Abstract 1. INTRODUCTION

Transcription

1 TEAM 2017,Sep.25-28,2017,Osaka,Japan Valdaton of Practcal Approaches for the Strength Evaluaton of Hgh-speed Catamaran under Beam and Quarterng Seas Po-Ka LIAO *1, Yann QUÉMÉNER 1, Yng-Chung SYU 1, Kuan-Chen CHEN 1, Ya-Jung LEE 2 1) R/D Secton, Research Department, CR Classfcaton Socety 2) Department of Engneerng Scence and Ocean Engneerng, Natonal Tawan Unversty *e-mal: pklao@crclass.org Abstract The structural scantlng of Hgh Speed Craft (HSC) of length less than 50 m s mostly drven by the local scantlng requrements related to the desgn pressure and acceleraton. However, for the case of catamaran-type HSC such as the two passenger shps consdered n ths study, the Class rules requre also to assess the Cross-deck structural strength under Beam and Quarterng Seas. For that purpose, ths study employed smplfed approaches whch the most common consst n (1) a Cross-deck grder undergong the Beam Sea nduced transverse bendng moment and (2) a system of longtudnal and transverse Fnte Elements beams to reproduce the nteracton between the Floats and the Cross-deck subjected to the Quarterng Sea nduced ptch connecton moment. Ths study valdated then the accuracy of the stresses predcted by the smplfed methods by comparson wth detaled fnte element analyss results. However, lmtatons were also dentfed regardng the effect of the stffness of the Float to Cross-deck connecton, the consderaton of the longtudnal component of stress and the superstructure addtonal strength. Ths study also conducted Seakeepng analyses for comparson wth the rules desgn vertcal acceleraton. Keyword: Catamaran, Strength, Beam & Quarterng Sea. 1. INTRODUCTION The structural scantlng of Hgh Speed Craft (HSC) of length less than 50 m s mostly drven by the local scantlng requrements related to the desgn pressure and acceleraton. However, for the case of catamaran-type HSC, the rules requre also to assess the Cross-deck structural strength under Beam and Quarterng Seas. The most precse approach conssts n a detaled fnte element analyss entalng a full shp FE model that at the least must reproduce the prmary support members of the shp structure usng Shell elements, whereas the stffeners can be represented through Beam elements. However, such an approach s very tme consumng n terms of modelng. Smplfed approaches are often proposed by Class that neglects the superstructure effect (e.g. passenger shps) and the longtudnal component of stress n the Cross-deck. Those methods are very practcal especally for the early stage of desgn, but they mght not be accurate enough for fnal strength verfcaton. The detaled FE model of the shp mght thus stll need to be produced upon Class request, but the extent of requred structural changes and consecutve remodelng wll be lmted snce the structure wll already conform to the frst prncples of the structural response as ensured by the smplfed approaches, and the FE modelng process would thus be optmzed. Ths study evaluated the Cross-deck structural strength of two passenger hgh-speed catamarans hereafter referred as HSC1 and HSC2. Tables 1 and 2 lst the man partculars and the Cross deck structural arrangement of the two nvestgated shps. In a frst secton, rules loads are calculated and Seakeepng analyses are conducted for comparson wth the rules desgn vertcal acceleraton. The second secton compares the Cross-deck stresses obtaned by the smplfed methods to those produced by detaled fnte element analyses. The thrd secton dscusses on the smplfed approaches lmtatons and possble ameloratons. Table 1. Shps man partculars. Table 2. Desgn loads and Cross-deck structural arrangement. HSC1 HSC2 HSC1 HSC2 Length at the water lne, Lwl 39.5 m 31.6 m Rules transverse bendng moment, Mbt 4482 kn.m 1750 kn.m Breadth, B 10.0 m 8.2 m Rules ptch connecton moment, Mtt kn.m 6522 kn.m Float wdth amdshp, BW 2.6 m 2.5 m Cross-deck heght, HCD 0.8 m 0.3 m Depth, D 3.4 m 2.9 m Cross deck wdth between Floats, S 3.4 m 2.7 m Draft amdshp, T 1.3 m 1.3 m Transverse frame spacng (avg.), w 1.0 m 0.8 m Servce speed, Vs 29.2 knt 15.0 knt Strength deck thckness, ts-deck 2 mm 6 mm Desgn vertcal acceleraton, ac g's g's Wet deck thckness, tw-deck 6 mm 6 mm g

2 2. RULES LOADS AND SEAKEEPING COMPUTATIONS It s known that shp moton n waves s one of the major source of structural loads, especally vertcal acceleratons are drectly related to shps loads for hgh speed crafts. Typcally there are two approaches to determne acceleratons: drect numercal smulaton, shown n Fgure 1, and rule calculaton. The former s based on potental flow theory, whle the latter n the present study s accordng to CR Rules [1]. The drect numercal method usually has hgher accuracy as consderng full hull geometry descrptons, but suffers theoretcal lmtatons, whch are 3D panel method by usng zero-forward speed Green functon n frequency doman, wth encounter-frequency correcton for forward speed effect. The soluton s lnearzed about mean water level and only calculates submerged hull surface under ths level. It should be recognzed that solutons become unrealstc as the wave heght ncreasng or too hgh forward speeds. Fgure 2 shows seakeepng results of HSC1, vertcal acceleraton at center of gravty at dfferent shp speeds were obtaned by the two aforementoned methods. The red lne was evaluated by drect numercal smulaton and the blue one s by rule calculaton. Sea condton was set at 2 m sgnfcant wave heght condton to meet the lnear wave assumpton. The two methods match each other at low speed, but obvously the drect smulaton sgnfcantly underpredcted than rule values and s ncapable n the hgh speed range. As a consequence, t s recommended and conducted to apply rule calculaton to determne vertcal acceleratons and hence shp loads for hgh speed crafts. Fg.1 Illustraton of shp hydrodynamc pressure by usng drect numercal method. Fg.2 Vertcal acceleraton at center of gravty at dfferent shp speeds. 3. STRUCTURAL RESPONSE EVALUATION For both target shps, HSC1 and HSC2, the structural response evaluaton was conducted usng smplfed approaches and, for valdaton, was also produced by detaled Fnte Element Analyses (FEA). Detaled Fnte Element Analyses Both shp FE models were made of Shell elements wth a global mesh sze of one tenth of frame spacng one half of stffener spacng for HSC1, and of one half of frame spacng one half of stffener spacng for HSC2. It worth beng noted that the coarser mesh adopted for HSC2 s suffcent to evaluate the global strength of the shp, whereas the fner mesh used for HSC1 enables also to evaluate the local yeldng n way of stress concentraton. The alumnum materal was set as sotropc lnear wth a Young's modulus of N/mm 2 and a Posson rato of Fgure 3 and Table 3 present the boundary condtons appled for the Beam and Quarterng Seas load cases. For the Beam Sea, the rules desgn transverse bendng moment M bt n the Cross-deck was reproduced by applyng nodal forces at the md-draft n way of the transverse web frames. Fgure 4 shows the load applcaton on the FE model wth the horzontal nodal forces taken Y-negatve for the starboard float and Y-postve for the port-sde float. The unform horzontal lne pressure n force per unt length was calculated usng Eq.(1). q M /( z T 2 ) L (1) y bt NA wl where z NA s the vertcal coordnate of the Cross-deck's neutral axs. For the Quarterng Sea, the rules desgn ptch connecton moment M tt n the Cross-deck was reproduced by applyng nodal forces at the keel lne n way of the transverse web frames. Fgure 5 shows the load applcaton on the FE model wth the nodal forces taken upwards for the aft half of starboard float and the fore half of port-sde float, and downwards for the fore half of starboard float and the aft half of port-sde float. The unform lne pressure n force per unt length was calculated usng Eq.(2). 2 qz 4M tt / Lwl (2) For both load cases, the appled forces were balanced, so that the reacton forces at the boundary condtons were neglgble. Fgures 6 and 7 show the FE results of HSC1 under both load cases.

3 Table 3. Boundary condton settngs. Beam Sea # UX UY UZ RX RY RZ CLA CLB SB PS Quarterng Sea # UX UY UZ RX RY RZ CLA CLB SB PS Fg.3 Boundary condtons locaton. Fg.4 Beam Sea load applcaton. Fg.5 Quarterng Sea load applcaton. Fg.6 Detaled FEA results for HSC1 under Beam Sea. Fg.7 Detaled FEA results for HSC1 under Quarterng Sea. Smplfed 'Cross-deck grder' approach for Beam Sea Ths approach s commonly used n CR Rules [1] to evaluate the bendng stress on the strength deck and the wet deck, whle neglectng the superstructure effect. Ths approach consders that the transverse bendng dstrbuton s constant though the Cross-deck wdth and that the Cross-deck grder secton s symmetrc. Ths last assumpton s vald for Cross-deck arrangement such as those of HSC1 and HSC2 where only the deck thckness slghtly changes along the shp. However, for catamaran's Cross-deck arrangement that sgnfcantly dffers along the shp (e.g. hgher strength deck at the bow), the non neglgble asymmetry of the secton would result n the rotaton of the secton's prncpal axes that, n vew of the structure, would decompose the external vertcal bendng moment nto a vertcal and a horzontal nternal bendng component as shown n Fgure 8 For HSC1 and HSC2, the bendng stress at the vertcal coordnate z of the strength deck and wet deck amdshp was calculated usng Eq.(3) derved from the Beam theory. yy Mbt zna z I yy (3) where z NA s the Cross-deck neutral axs vertcal coordnate from the base lne, z s the vertcal coordnate of the pont on the structure at whch the stress s calculated and I yy s the vertcal sectonal moment nerta. Fgures 11 and 15 present the transverse bendng results of HSC1 and HSC2 respectvely. It can be observed that the transverse stress dstrbuton along the Cross-deck was fluctuatng to values close to those obtaned by the Cross-deck grder approach. The stress peaks corresponded to the transverse bulkheads locaton that are stffer area n the Floats and thus that transmt more transverse bendng loads to the Cross-deck. For HSC1, the fluctuatons were very large wth stresses at the bulkheads that were approxmately two tmes and three tmes hgher than stresses between bulkheads for the strength deck and the wet deck respectvely. Table 4 presents the transverse stresses averaged over the length of the Cross-deck produced by detaled FEA and those obtaned by the Cross-deck grder approach that cannot reproduce the stress concentratons at the bulkhead. It can be observed that the averaged stresses were relatvely close to the Cross-deck grders values, except for the HSC1's wet deck whch the stress was sgnfcantly (-

4 38%) underestmated by the Cross-deck grder approach. To determne the cause of those dscrepances, the FE model secton propertes were compared to those calculated for the Cross-deck grder method, the results are lsted n the Table 4. The FE model cross secton area of the Cross-deck was drectly read-out from the FE model, whle ts neutral axs and moment of nerta were deduced from the FE stress at the strength deck (z strength deck) and on the wet deck (z wet deck) usng the Eq.(4) and (5) that are derved from Eq.(3). wet deck zstrength deck strength deck zwet deck zna (4) I yy wet deck strength deck strength deck M bt zna zstrength deck (5) It appeared that the secton areas produced by both methods were smlar for both shps. However, the neutral axs vertcal coordnate z NA and the sectonal vertcal moment of nerta I yy devated between both approaches. Especally, HSC1's moment of nerta produced by the Cross-deck grder approach was 88% of that derved from the detaled FEA results. Therefore, the Cross-deck grder approach can slghtly overestmate the transverse bendng strength of the structure. Fg.8 Asymmetrc Cross-deck grder. Table 4. Comparson between detaled FEA and Cross-deck grder methods. HSC1 HSC2 Cross-deck FEA grder a CDgr./ Cross-deck FEA FEA grder a CDgr./ FEA σstrength deck N/mm % % σwet deck N/mm % % zstrength deck mm 3400 b b - zwet deck mm 2618 b b - A mm % % zna mm % % Iyy mm % % a) FEA stresses are averaged over the Cross-deck length b) Decks coordnate from base lne at the mdshp Smplfed approach for Quarterng Sea assumng a Cross-deck structure connected to rgd Floats Ths smplfed approach s proposed by Class [2] for sngle platng transversely framed Cross-deck arrangement. However, ths study evaluated ts valdty for the double platng transversely framed Cross-deck arrangement of HSC1 and HSC2. Ths smplfed approach assumes that the Cross-deck structure s connected to rgd Floats, whch s smlar to consder that the Cross-deck structure s very soft compare to the Float stffness. Ths assumpton leads to a lnear dstrbuton of the Cross-deck vertcal deformaton along the Float connecton that orgnates from the center of the stffnesses r of the Cross-deck structure located at the abscssa a r defned usng Eq.(6) and that propagates wth a slope ω calculated usng Eq.(8). Those equatons are formulated for a Cross-deck structural modelng that conssts n ndependent parallel transverse beams located at each transverse frame and for whch a typcal cross-secton s shown n Fgure 9. r x a r (6) r wth the beam bendng stffness expresson assumng restraned beam ends deformaton, 12E I yy, r 3 S (7) where x s the X-coordnate of the beam, E s the Young's modulus, I yy, s the beam sectonal vertcal moment of nerta and S s the beam span or the Cross-deck wdth taken between the nner hull of each float. M tt 2 r d (8) wth d x ar (9) Eventually, the beams sectonal shear force and vertcal bendng moment at the Float connecton can be calculated usng Eq.(10) and Eq.(11), respectvely. Ths approach s thus very practcal snce the bendng and shear stress at the end of each beam can be analytcally determned.

5 F d r (10) M F S 2 (11) Fgures 12 to 14 and 16 to 18 present the Cross-deck torson results of HSC1 and HSC2 respectvely. It can be observed that except for the Cross-deck ends, the smplfed approach, referred as 'rgd Float' n the Fgures, resulted n transverse and shear stress values greater than the detaled FEA results for HSC1, whereas the stress predctons were very smlar by both approaches for HSC2. At the Cross-deck ends, the stresses were often largely underestmated by ths smplfed method. In addton, especally for HSC1, the smplfed approach sgnfcantly underpredcted the stresses n way of the transverse bulkheads. Fnally, t worth beng noted that ths approach gnores the axal torson of the beam nduced by the vertcal deflecton at the Float connecton whereas Zheng et al (2010) [3] hghlghted that ths effect on the stress mght not be neglgble especally at the Cross-deck ends. Smplfed approach for Quarterng Sea assumng a Cross-deck structure connected to deformable Floats Ths smplfed approach s proposed by EEIG UNITAS [4] for catamaran and t ncludes the Float deformaton effect. Compared to the smplfed method assumng rgd Floats, ths method s a bt more complex to conduct snce t entals the use of FEA, but the FE model remans very smple to buld as shown n Fgure 10. The model conssts n a system of transverse FE Cross-deck beams wth span and sectonal propertes dentcal to the rgd Float approach, that are attached at one end to the longtudnal FE Float beam model whle the other end s set as fxed. Two opposte concentrated nodal forces, as calculated by Eq.(12), are appled at each end of the Float beam to reproduce the ptch connecton moment. The Float beam deformaton are then mposed to the Cross-deck beams usng rgd connectons, whch would nduce a more realstc load dstrbuton of the ptch connecton moment M tt through the Cross-deck. (12) F M tt L wl Fg.9 Cross-deck connected to rgd Floats. Fg.10 Cross-deck connected to a deformable Float. Fgures 12 to 14 and 16 to 18 present the Cross-deck torson results of HSC1 and HSC2 respectvely. It can be observed that at the Cross-deck ends, the transverse and shear stress dstrbuton, referred as 'deformable Float' n the Fgures, was very smlar to those produced by the detaled FEA. However, n the remanng of the Cross-deck, the stresses were sgnfcantly underestmated for HSC1 and very smlar for HSC2. Fnally, especally for HSC1 the stresses n way of the bulkhead were underestmated snce ths smplfed approach cannot reproduce ther stress concentraton effect. In the future, a smlar modelng wth two deformable Floats connected to the Cross-deck could be consdered. 4. DISCUSSION OF THE RESULTS Float to Cross-deck connecton stffness The HSC1's deck transverse stresses obtaned by the detaled FEA showed very large stress fluctuatons along the Cross-deck wth peaks at the transverse bulkheads, whereas the stress varatons were much smaller for HSC2. Ths dfference would drectly be lnked to the stffness of the connecton between the Float were the load s appled and the Cross-deck where the stress was read-out. Table 5 presents the Float and Cross-deck bendng stffness r calculated usng Eq.(7) for a pece of the Cross-deck (see Fgure 19) located amdshp and extendng over the average transverse bulkheads spacng. It appeared that the Float bendng stffness of HSC1 was about 70% hgher than that of the Crossdeck structure, whereas for HSC2 that bendng stffness rato reached 633%. Therefore, HSC2's Float to Cross-deck connecton relatve stffness was sgnfcantly hgher than the one of HSC1.

6 Fg.11 Transverse stress on the Cross-deck structure at the Centerlne for the HSC1 under Beam Sea. Fg.15 Transverse stress on the Cross-deck structure at the Centerlne for the HSC2 under Beam Sea. Fg.12 Transverse stress on the Cross-deck's strength deck at the float connecton for the HSC1 under Quarterng Sea. Fg.16 Transverse stress on the Cross-deck's strength deck at the float connecton for the HSC2 under Quarterng Sea. Fg.13 Transverse stress on the Cross-deck's wet deck at the float connecton for the HSC1 under Quarterng Sea. Fg.17 Transverse stress on the Cross-deck's wet deck at the float connecton for the HSC2 under Quarterng Sea. Fg.14 Shear stress on the Cross-deck's transverse structure at the float connecton for the HSC1 under Quarterng Sea. Fg.18 Shear stress on the Cross-deck's transverse structure at the float connecton for the HSC2 under Quarterng Sea.

7 Fg.19 Local Float to Cross-deck model extent. Table 5. Float and Cross-deck structure stffness amdshp. Cross-deck vertcal flexural stffness over average bulkhead spacng, rcrossdeck Float vertcal flexural stffness amdshp wth S = average bulkhead spacng, rfloat HSC1 HSC2 N/m N/m rfloat / rcrossdeck - 170% 633% The Floats' stffness and transverse bulkhead spacng effects were already dentfed by Yasuhra and Hroyasu (2002) [5] when they compared the results of an dealzed 'box-type catamaran' under Quarterng Sea produced through detaled FEA. One mght antcpate that a Float to Cross-deck connecton rgdty crteron (K r) satsfyng Eq.(13) could be extracted from a senstvty analyss based on detaled FEA of such smplfed 'box-type catamaran' models. Applyng ths crteron would ensure mnmzng the stress concentratons at the transverse bulkheads and would also make the smplfed approaches stress predctons relable. 3 r I Float yy, Float S w K 4 r r I L (13) Crossdeck yy, CDbeam bhd where w s the average frame spacng, L bhd s the average bulkhead spacng, and I yy,cdbeam s the vertcal sectonal moment nerta of the Cross-deck transverse beam element as shown n Fg.18. Fg.20 Cross-deck transverse stress vs. longtudnal stress for HSC1. Fg.21 Cross-deck transverse stress vs. longtudnal stress for HSC2. Longtudnal component of stress The smplfed approaches presented n ths study neglects the longtudnal stress n the Cross-deck structure. Fgures 20 and 21 relate the transverse stress to the longtudnal stress n the Cross-deck structure obtaned by detaled FEA for Beam and Quarterng Seas, of HSC1 and HSC2 respectvely. As for Fgures 11 to 18, the stresses were extracted from the elements along the Cross-deck centerlne for the Beam Sea and along the Float connecton for the Quarterng Sea. It appeared that the relaton between the two stress components was much more scattered for HSC1 than for HSC2. As a rough estmate, t can be concluded that, the longtudnal stresses were mostly comprsed between 25% and 50% of the transverse stresses, wth peaks at 100% for the HSC1 n way of the transverse bulkheads. The longtudnal stresses would thus be non neglgble for strength verfcatons usng stress combnaton crtera e.g. Von Mses stress or bucklng rato. Therefore, a reasonable approach for safe strength evaluaton through smplfed methods would consst n ncludng longtudnal stresses correspondng to 50% the evaluated transverse stresses. Superstructure addtonal strength The HSC1 s a 2-deck passenger shp whch the superstructure extends over the full shp breadth and over 80% the shp length. Therefore, the detaled FEAs of HSC1 ncludng the superstructure were conducted for both load cases n order to evaluate the benefcal effect of the superstructure on the Cross-deck stresses. Fgures 22 and 23 present the transverse stress results obtaned by detaled FEA wth and wthout the superstructure for both load cases. It can be observed that the contrbuton of the superstructure decreased the transverse stress by more than 50%. The strength margn provded by omttng the superstructure from the calculatons would thus be suffcent to cover the uncertantes of the smplfed methods such as the stress concentratons due to soft Float to Cross-deck connecton or the omsson of the longtudnal stress component as dscussed above.

8 Fg.22 Transverse stress on the Cross-deck structure at the Centerlne from detaled FEA wth and wthout superstructure for HSC1 under Beam Sea. Fg.23 Transverse stress on the Cross-deck structure at the float connecton from detaled FEA wth and wthout superstructure for HSC1 under Quarterng Sea. CONCLUSIONS Ths study evaluated the valdty of smplfed approaches for the Cross-deck structural strength evaluaton of two passenger hgh speed catamarans under Beam and Quarterng Seas by comparson wth detaled Fnte Element Analyses. The desgn loads where calculated accordngly to the rules, and the desgn acceleratons were compared to the results of drect Seakeepng analyses for the desgn sea state. For the Beam Sea, the Cross-deck grder approach enabled satsfactory assessment of the transverse bendng stress on the strength deck and wet deck compared to the detaled FEA stresses averaged along the Cross-deck centerlne. For the Quarterng Sea, the smplfed approach assumng the Cross-deck connected to rgd Floats resulted n safe stress predctons n vew of the strength, at the excepton of the Cross-deck ends. However, when consderng deformable Floats, the smplfed approach Crossdeck ends' crtcal stresses became very close to the detaled FEA results. Ths study provded also a dscusson about the lmtatons and possble ameloratons of the smplfed approaches by the observaton of the detaled FEA results. Frst, large stress fluctuatons were observed along the Cross-deck of HSC1 that would be consstent wth the softer Float to Cross-deck connecton of HSC1 compared to that of HSC2 whch would result n sgnfcant stress concentratons n way of the stffer transverse bulkheads. Such 'soft' desgn should be avoded and a possble Float to Cross-deck connecton rgdty crteron formulaton was provded. Then, the detaled FEA showed that the longtudnal stresses should not be omtted by the smplfed approaches. For those two shps, a reasonable estmate would consst n takng the longtudnal stresses as 50% the transverse stresses obtaned by the smplfed methods. Fnally, the extended superstructures of passenger shps would result n sgnfcant addtonal strength that makes the smplfed approach very conservatve. However, for new types of hgh speed catamarans such as the Offshore Wnd Farm Support Vessels, such addtonal strength margn cannot be consdered wth regard to the lmted extent of the superstructure. ACKNOWLEDGEMENTS Ths project s funded by the Mnstry of Scence and Technology (MOST) (MOST E ) REFERENCES [1] CR Classfcaton Socety, Rules for the Constructon and the Fabrcaton of Hgh speed Craft, (2008). [2] Bureau Vertas, Rules for the Classfcaton of Hgh speed Craft, NR396, (2002). [3] Zheng J., Xe W., YangL.,&Yao-wu H., Smplfed Calculaton of Catamaran Cross-Deck Structural Strength, Chnese Journal of Shp Research,4, (2010), [4] Bureau Vertas, Hull Structure and Arrangement for the Classfcaton of Cargo Shps less than 65 m and Non Cargo Shps less than 90 m, NR600, (2014). [5] Yasuhra Y., Hroyasu T., On smplfed method to analyze the cross-deck floor strength of catamaran subjected to ptch connectng moment, Journal of the Socety of Naval Archtects of Japan,191,(2002),