,V,W cn be represented in double Fourier ters s the ptch loding. In our study we used the literture equtions nd nipulted the so tht they cn stisfy our probles boundry conditions. fter nipultio the double Fourier series of cting force cn be rewritten s P x n 0 0 n p.cos nθ.cosλ x ( P p sin nθ.sin λ x ( θ P r n 0 p cos n.sin λ x θ ( Using bove double Fourier serious for, the deflection in ll three direction (U,V,W cn express s follow W U V Where n 0 n 0 P P r, n 0 w u v cosnθ.sin λ x ( cosnθ.sin λ x ( sin nθ.sin λ x (6 λ π, β θ β nd L ( b x x ( b x (. π. b. os(. π. c. Sin(. β 8P n,. Sin n (7. π L L p Using the trix eqution nd rer s rule vlue of u,, v n,, w n, cn be clculted s ( n w ( n λ λ n. p 6 Den ( IJMME-IJENS June 0 IJENS

3 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 0 u v ( n λ λ n λ λ n. p λ Den ( n λ λ n λ n n. p Den (0 Where (9 contct force by 60 degree nd it reined in the se condition up to end. Den n λ λ n λ n λ n λ n λ n 6 6 n, λ 9λ 0λ n n 6 7 ( In the eqution bove is function of rry stiffness trix which is explined ore in ppendix the vlue of p n, for the rdil ptch loding is given by the eqution (7 tht is consider of length of cylindricl shell between two supports, of length (L, unifor thickness (t of wll nd in rdius (.. FEM Results V. RESULTS ND DISUSSION fter odeling the ipct otion on the BQUS softwre the contct force history hs been recorded nd is plotted in fig.. Furtherore, rdil deflection of the cylinder shell long the circuferentil direction is shown in fig.. Fig.. Rdil deflection of the coposite cylindricl shell t the point of ipct during ipct period (00 µ s B. FEM Results Vlidtion Since our ipct condition nd properties ws exctly the se s [0], s the benchrk nd to deterine the ccurcy of the odeling nd lso the results obtined fro FEM pproch we copred the obtined contct force history with the one which is published in [0]. Fig. shows the coprison between current contct force nd published one. Fig.. ontct force of the coposite cylindricl shell t the point of ipct during ipct period s you cn see in Fig., the xiu rdil deflection occurs exctly t the contct point of the coposite cylinder. By pssing fro contct point through the circuferentil pss this deflection decresed due to deduction of the contct force effect. This vlue reched to lost zero when we pssed the Fig.. oprison of contct force history in cylinder s contct point s you cn see in bove figures, the contct force history of the contct point on the cylinder which hs been investigted in this study through the FEM odeling hs gret siilrity with the literture results. This reseblnce of the dt cn show high ccurcy of the odeling. Furtherore, s it ws expected nd entioned in Literture [0] the ipct otion produced prbolic contct force which cn be seen in both IJMME-IJENS June 0 IJENS

4 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 of the plotted dt.. nlyticl Results Now the contct force history which ws obtined in FEM results nd vlidted with published dt is used s continuous ptch loding cting on the surfce of the cylinder in nlyticl pproch. In nother word, the obtined contct force history s the rdil pressure ( P r is pplied nd used on the ptch loding derived equtions to clculte the Fourier series ters nd corresponding deflectio For this purpose, the governing equtions (- re represented in Mtlb code to deterine the coponentil force ( P n, nd its corresponding coponentil nd finlly totl rdil deflectio Fig. illustrtes the rdil deflection of coposite cylinder subjected to continuous ptch loding for every (0 µ s pssing fro the loding tie. Fig. 6. Totl ount of rdil deflection on the coposite cylinder subjected to continuous prbolic ptch loding in whole ipct durtion D. oprison of Rdil Deflection of Ipct Motion nd ontinuous Ptch Loding Now to deterine the pplicbility of odeling the ipct loding s continuous ptch loding, we copred the rdil deflection of cylinder which hs been chieved for exct ipct odeling through FEM ethod with the one chieved through the continuous ptch loding. Fig.7 shows the rdil deflection which ws chieved through both odeling. Fig.. Increentl rdil deflection of coposite cylinder subjected to continuous ptch loding By sution of ll bove increentl vlues of rdil deflections the totl ount of rdil deflection will be chieved for the coposite cylinder in whole ipct durtio Fig.6 illustrtes the totl ount of rdil deflection for the coposite cylinder subjected to continuous prbolic ptch loding in whole ipct durtion Fig. 7. oprison of rdil deflection in ipcted coposite cylinder nd cylinder subjected to continuous ptch loding ccording to the coprison which is shown in bove figure, rdil deflection of the cylinder subjected to rel ipct loding hs gret siilrities with the one which is subjected IJMME-IJENS June 0 IJENS

5 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 to the ptch loding odel of ipct. s discussed erlier, in both results the xiu deflection occurred t the contct point of coposite cylinder nd by getting fr wy fro this criticl point the deflection decresed till it got to zero vlue. VI. ONLUSION The developed siple ethod for odeling the ipct on coposite cylindricl shell s continuous ptch loding cn be used in different type of ipct otions on coposite cylinder with different operting preters such s different initil velocity or ss of the striker. Furtherore, by nipulting the derived double Fourier series ters of deflection nd pplied forces dynic response of the other coposite structures subjected to ipct cn be investigted esily. Results of this reserch cn be used for filure nlysis of the ipcted coposite cylinder using the fous filure criterion such s Tsi-Wu, Tsi-Hill, strin energy nd xiu stress. D ( D D ( D ( ( ( D ( D D D 6 D D ( ( ( ( PPENDIX The reltionship between the constnt (,,... which 0 re used in equtions (8- nd the linte stiffness is D ( ( D ( D D ( D 6 ( D D ( D ( D 6 D 6 ( D 6 ( ( ( 6 D D D D ( D ( d 7 D D D D (6 (7 D (6 6 ( D D (7 ( 7 (8 8 D D (9 (0 9 0 D ( [ ( ] 8 (8 (9 9 D D (0 0 D ( [ ( ] ( D ( IJMME-IJENS June 0 IJENS

6 Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 D ( ( ( (6 [] Yng SH, Sun T. (98. Indenttion lw for coposite lintes. NS R-0. [] Tn TM, Sun T. (98. Use of stticl indenttion lws in the ipct nlysis of linted coposite pltes. Trns SME, Journl of pplied Mechnic :6. [] Tooth,. S., Bnks, W. M. nd Rh D. H.., (988 The specilly orthotropic GRP ulti-lyered cylindricl shell- theoreticl pproch for the generl loding cse, oposite Structures, (7 6 ( (8 7 8 ( D (9 9 D (0 ( 0 REFERENES [] J. N. Reody. Mechnic of linted coposite pltes nd shells. (nd ed.new York: R PRESS. (00. [] Debbrt hkrborty. (006. Delintion of linted fiber reinforced plstic coposite under ultiple cylindricl ipct. Journl of Mterils nd Desig [] F.ollobet, X. Llbin nd J. L. Ltillde. (998. Ipct behvior of linted coposites: physicl bsis for finite eleent nlysis. Journl of coposite science nd technology [] Zeuleyh sl Rzn Krkuzu, Buket Okut (00. The response of linted coposite pltes under low-velocity ipct loding. Journl of oposite Structures [] His Yung T. Wu nd Fu Kuo hng. (987. Trnsient dynic nlysis of linted coposite pltes subjected to trnsverse ipct. Journl of coputers & structures. -. [6].-L. Lio nd J.-S. Tsi. (99. Dynic nlysis of linted coposite pltes subjected to trnsverse ipct using prtil ixed - d finite eleent. Journl of coputers & structures. 00_799(9Eo6. [7] Lu chun nd K. Y. L. (998. Dynic response of fully-clped linted coposite pltes subjected to low-velocity ipct of ss. Interntionl journl of solids structures., pp [8] B.B. Mhnt, Debbrt hkrborty, njn Dutt. (00. ccurte prediction of delintion in FRP coposite lintes resulting fro trnsverse ipct. Journl of coposites science nd technology [9] K.S. Krishnurthy, P. Mhj R.K. Mittl. pretric study of the ipct response nd dge of linted cylindricl coposite shells. Journl of coposites science nd technology , (00. [0] K.S. Krishnurthy,P. Mhj R.K. Mittl. (00. Ipct response nd dge in linted coposite cylindricl shells. Journl of coposites structure [] Rhul, D. hkrborty,. Dutt. (00. Optiiztion of FRP coposites ginst ipct induced filure using islnd odel prllel genetic lgorith.. Journl of coposites science nd technology [] Edited by S.S.GILL, Interntionl series of onogrphs in echnicl engineering, the stress nlysis of pressure vessels nd pressure vessel coponents, volue IJMME-IJENS June 0 IJENS