Available online at ScienceDirect. Procedia Engineering 152 (2016 )

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1 Avilble online t ScienceDirect Procedi ngineering 152 (2016 ) Interntionl onference on Oil nd Gs ngineering, OG-2016 Simulting of the composite cylindricl shell of the pipe of the supply pipelines bsed on ANSYS pckge Tsyss V.G., Sergev M.Yu. * Omsk Stte Technicl University, 11, Mir Pr., Omsk , Russin Federtion Abstrct The simulting of the composite cylindricl shell of the ntivibrtion pipe bsed on study of stress-strin stte cused with excess pressure ws crried out. ontcting interction of the pipe shll wll in the re bordering the metl flnge ws conducted. The conducted finite element nlysis of the stress stte of the composite shell revels the most loded res which represent potentil dnger in terms of the destruction of rubber-cord rry Published The Authors. by lsevier Published Ltd. by This lsevier is n open Ltd. ccess rticle under the BY-N-ND license ( Peer-review under responsibility of the Omsk Stte Technicl University. Peer-review under responsibility of the Omsk Stte Technicl University Keywords: composite shell, pipe, pipeline, simulting, stress-strin stte, overpressure, orthotropic mteril, isotropic mteril, finite element model, the contct re, metl flnge. 1. Introduction At present ntivibrtion pipes get wide ppliction bsed on composite shells, which re designed for instlltion in pipelines of vrious systems s flexible joints in order to compenste deformtions rising in the pipelines nd to reduce vibrtions trnsmitted through them. The bsic requirements pplied to the pipes re lck of force trnsfer from the fluid pressure cting on the shnk bore of the pipe on the pipelines flnges or connected mechnisms. The im of this work is to simulte cylindricl composite shell of the ntivibrtion pipe bsed on study of stress-strin stte from the ction of internl overpressure. orresponding uthor. Tel.: ; -mil ddress: mjsergew@mil.ru Published by lsevier Ltd. This is n open ccess rticle under the BY-N-ND license ( Peer-review under responsibility of the Omsk Stte Technicl University doi: /j.proeng

2 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) Study subject The bsis for the cretion of thrustless ntivibrtion pipe is the theory of the equilibrium configurtion of grid shells [1]. Structurlly the pipe consists of two metllic flnges with which it is connected with the flnge of the supply pipelines or mechnisms. At the sme time specil profile of flnges llows, providing strong fstening to pipe fittings, to chieve the desired tightness of the shnk bore. The cylindricl composite shell of the pipe hs the following construction. There is seling rubber lyer on the inner prt of the shnk bore which protects the bering frme from the dmge ctions of the working environment nd ensures tightness of the pipe wll. Next there is even number of mutully intersecting lyers of the bering frme mde on the bsis of synthetic or metl cords. The bering frme is designed to resist efforts from the pressure of working environment of the pipe. The pipe hs protective rubber coting lyer outside, which mkes the bering frme sfe from mechnicl dmges nd ctions of ggressive components of the environment. There re rims t the end fces of the pipe tht re used for its fstening. There re metl rings of circulr cross-section inside the rims nd the lyers of the bering frme re wrpped round them. The rims re covered with rubber outside to provide bond strength of the covered lyers of the cord nd the tightness of the rims connections. When simulting the stress stte of the pipe one considers two types of the mteril: orthotropic - for simulting the rubber-cord (index "") nd isotropic for simulting rubber (index "c"). The initil dt for the study re given in the tble (Tble 1). Tble 1. The initil dt for the reserch. The tsk prmeters Inner pressure, МP 6.4 The initil dt for determining the specifictions of the rubber cord re elstic constnts of rubber nd cord included in its composition. Modules of elsticity nd Poisson's rtio ν, re the following: c = МP; nd ν с = for rubber; а = М; nd ν а = 0.34 for cord. oefficient of chrge m=0.65. We introduce the following nottions: Vlues Nominl dimeter, mm 250 The length of the exmined re, mm 1000 Mteril of the pipe shell rubber cord G ; 1 3 m(1 m) G1.652

3 334 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) mm 1m 1 G2.002 G m G Modulus of elsticity in the direction of reinforcement is defined in the following wy: 8 1 m 1m МP. Poisson's rtio is 12 m 1m Modulus of elsticity in isotropic plne is determined Sher modulus is P. 1m 1m G G12 G М 1m 1m G G Then М P МP G23 m m Methods The simulting ws performed with considering the pipe shell consisting of three res (Fig. 1). ; Fig. 1. Finite-element model of the cylinder shell of the pipe. Fig. 2. The rrngement of mteril lyes in the shell element.

4 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) Ares of section 1 hve fine grid for the simultion of the boundry disturbnce. Ares of section 2 hve corser grid, since deformtion would be permnent in this zone. As the finl element the membrne element hs been chosen intended for simulting of thin-wlled shells nd the shells of the middle thickness. Moreover, this element supports the shell configurtion tsk representing multilyer structure. This type of construction, hving smll thickness compred with its length is clculted in ANSYS softwre pckge [2]. One shows the configurtion of the cylindricl composite shell of the pipe on the figure (Fig. 2). The ngle of rottion of the lyer reltive to the shell rdius is shown on the left; the mteril identifiction number is on the right (1 is rubber cord, 2 is rubber). 4. Results nd discussion The loding of cylindricl shell off the pipe with inner pressure ws performed in stges to mximum of 6.4 MP. The next step of loding ws to pply to the upper level of the shell n xil displcement of 10 mm. The finl third step ws to pply to the upper level the dditionl sher displcement of 10 mm. The results of the first lod step (with inner pressure) re shown on the figure (Fig. 3). The results of the second step of loding (with dditionl pplied xil displcement of 10 mm) re given below (Fig. 4). Fig. 3. Stress-strin stte of the pipe shell fter the first lod step (on the right deformtion, on the left - stress). Fig. 4. Stress-strin stte of the pipe-shell fter the second lod step (on the right deformtion, on the left stress). The results of the third loding step of the pipe shell (with dditionl pplied sher to the upper level to 10 mm) re shown on the figure (Fig. 5). Distribution grphs of the min (S1, S2, S3) nd the equivlent stresses ccording to Mises with loding of the ntivibrtion pipe with internl pressure re shown on the figure (Fig. 6). Fig. 5. Stress-stin stte of the pipe shell fter the third lod step (on the right deformtion; on the left - stress). Fig. 6. The min nd equivqlent stresses of the ntivibrtion pipe.

5 336 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) Of gretest interest is the study of contct interction of the pipe shell wll in n re bordering with metl flnges (Fig 7.). As for the physicl constnts for the simulted mteril the following vlues re tken: А1 is metl, isotropic mteril Е х =2.111; ν =0.3; А2 is rubber, hyper elstic mteril with the following prmeters: Е х =56; ν=0.499; Mooney-Rivlin constnts С 1 =2.935; С 2 =1.775; А3 is orthotropic mteril with the following prmeters: Е х =7.178; Е у =Е z =2.297; ν xy =0.396; ν yz =ν xz =0.634; G xy =1.187; G yz =G xz = When prtitioned into finite elements in the contct re, the following elements were used [3,4]: ONTA172 is n element for simulting two-dimensionl problems with three-nodl contct elements (used to clculte the contct nd sliding between the trget (TARG169) nd deformble surfce; TARG169 is n element for simulting vrious two-dimensionl surfces connected with the surfces presented with the element ONTA172; HYPR74 is n element for simulting solid hyper elstic structures. This element is suitble to describe virtully incompressible rubber-like mterils with rbitrrily lrge displcements nd deformtions. The flt element hs two degrees of freedom t ech node (displcements long the xes X nd Y); PLAN82 is n element providing firly ccurte results for the mixed squre nd tringulr shpes with utomtic prtitioning nd cn stisfy the conditions of n irregulr grid without significnt loss in ccurcy. The contct elements re superimposed on the top of the solid-stte elements nd describe the boundry conditions between deformble bodies potentilly in contct. A digrm of the ppliction of the boundry conditions to the finite element model is shown on the figure (Fig. 8). Fig. 7. Finite-element model of the contct re of the pipe shll wll nd the metl flnge. Fig. 8. The scheme of pplying boundry conditions to the finiteelement model. The limittion of displcement is pplied long the X xis to the left side of the model s well s the limittion of displcement is pplied long the Y xis on the top of the elements simulting the metl flnge. The inner pressure is pplied to the shnk bore surfce of the elements simulting the pipe. The lods Fx=100H, Fy=10H re pplied to the right of the model in the nodes. The clcultion ws mde considering lrge deformtions [5]. This option is necessry to consider the incompressibility of rubber. A condition is imposed on the contct surfces tht they re in contct nd the contct is not disturbed. As result of the pplied lods nd limittions, the bove results re shown in the figures (Fig. 9) nd (Fig. 10). Fig. 9. The deformtion grph (nodl decision). Fig. 10. The stress grph (clculted s contunuous loop of nodl stresses).

6 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) As seen from the figures, the stresses in the upper nd lower lyer of the shell cord of the pipe re prcticlly identicl. Figure (Fig. 9) is developed with the help of progrm tht cretes continuous loop by verging the nodl stresses. The loop is determined with liner interpoltion within ech element using nodl vlues verged t the contct nodes of the elements. The figure (Fig. 10) shows the mp of the stresses developed using per element solutions with discontinuities t the boundries of the elements. The loop is determined with liner interpoltion within the element. The result verging in the nodes is not crried out becuse the loop is developed independently from the djcent elements. The results of the contct interction re shown in the figures (Fig. 11, 12, 13). The coefficient of friction between the outer contour of the rubber nd the metl flnge is ssumed to be 0.5, nd between the lyers of the cord, rubber lyers nd shell cord of the pipe it is equl to 0.9. The totl stress in the contct re shown on the figure (Fig. 12) differs from the contct (Fig. 11) s it considers the stresses rising in the lyers slip ginst ech other. Shering re of the lyers in the contct re of the shell nd the metllic flnge is shown in the figure (Fig. 13). Fig. 11. Pressure in the contct re. Fig. 12. Full stresses in the contct re. Fig. 13. Slip in the contct re. 5. onclusion Thus, s result of investigtions of stress-strin stte of nti-vibrtion pipe the following results were obtined: 1. The simultion of the composite cylindricl shell of the pipe from the internl pressure ws crried out. 2. Investigtions of contct interction of the pipe shell wll in the re djoining the metl flnge were completed. 3. Finite element nlysis ws conducted of the stress stte of the cylindricl shell of the pipe reveling the most loded re which represents potentil dnger in terms of the destruction of rubber-cord rry.

7 338 V.G. Tsyss nd M.Yu. Sergev / Procedi ngineering 152 ( 2016 ) References [1] V.L. Biedermn, Mechnics of thin-wlled structures, M., ngineering, [2] A.S. Krvchuk, lectronic Librry of mechnics nd physics. Lectures on ANSYS with exmples of problem solving in five prts, Minsk, [3] J.M. Berthelot. Mteriux composites. omportement mecnique et nlyse des structures, second ed., Msson, [4] K. Mitl Subodh, L.N. Murthy Pppu, K. Goldberg Robert, Micromechnics for prticulte reinforced composites, NASA TM, , [5] P.Areis, K. Mtous. Finite element formultion for modeling nonliner viscoelstic elstomers. omput. Methods Appl. Mech. ugrg, 197 (2008), pp