OPTIMIZATION OF PRESSURE HULLS OF COMPOSITE MATERIALS J.Franco a, A.Corz a*.a.peña b a Materal Composte Group. Unversdad de Cadz. Avda/Ramon Puyol s/n. 11205 Algecras (Span) *alcorz@caltech.es b Calpe Insttute of Technology. c/luna nº11d-11205 Algecras (Span) Keywords: Pressure hulls, composte materal, bucklng, optmzaton. Abstract The conventonal submarnes are made up of hgh strength steel, allowng them to go to great depths n spte of ther large dead weght. In the present work, the pressure hull of a submarne s consdered both n steel and n composte materal. Materals wth hgh strength to weght rato nclude carbon-fber compostes. Carbon-fber renforced polymer (CFRP) s a materal contanng carbon-fber on varous orentatons. A parametrc study s conducted to fnd the optmum thckness of ply by employng a Fnte Element Analyss Software package, ANSYS. Lnear bucklng analyss s used to predct the feasblty of CFRP submarne pressure hull at deep waters. From the studes conducted regardng the weght reducton, t s estmated that replacng steel by CFRP results saves up to 60% n the structural weght. 1. Introducton The development of submarnes n the future wll keep on requrng desgns to allow them to reach ncreasngly greater depths. Pressure hulls are one of the keys n the desgn of these vehcles, and ths paper s focused on ths matter, fgure 1. The problem s smlar to other felds, lke a vessel subjected to external pressure, whch has to resst that load wth the best possble desgn. Fgure 1. Example of pressure vessel n a submarne. The problem wth vessels under external pressure s ther falure due to shell nstablty, n other words, the bucklng. Maxmum external pressure to be consdered durng desgnng n vacuum operatng condtons n ndustral equpment s 1 Kg/cm 2, but n submarnes desgn the external pressure reaches very hgh values, n the order of 100 Kg/cm 2, dependng on the mmerson depth lmt. Also, the sze of these pressure vessels have attracted the nterest of 1
many researchers snce the ntal developments of these vehcles durng S. XIX, the forgotten I. Peral beng among them [1]. The problem wth bucklng of cylndrcal shells under external pressure has been studed by many authors from Bresse [2] and Tmoshenko [3], up to specalsts n ths feld as Ross [4]. The usage of composte materals to mprove the bucklng of pressure vessels has been largely revewed by Ross [5], Matha [6], and others, who have been dong a great nvestgaton effort for understandng both smulatons and laboratory tests results. The nterest of ths matter has a renewed mportance due to the ssues detected n the S-80 submarne, currently beng constructed at the Navanta shpyard and precsely named Isaac Peral. The weght of ths pressure shell has exceeded the expected, compromsng the buoyancy of the submarne. The report from the consultants has determned the only soluton for ths ssue s to enlarge the length of the submarne, fgure 2. Fgure 2. Submarne S.80 (Navanta). Hgh strength Steel In ths study, the usage of compostes n addton to FEM optmzaton technques are the tools we have proposed n order to assess f the mstakes that may happen n these elements may have a better soluton wth compostes nstead of steel, avodng costly modfcatons as n the case exposed. 2. Structural desgn of the pressure vessel The pressure hull s a pressure vessel that operates n deep waters. Ths hull type s desgned to wthstand safely the hydrostatc pressure at the operatonal deep. The desgn of these pressure vessels s made wth reduced thckness walls and rng stffeners joned to the walls, wth an arrangement as shown at fgure 3. Fgure 3. Arrangement of a Steel Submarne Hull 2
t 1 H 1 H 2 t L t 2 Fgure 4. Confguraton of Steel Submarne Hull 2.1. Steel model A Fnte Element Model has been developed wth the software ANSYS [7], accordng to the followng ntal parameters, table 1. Ls N r R t l t 1 t 2 H 1 H 2 P_d Weght Volume 10 20 3 0.1 0.08 0.1 0.3 0.3 25E+5 293,202 283 Table 1. Confguraton of Steel Submarne Hull model In ths table, N r s the number of stffeners rngs, and P_d s the desgn pressure, n N/m 2, consderng a safety coeffcent, η=2, over the lnear bucklng pressure. The remanng parameters are shown at fgures 3 and 4, n meters. The elastc module of the steel s E = 2.1E11 N/m 2 and a Posson s rato ν = 0.3. A Fnte Element Model has been developed wth these parameters usng the element Shell181 [7]. A vew of the model s shown n fgure 5. Fgure 5. FEM Steel Submarne Hull 3
2.2. Optmzaton of the steel model The optmzaton problem s presented as a classc gradent method [8], accordng to the formula (1) Mnmze : subject to : Vol = V ( h, t, t ) p σ mx mx h t t ll l l p σ t l cr h cr t l h t t h lh h = 1,2 = 1,2 (1) Where we have appled the restrctons of bucklng and the Von Mses stress. The desgn varables between ts upper and lower lmts have also been lmted. The evoluton durng the materal volume optmzaton n ths secton of the shell s shown at fgure 6, and multplyng t by the densty of steel, 7850 Kg/m 3, the optmzed total weght s obtaned. Tvol 4,00E+01 3,50E+01 3,00E+01 2,50E+01 2,00E+01 1,50E+01 1,00E+01 5,00E+00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Set Number Fgure 6. Total volume optmzed for Steel materal The optmzaton fnal result for 250 m of operatonal deep s shown at table 2: t L t 1 t 2 H_1 H_2 Weght 0.3E-1 0.25E-1 0.1E-1 0.16 0.16 60,445 Table 2. Confguraton of Steel Submarne Hull model The frst bucklng form obtaned s composed of three lobes, as shown at fgure 7. 4
Fgure 7. Bucklng form The followng table s obtaned by repeatng the calculatons wth ncreasngly larger operatng depths of 500, 1000 and 2000 meters of water column: 2.3. Composte model Depth 250 500 750 1000 1250 1500 Weght 60,445 105,033 145,225 188,400 238,326 289,665 Table 3. Depth and weght for Steel Submarne Hull model Now the composte model s revewed, wth a smlar geometry to the steel model, and a lamnate stackng for the pressure vessel shell [90º/0º/-45º/+45º/+45º/-45º/0º/90º] as shown at fgure 8. Fgure 8. Lamnated pressure hull desgned for operatonal depth of 250 m The element Shell181 has been used, and the ntal parameters for ths case are 5
t 1 t 2 t 3 t 4 H_1 H_2 Weght 0.01 0.01 0.01 0.01 0.3 0.3 47,700 Table 4. Confguraton of Composte Submarne Hull model The elastc constants of CFRP, that s the materal used for the layers of the lamnate, are n table 5: Ex Ey Ez Gxy Gxz Gyz xy xz yz dens 120.7E9 8.5E9 8.5E9 3.4E9 2.7E9 2.7E9 0.253 0.421 0.421 1,500 Table 5. Materal propertes of CFRP used The stress parameters for obtanng the Tsa-Wu crteron are n table 6: Xten Yten Zten XY XZ YZ 120.7E9 8.5E9 8.5E9 3.4E9 2.7E9 2.7E9 2.4. Optmzaton of the composte model Table 6. Falure propertes of CFRP used The optmzaton problem s presented as a classc gradent method [8], accordng to the formula (2), where we have appled the restrctons of bucklng, and the Tsa-Wu crteron. The desgn varables between ts upper and lower lmts have also been lmted. Mnmze : Vol = V ( h, t ) subject to : ITW 1 h p l t l mx p h t cr h t h h = 1,2 = 1,4 (2) Where t are the thcknesses of the layers, h are the dmensons of the rng stffeners, as n the case of the steel model, and ITW s the Tsa-Wu ndex. Tvol 3,30E+01 3,10E+01 2,90E+01 2,70E+01 2,50E+01 2,30E+01 2,10E+01 1,90E+01 1,70E+01 1,50E+01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Set Number Fgure 9. Total volume optmzed for composte materal 6
The evoluton durng the materal volume optmzaton n ths case s shown at fgure 9. t 1 t 2 t 3 t 4 H_1 H_2 Weght 0.50E-2 0.58E-2 0.51E-2 0.51E-2 0.29 0.26 24,800 Table 7. Confguraton of Composte Submarne Hull model The followng table s obtaned by repeatng the calculatons wth ncreasngly larger operatng depths of 500, 1000 and 2000 meters of water column: Depth 250 500 750 1000 1250 1500 Weght 24,800 34,100 49,600 68,200 85,250 105,400 Table 8. Depth and weght for Composte Submarne Hull model 3. Results and conclusons. The dsplacement s the same n both cases and s only a functon of the length L and dameter D. Thus, consderng a densty of 1000 kg/m3 water, we obtan: 2 πd Dspl. = Lρ = 282.744 Kg 4 Dspl. = 282.744 Kg /10m (3) The quotent between the weght and the dsplacement, results n a rato ndcatng the percentage dedcated to buoyancy the hull, and to the payload allowance. If we compare the effect of usng steel and the effect of usng composte materal, two desgn curves are obtaned, as shown at fgure 10 Fgure 10. (DW/Desp) Depth Rato 7
If we consder the partcular case of the S-80, for an operatng depth of 500 m, the dfference of composte pressure hull versus of steel s: Δ W = 5*(105,033 34,100) = 5*70,933 = 354,665 Kg 355 Tn (4) The submarnes are desgned to operate near ths depth, 400 m to 600 m. As you can see n fgure 11, the dfference n payload n ths depth s more than 60%. As a result of these mportant dfferences between the pressure hull made n steel, and pressure hull n composte, we may conclude: -The use of Composte allows a great ncrease of the payload. -The depth that can be acheved wth the pressure hull made of composte s hgher than the one acheved wth the steel hull. -An extra margn for buoyancy reserve s allowed n the presence of desgn errors -The resstance to corroson of pressure hull made of composte s larger than for steel n Marne envronment. -The fabrcaton process of these elements has a precson much larger than the smlar task for the steel, n whch the dstortons at the weldng process are very dffcult to control. References [1] A.R. Rodrguez Gonzalez. Hstora de una frustracón. Grafte Edcones. 2004. [2] M. Bresse. Cours de Mecanque Applquee. Pars. 1866 [3] Tmoshenko. Theory of Elastc Stablty. McGraw-Hll. New York. 1936 [4] Carl T.F. Ross. Pressure Vessels: External Pressure Technology (Woodhead Publshng n Materals). Cambrdge. 2011 [5] Paul T. Smth, Carl T.F. Ross and Andrew P.F.Lttle. Collapse of Composte Tubes under Unform External Hydrostatc Pressure. Journal of Physcs: Conference Seres 181. IOP Publshng. 2009 [6] A. Matha, S. Subramanan, G. John. Analytcal nvestgatons of carbon fber renforced polymer stffened cylndrcal submarne hull. Internatonal Journal of Engneerng Scence and Technology. [7] ANSYS Manual. Release 14.5. Documentaton for ANSYS. 2013 [8] G.N. Vanderplaats. Numercal optmsaton technques for engneerng desgn. Ed. MacGraw-Hll 1984 8