STRESS STATES IN PLANE AND RIBBED CIRCULAR PLATES

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1 Pocdings in Manufactuing Systms, Volum 8, Issu 1, 013 ISSN STRESS STATES IN PLANE AND RIBBED CIRCULAR PLATES Camn T. POPA 1,*, Radu I. IATAN, Ciian I. MANESCU 3 1) Lctu, PhD, ng., Datmnt of Food Engining, Univsity Valahia, Tagovist, Romania ) Pof., PhD, ng., ng., Univsity Polithnica, Buchast, Romania 3) Assist., PhD, ng., Invntiv SRL, Ploisti, Romania Abstact: Cicula o annula lats and mostly ibbd stuctus hav multil utilizations in numous ngining domains: ocssing quimnts, naval, mtallugy, civil constuctions industis. Th ngining ability, imlmntd in actic, intoducd to duc th consuming of matials, but also th ngy consuming, altnativ solutions: matials fo lacmnt o igidifying using ibs. Th toic of this a taks into discussion th aticula cas of th stuctus with constuctiv othotoy. In this a is sntd th analysis of stsss stats fo a lan and fo a ibbd lat, to obsv th advantag of th igidifying. Th snc of th ibs lads to duc th consuming of mtallic matial. Th lats, of th sam dimnsions, a solicitd at 0.3 MPa ssu. Fo comaison, w usd th analytical, finit lmnts and ximntal mthods fo th lan lat and fo th ibbd lat, w usd th finit lmnts and ximntal mthods. In th tchnical litatu, fo th ibbd lat th is an analytical mthod fo calculating of th dfomation and stsss stats, only som aoximations fo aticula cass. Finally, as w inf fom th comaison of th sults, w obsv th advantag of th igidity of th lat. In this cas th valu of th stsss low about th tims. Closd valus a obtaind using th vaiants of calculus: analytical, finit lmnts and ximntal. Howv, w not that at th mbddd lats th maximum of stsss is locatd on th contou. Ky wods: lan cicula lat, cicula lat with ibs, stsss stats, numical mthod, ximntal mthod, analytical mthod. 1. INTRODUCTION 1 Th ngining ability, imlmntd in actic, intoducd to duc th consuming of matials, but also th ngy consuming, altnativ solutions: matials fo lacmnt o igidifying using ibs. Th toic of this a taks into discussion th aticula cas of th stuctus with constuctiv othotoy. Cicula o annula lats [1], of constant o vaiabl thicknss, connctd with igidity lmnts-by casting, bonding o wlding, a mt in numous ngining domains [ and 3]. Radial and/o annula ibs can b disosd symmtical o not, towad th middl sufac of th o lat. Th sachs had bn don to stablish th dislacmnts and stsss stats at lats igidifid with ibs can b goud in: a) Aoximat calculus mthods of th stsss and dislacmnts stats; b) Mthods which abas th study at bhaviou of th comound lmnts: lats and ibs, that a considd with diffnt laning ways; c) Calculus mthods that abas th stuctual othotoic at matial othotoic; * Cosonding autho: Univsity Valahia fom Tagovist, Tl.: ; Fax: ; addsss: camnoa001l@yahoo.com (C. Poa), _iatan@ yahoo.com (R. Iatan), cmanscu@yahoo.com (C. Manscu) d) Numical mthods [4 9]; ) Eximntal mthods [10]. In this a th following ascts a alizd: th dtmination of th stsss stats fo a lan lat, using th mthods: analytical, finit lmnts and ximntal; dtmination of th stsss stats fo a lan lat, using th mthods: analytical, finit lmnts and ximntal; th dtmination of th stsss stats fo a ibbd lat, using th mthods: finit lmnts and ximntal. Th analytical mthod fo th ibbd lat was analyzd in th scintific ublication only fo som aticula cass; comaison of th obtaind valus.. PLANE PLATE ANALYZE.1. Elmnts finit mthod W analyz th lan lat, having 3 hols, and gomtical chaactistics fom Fig. 1, using finit lmnt mthod. W consid that th lat is fixd on cicumfnc of th hols fo th scws, which clam this lat by th ximntal ciint [13]. Using th ogam, th lat was dividd in msh-ty ttahdon lmnts. Th lan lat with 3 hols w dividd in a total of lmnts and nods. W snt th calculus vaiant with finit lmnts, th lat stsss distibution at 0.3 MPa bing sntd in Fig.. Stsss fom Fig. 3 a obtaind at ssu of 0.3 MPa,

54 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / 53 58 Fig.. Stsss of th fixd lan lat, at ssu 0.3 MPa. Fig. 1. Gomtical chaactistics of th cicula lan lat.

2 54 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / Fig.. Stsss of th fixd lan lat, at ssu 0.3 MPa. Fig. 1. Gomtical chaactistics of th cicula lan lat. using a lan which asss though th cnts of two xactly contay hols, which a situatd btwn two nighbou hols. Stsss valus a givn in Tabl 1... Analytical mthod In this cas th lan lat is considd fixd on th lin of th cnts of th hols, at c = 85 mm. W us th lations (1,, and 3) fo th valuation of stsss on th cicumfnc of laning [11]: θ = ± 0,5 = ± 0,75 c c ; (1) ; () ( ) = + θ θ IV. (3) Th adial and cicumfntial stsss at a ctain adius a stablishd with th lations: 6 6 = ± M ; = ± M. (4) θ θ Th xssions of th bnding momnts a: M ( = 1,3 c 3,3 ); (5) 16 M = ( 1,3 c 1,9 ). (6) θ 16 wh:, θ, a adial, cicumfntial, quivalnt stsss at mdian sufac of th lat; unifom distibutd ssu on th sufac of th lat; c adius of th mbddd cicumfnc of th lat; Stsss [N/mm ], at 0.3 MPa ssu, fo th fixd lan lat [mm] [N/mm ] Tabl 1 Fig. 3. Stsss of th fixd lan lat, at 0.3 MPa ssu.

3 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / Tabl Stsss [N/mm], at 0.3 MPa ssu, fo th fixd lan lat, using finit lmnts and analytical mthods [N/mm ] [mm] Finit lmnts Analytical mthod mthod thicknss of th lat; M, M θ adial bnding momnt (acting in a diamtal lan of th lan cicula lat), sctivly annula bnding momnt; cunt adius. Th valu of quivalnt stss on th laning contou of th lat is m a x = N/mm, fo th ssu of 0.3 MPa. Th quivalnt stss at adius = 5 mm (bcaus at adius c = 85 mm in MEF lag incass of th stss a codd) is = 75 N/mm. As sn fom Tabl, wh th maximum valus of stsss stablishd by th two mthods fo calculating a ocssd, th valus of stsss fond by finit lmnt mthod a lativly clos to thos found by analytical mthod. In th cas of finit lmnt analysis, th lat had bn fixd on th intnal contou of th hols, and in th cas of analytical mthod, th lat had bn fixd in th continuous outlin gnatd of th cnt hols. If it is suosd at a valu of th ssu of 0.3 MPa, w obtain th maximal valu of stss on th fixd lin, lik in Tabl..3. Eximntal mthod In th ximntal cas, w tak into account th masuing of scific lina dfomations of th xtnal oints of th lat and calculus of th adial, cicumfntial and quivalnt stsss, in th sam conditions, using th stain gaugs [5]. Th comonnts of th ximntal stall a sntd in Fig. 4, wh: 1 vssl with th lats fo tsting; manomt; 3 banch; 4 ta (on duing th filling with wat of th ta and closd duing ssing); 5 bnd; 6 um gou; 7 funnl fo th filling of th installation Fig. 5. Th osition of th stain gaugs on th lan lat. To assss th stsss dvlod both on th u sufac of lan lat and on th lat with adial ibs, und th action of th ssu catd insid th ximntal vssl, two ndicula dictions w acctd to b ovidd in th coss tansducs, numbd with odd numbs (thos in th diction adial) and with vn numbs (tansducs ointd in cicumfntial diction). Th zons wh th stain gaugs a fixd on th lat a sntd in Fig. 5. Th usd stain gaugs a KM10, with R = 10 Ω sistanc and K =.04 ± % lastic constant. W masud th adial and cicumfntial dfomations valus, both at th incas and dcas of th ssu, obtaining th valus: 0.05; 0.1; 0.15; 0.; 0. 5; 0.3 MPa. W had bn alizd th ocssing of th ximntal data using mathmatical ogam, accting a lina vaiation, which dnds on aamt ssu. W obtaind th quivalnt stsss valus, which a sntd in th Tabl 3, using th fouth sistanc cition. On thi basis, th diagam in Fig. 6 was obtaind. Usd to calculat th adial, annula and quivalnt stsss a th lations: M M 5 6 Fig. 4. Schma of th ximntal stall. Fig. 6. Th vaiation of th quivalnt stsss which a calculatd on th basis of th fouth sistanc thoy.

56 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / 53 58 E = 1 ν ( ε + ν ε ); θ (7) E = ( ε + ν ); ε (8) θ θ 1 ν ( ) = +.

4 70.7 ( IV) Fig. 7. Gomtical chaactistics of th cicula ibbd lat. Fig. 8. Stsss of th fixd ibbd lat, at 0.3 MPa ssu. Stsss [N/mm ], at 0.

4 56 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / E = 1 ν ( ε + ν ε ); θ (7) E = ( ε + ν ); ε (8) θ θ 1 ν ( ) = +. IV θ θ (9) Tabl 3 Th valus of th quivalnt stsss at 0.3 MPa [MPa] [mm] [ ] N mm 0.3 MA MEF ME Obs v ( IV) ( IV) ( IV) ( IV) Fig. 7. Gomtical chaactistics of th cicula ibbd lat. Fig. 8. Stsss of th fixd ibbd lat, at 0.3 MPa ssu. Stsss [N/mm ], at 0.3 MPa ssu, fo th fixd lat with ibs [mm] = MPa Tabl

5 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / Fig. 9. Stsss of th fixd ibbd lat, at 0.3 MPa ssu. 3. RIBBED PLATE ANALYZE 3.1. Elmnts finit mthod W analyz th ibbd lat, having 3 hols, and gomtical chaactistics fom Fig. 7, using finit lmnt mthod. W consid that th lat is fixd on cicumfnc of th hols fo th scws, lik in th cas of th lan lat [13]. Also, w snt th calculus vaiant with finit lmnts. Th lat stsss distibution, at 0.3 MPa ssu is sntd in Fig. 8. Stsss fom Fig. 9 a obtaind at ssu 0.3 MPa, using a lan, which asss though th cnts of two xactly contay hols, which a situatd btwn two nighbou hols. Stsss valus a givn in Tabl Eximntal mthod In th ximntal cas, w tak into account th masuing of scific lina dfomations of th xtnal oints of th lat and calculus of th adial, cicumfntial and quivalnt stsss, in th sam conditions, lik in th cas of th lan lat, using th stain gaugs [13]. Th zons wh th stain gaugs a fixd on th lat a sntd in Fig. 10. W also usd th stain gaugs Fig. 10. Th osition of th stain gaugs on th ibbd lat. 150 Fig. 11. Th vaiation of th quivalnt stsss which a calculatd on th basis of th fouth sistanc thoy. Tabl 5 Th valus of th quivalnt stsss, which a thotical and ximntal calculatd (MA), (MEF) and (ME), at 0.3 MPa ssu, fo th ibbd lat [MPa] 0.3 [m m] [ N mm ] MA MEF ME Obs ( IV) ,4 ( IV) ( IV) ,7 ( IV) W obtaind th quivalnt stsss valus, which a sntd in th Tabl 5, using th fouth sistanc cition. Figu 11 divd fom ths sults. 4. CONCLUSIONS ME MEF W tak into account th dfomations, sctivly stsss valus, which a oducd in diffnt oints of th lat. As w inf fom th comaison of th sults, w obsv th advantag of th igidity of th lat. In

6 58 C. Poa, R. Iatan and C. Mănscu / Pocdings in Manufactuing Systms, Vol. 8, Iss. 1, 013 / this cas th valu of th stsss low about th tims. Closd valus a obtaind using th vaiants of calculus: analytical, finit lmnts and ximntal. Howv, w not that at th mbddd lats th maximum of stsss is locatd on th contou. REFERENCES [1] R.T. Iatan, C. Poa, Thmal stss in monolay lan and cicula lats vaiabl tmatu in th diction of adius, Rvista d Chimi, Vol. 60, Iss. 5, 009, [] V.V. Jinscu, Utilaj thnologic ntu industii d ocs (Tchnological quimnt fo ocss industis), Edit. Thnicǎ, Buchast, 1983, [3] A.l. Pavl, Elmnt d ingini mcanicǎ (Mchanical ngining lmnts), Edit. Didacticǎ şi Pdagogicǎ, Buchast, [4] M.H. Kaganovin, S.A. Faghidian, Y. Fajami, G.H. Faahi, Alication of homotoy-padé tchniqu in limit analysis of cicula lats und abitay otational symmtic loading using von-miss yild cition, Communications in Nonlina Scinc and Numical Simulation, Vol.15, Iss. 4, 010, [5] E. Mlski, Cicula lat analysis by finit diffncs. Engy aoach, Jounal of Engining Mchanics, 115 (6), 1989, [6] M. Kadkhodayan, An invstigation to th othotoic lats by using igula ctilina msh, Pocdings of th IASTED Intnational Confnc on Modlling, Idntification, and Contol, MIC, 007, [7] M. Mak, M. Kzysztof, Otimal dsign of sandwich ibbd flat baffl lats of a cicula cylindical tank, Intnational Jounal of Pssu Vssls and Piing, Vol. 8, Iss. 3, Mach 005, [8] N.J.H. Holoyd, J. Caigan, W. Hls, Y. Gao, Dsign otimization of flat-bottomd high ssu gas cylinds, Pocdings of th ninth intnational confnc on ssu vssl tchnology, Sydny, 000, [9] O. Zinkiwicz, Th finit lmnt mthod, Vol. 1, Mc Gaw-Hill, London, [10] C. Poa, Cctăi ivind solicităil lăcilo lan cicula ididizat cu nvui adial cu gomti vaiabilă (Rsachs gading cicula lan lat loading infocd by adial ibs with vaiabl gomty), PhD thsis, Buchast, 006. [11] G. Buzdugan, Rzistnţa matiallo (Stngth of matials), Edit. Thnică, Buchast, [1] M. Chung, L. Wnchang, Finit sti mthod combind with oth numical mthods fo th analysis of lats, Comuts and stuctus, Vol. 45, No. I, 199, [13] W.A. Hny, Elmnts of ximntal stss analysis, Pgamon Pss, London, [14] S.P. Thocais, Eximntal stss analysis, Tchnical Pss, Buchast, 1977.

ON THE PREFRACTURE ZONE MODEL IN ELASTIC BODY AT THE CRACK TIP ON THE INTERFACE OF MEDIA

8 Ulusla Aas lma onfans Bildiil itab 7 9 as m 7 Poocdings of 8th Intnational Factu Confnc 7 9 Novmb 7 Istanbul/TUREY ON THE PREFRACTURE ZONE MODEL IN ELASTIC BODY AT THE CRAC TIP ON THE INTERFACE OF MEDIA