IMPROVED METHODOLOGY OF SHIP HYDROELASTIC ANALYSIS

Transcription

1 Hydroelaticity in Marine Technology 01 Tokyo, JAPAN IMPROVED METHODOLOGY OF SHIP HYDROELASTIC ANALYSIS Ivo Senjanović, Neven Hadžić and Nikola Vladimir Univerity of Zagreb, Faculty of Mechanical Engineering and Naval Architecture Ivana Lučića 5, Zagreb, Croatia, ABSTRACT The paper preent improved methodology of hip hydroelaticity analyi, baed on the modal uperpoition method and including tructural, hydrotatic and hydrodynamic model. Structural beam model i ued compriing a reliable advanced thin-walled girder theory taking into account hear influence on torion a well a the contribution of bulkhead and the engine room tructure, a tructure dicontinuitie, to the hip hull tiffne. Conitent retoring tiffne i included in the analyi via hydrotatic model. Hydrodynamic loading and added ma and hydrodynamic damping are a part of the hydrodynamic model and are determined baed on the radiation / diffraction theory. Alo, the analyi of pringing effect on the hip fatigue life i introduced uing the combination of the improved hydroelatic model and 3D FEM ubtructure model. It i hown that the improved beam hydroelatic model can be efficiently ued in the aement of tre concentration of hip tructural detail. Applicability of the developed theory i proved within global hydroelatic analyi of a TEU container hip a well a tre concentration determination in the elected tructural detail. KEYWORDS Hydroelaticity; Improved beam model; Hydrodynamic; Retoring tiffne; Springing; Stre concentration 1. INTRODUCTION It i well known that the hydroelatic problem can be olved at different level of complexity and accuracy 1,. In thi paper the ophiticated beam model i coupled with 3D hydrodynamic model in order to invetigate the theoretical and practical threhold of beam model applicability. Due to that the exiting hydroelatic model i extended to determination of tre concentration tranfer function which are neceary for aement of fatigue damage/life of hip tructural detail. Stre concentration tranfer function calculation repreent the firt tep in the fatigue damage aement procedure 3. The global hydroelatic repone i calculated in the frequency domain uing beam tructural model and the modal diplacement are impoed to the 3D FEM fine meh ubtructure model. Stre concentration RAO are then obtained for the conidered tructural detail. The global and local hydroelatic repone are finally verified through the comparion with thoe obtained by fully coupled 3D FEM + 3D BEM hydroelatic model

2 . MATHEMATICAL MODEL.1 Structural model The advanced beam model take hear influence on bending and torion into account in a reliable way, a well a the contribution of tranvere bulkhead and engine room tructure to the hip hull global tiffne, o it can give quite accurate reult. Total beam deflection and twit angle conit of pure bending and torion, repectively, and their hear contribution 5 EI d w EI d ψ w= w + w = w = + =, (1) GA GI x b b w t b b, ψ ψ t ψ ψt d x d where I b i moment of inertia of cro-ection, A i hear area, I w i warping modulu and I i hear inertia modulu. E and G are Young' and hear modulu, repectively. One can ee that there i an analogy between bending and torion 5,6,7 Q A = = T, da w, I τqda τw A A () where Q and T w are hear force and torque due to retrained warping, and τ Q and τ w are correponding hear tree, repectively. The effect of large number of tranvere watertight and upport bulkhead taken into account a 7 ( + ν ) a 41 C U It = It, C =, l1 Il t 0 Eψ t (3) where, according to Figure 1, a i the web height of bulkhead girder, l 0 i the bulkhead pacing, l1 = l0 a i the net length, C i the energy coefficient, ν repreent Poion' ratio, and U i the bulkhead grillage and tool train energy due to warping of cro-ection. Warping hape function can be aumed by the following expreion: y z z u( yz, ) = u( yz, ) ψ t = y ( z d) + 1 ψ t, b H H (4) where H i the hip height, b i one half of bulkhead breadth, d i the ditance of warping centre from double bottom centroid, while y and z are tranvere and vertical coordinate, repectively. The bulkhead grillage train energy i defined a H 3b 8Hb 143Hb U = ( ) ( 1 ) g i + i + ν i + i + ν i Eψ 1 ν 35b y 105H z 75 y z 75 t (5) where i y, i z and i t are the average moment of inertia of cro-ection and torional modulu per unit breadth, repectively. The tool train energy i given a 116

3 Figure 1: Longitudinal ection of container hip hold U = h I ( ) b h Ib 9bIt 7 1 ν 3 b b A 10 1 ( + ν ) Eψ, (6) where I b, A and I t are the moment of inertia of cro-ection, hear area and torional modulu, repectively. Quantity h i the tool ditance from the inner bottom. Ultra Large Container Ship have relatively hort engine room tructure with length of about a half of hip breadth. Such tructure behave like a egment of the open cro ection with increaed torional tiffne due to deck contribution 9. The effective torional modulu which include both open cro-ection and deck egment can be written in the form: I t ( ) = 1 + C I, t (7) where I t defined a i the torional tiffne of an open cro-ection egment and C i energy coefficient, 3 a 41 ( + ν ) t1 ( wd wb ) k E i b + V i h i C = =, k =, (8) Et a V1 h ( + ν ) Ia t b where V i repreent volume of particular deck, w D and w B are value of deck and bottom warping function, repectively. The other geometric quantitie in the above formula are illutrated in Figure. Figure : Engine room deck deformation and double bottom rotation, a) bird eye, b) lateral view 117

4 Finally all tiffne contribution are ummed up in a well-known dry natural vibration matrix equation ( Ω ) K M δ = 0, (9) where K i tiffne matrix, M i ma matrix, Ω i dry natural frequency and δ i dry natural mode. If 1D analyi i applied the beam vibration mode hould be pread to the hip wetted urface. The general expreion for preading nodal diplacement to the wetted urface 10,11,1 yield: dwv dwh dψ h = ( Z zn ) + Y + u + wh ψ ( Z zs) + [ wv + ψy]. dx dx dx i j k (10) where w v i hull vertical deflection, w h i hull horizontal deflection, ψ i twit angle, y and z are coordinate of the point on hip urface, and z N and z S are coordinate of centroid and hear centre repectively, and u= uxyz (,, ) i the cro-ection warping intenity related to the wetted urface. Z and Y, repreent global coordinate, while i, j and k are unit vector, repectively. The expreion for nodal diplacement of beam model and 3D FEM ubtructure model can be extracted from Eq. (11) dwv dwh dψ δx = ( Z zn ) + Y + u, δy = wh ψ ( Z zs), δz = wv + ψy. (11) dx dx dx Thee diplacement are then impoed to the aft and fore 3D FEM ubtructure boundarie, and tre concentration, a reult of their difference, i calculated.. Hydrodynamic model The full detail decription of the ued hydrodynamic model i given in a number of reference 9,10,11, o only the brief decription i given here. The ued hydrodynamic model i olved in the frequency domain uing the modal uperpoition method baed on the potential theory aumption. In that way hydrodynamic ma and damping matrice are extended to elatic mode and are defined a A = ρre j hnd S, B = ρim j hn ds. (1) ij Rj i ij Rj i S S where ρ repreent fluid denity, j Rj i the radiation potential and h i and n are dry natural mode and normal vector of the wetted urface S..3 Hydrotatic model Hydrotatic model take into account the hydrotatic part of the total preure obtained by Bernoulli equation. There are everal retoring tiffne formulation a for example formulation of Price & Wu 14, Newman' formulation 15, formulation of Huang & Rigg 16, Malenica 17, Senjanović et al 18,19. Phyically conitent formulation of retoring tiffne for hip tructure, developed recently by Senjanović et al. 18, i ued here. Retoring tiffne repreent the relation between excitation force and diplacement and i derived baed on the modal uperpoition method uing the variational or perturbation method. It conit of hydrotatic and gravity part. The hydrotatic component i compried of preure and normal vector and mode part that are defined a 118

5 ( ) p j nh C = ρg h h n d S, C = ρg Zh h n ds. (13) ij i z ij i j S S The gravity part of the retoring tiffne read j ρ ( h ) d, C = g h V m ij i z V (14) where i Hamilton differential operator. Finally, the complete retoring tiffne coefficient are obtained by umming up it contitutive part C = C + C + C. p nh m ij ij ij ij (15).4 Hydroelatic model The governing modal matrix differential equation for coupled hip motion and vibration yield 10,11 : ( ( )) ( ( )) k+ C iω d+ B ω ω m+ A ω ξ = F, (16) where k, d, and m are tructural tiffne, damping and ma matrice, repectively, C i retoring tiffne, B(ω) i hydrodynamic damping, A(ω) i added ma, ξ are modal amplitude, F i wave excitation and ω i encounter frequency. All quantitie, except ω and ξ, are related to the dry mode. 3. COMPUTER SOFTWARE Baed on the outlined theory computer program have been developed and checked by correlation analyi of the imulation reult and the meaured one for a flexible egmented barge 1,0. Hydroelatic model baed on the coupling of 1D FEM and 3D BEM model and it wave repone i formulated and olved by program HYELACS 1, Figure 3. Beam model i formulated by program STIFF, baed on the theory of thin-walled girder. It calculate cro-ection area, moment of inertia, hear area, torional modulu, warping and hear inertia modulu for both cloed and open cro ection. STIFF Sectional geometrical propertie Governing data, Inertial propertie, Loading condition, Finite element ubdiviion. AMG Hydrodynamic meh generation Governing data, Ship peed, Enquentring angle, Frequencie. DYANA Dry natural vibration, tructural and hydrodynamic model coupling, modal ma, tiffne and retoring tiffne HYDROSTAR Hydrodynamic propertie Governing data, Damping, Section. MECAP Motion equation olving in frequency domain TDP Motion equation olving in time domain Governing data, Damping, Time and wave parameter. Figure 3: Program HYELACS flowchart 119

6 Model of the hydrodynamic wetted urface i automatically generated by program AMG3and i tranferred to program DYANA4 in order to calculate the modal retoring tiffne. Modal hydrodynamic propertie are determined uing program HYDROSTAR5, and finally hydroelatic problem i olved by program MECAP1. Program HYELACS alo allow olving problem of tranient vibration in time domain. 4. NUMERICAL EXAMPLE 4.1 Ship particular A large container hip of TEU i conidered4, Figure 4. The veel length between perpendicular, breadth and draft are 348 m, 45.6 m and 15.5 m, repectively. Figure 4: TEU container hip 4. Beam model verification The reliability of the beam model i checked by comparing the lighthip and full load dry natural frequencie, Table 1, and mode hape, Figure 5 and 6 with the one obtained from 3D FEM analyi performed by NASTRAN6. Very good agreement of the reult i found. TABLE 1 DRY NATURAL FREQUENCIES OF THE LIGHT CONTAINER SHIP, wi (HZ) No. 1 3 Vertical D Coupled Vertical D Coupled Dicrepancy, % Vertical Coupled ,69 Figure 5: The 1t and the nd lighthip vertical vibration natural mode, 3D and 1D 10

7 Figure 6: The 1t and the nd lighthip coupled horizontal and torional vibration natural mode, a) bird eye, b) lateral view, 3D and 1D 4.3 Global hydroelatic repone Numerical calculation of hip repone to wave i performed for everal loading condition, unit harmonic wave amplitude, and et of heading angle, hip peed and wave length. Tranfer function of vertical bending moment, horizontal bending moment, and torional moment at the amidhip ection, obtained uing 1D FEM + 3D BEM hydroelatic model for the cae of fully loaded hip, are hown in Figure 7. The angle of 180 correpond to the head ea. They are compared to the rigid body one determined by program HYDROSTAR5. Very good agreement i obtained in the lower frequency domain, where the hip behave a a rigid body, while large dicrepancie occur at the reonance of the elatic mode, a expected. Further on, hydroelatic repone obtained by 1D FEM + 3D BEM hydroelatic model i compared to the one obtained by Figure 7: Tranfer function for vertical and horizontal bending moment and torional moment, χ=10, U=4.7 kn, x=175 m 11

8 fully coupled 3D FEM + 3D BEM hydroelatic model, Figure 8, where quite good agreement i obviou. In thi particular cae, the loading condition No. 7 from the trim and tability book and lightly lower hip peed wa elected. Figure 8: Tranfer function for vertical and horizontal bending moment and torional moment, χ=10, U=15.75 kn 4.4 Local repone The elected tructural detail for tre concentration aement i a knee in the hatch corner at the upper deck level in the middle part of the hip, Figure 9 and 10. For tre concentration analyi a 3D FEM ubtructure model with refined meh in the vicinity of the elected tructural detail, ha been build in program NASTRAN6. It hould be pointed out that the real and imaginary component of the repone hould be calculated eparately, and at the end, at the level of tree hould be ummed up a a complex quantity. Figure 10 how the tre ditribution in the conidered tructural detail for the elected frequency ( ω = 0.9 rad/ ). The analyzed tre i normal tre along the knee boundary. In order to regiter it, bar element are fitted on the knee boundary. Tranfer function of tre concentration obtained by 1D FEM +3D BEM and 3D FEM + 3D BEM hydroelatic model are preented in Figure 11. In the low frequency domain rather high dicrepancie can be noticed, while in the high frequency domain, where the pringing influence on fatigue damage accumulation i pronounced, quite good agreement i achieved. Figure 9: Longitudinal poition of the elected detail 1

9 Figure 10: Selected tructural detail and tre ditribution Figure 11: Tranfer function of tre concentration 5. CONCLUSION Beam tructural model, commonly ued in the preliminary deign phae, repreent powerful and reliable deign tool. Therefore it i important to know the threhold of the beam model applicability. Due to that the exiting methodology of hip hydroelaticity analyi wa extended to aement of fatigue damage of hip tructural detail. The improved methodology of hip hydroelaticity analyi wa illutrated by one example, i.e TEU container hip and after the verification of beam model importance of hydroelaticity analyi wa demontrated by comparion of the bending moment tranfer function for the cae of rigid and flexible hip tructure. Alo, applicability of the beam tructural model within the hydroelaticity methodology wa demontrated by comparion of the tranfer function of tre concentration for the elected tructural detail in the cae of 3D and 1D FEM tructural model. Although, very good agreement i achieved, epecially in the high frequency range where pringing influence i pronounced, ome minor improvement in the low frequency domain could be done to increae the accuracy of fatigue damage calculation. In the future work it i neceary to proceed further to hip motion calculation in irregular wave for different ea tate, baed on the known tranfer function. Alo, model tet and full-cale meaurement hould be performed to enable the complete validation of the improved model and to extend the Claification Rule for the deign and contruction of ultra large container hip. ACKNOWLEDGEMENTS Thi reearch wa upported by the EU FP7 project Tool for Ultra Large Container Ship - TULCS (Project No ). 13

10 REFERENCES 1.Chen, X.J, Wu, Y.S., Cui, W.C. and Juncher Jenen, J.: Review of hydroelaticity theorie for global repone of marine tructure. Ocean Engineering, Vol. 33, 006, Wu, Y.S. and Cui, W.C.: Advance in three-dimenional hydroelaticity of hip. Proc. IMechE Part M: Journal of Engineering for the Maritime Environment, Vol. 3, No. 3, 009, Boutillier, V., Maherault, S., Huther, M., Henry, J., Parmentier, G.: Fatigue damage calculation of ULCS due to quai-tatic wave repone and pringing repone. Proceeding of the PRADS Conference, Rio de Janeiro, Brazil, 010, Vladimir, N.: Hydroelaticity and fatigue trength of large container hip, PhD thei, Univerity of Zagreb, Zagreb 011. (In Croatian) 5.Senjanović, I., Tomašević, S., Vladimir, N.: An advanced theory of thin-walled girder with application to hip vibration. Marine Structure, Vol., No. 3, 009, Pavazza, R.: Torion of thin-walled beam of open cro-ection with influence of hear. International Journal of Mechanical Science, Vol. 47, 005, Senjanović, I., Rudan, S., Vladimir, N.: Influence of hear on the torion of thin-walled girder. Tranaction of FAMENA, Vol. 33, No., 009, Senjanović, I., Tomašević, S., Rudan, S., Senjanović, T.: Role of tranvere bulkhead in hull tiffne of large container hip. Engineering Structure, Vol. 30, No. 9, 008, Senjanović, I., Vladimir, N., Tomić, M.: Effective tiffne of the engine room tructure in large container hip. Brodogradnja, Vol. 6, No. 1, 011, Senjanović, I., Malenica, Š., Tomašević, S.: Invetigation of hip hydroelaticity. Ocean Engineering, Vol. 35, 008, Senjanović, I., Malenica, Š., Tomašević, S.: Hydroelaticity of large container hip. Marine Structure, Vol., No., 009, Tomašević, S.: Hydroelatic model of container hip dynamic repone in wave, PhD thei, Univerity of Zagreb, Zagreb 007. (In Croatian) 13.Malenica, Š., Molin, B., Remy, F., Senjanović, I.: Hydroelatic repone of a barge to impulive and non-impulive wave load. Proceeding of the International Conference on Hydroelaticity in Marine Technology, Oxford, UK, 003, Price, W.G., Wu, Y.S.: Hydroelaticity of Marine Structure. Theoretical and Applied Mechanic, Niordon, F.I. and Olhoff, N. (ed), Elevier Science Publiher BV, 1985, Newman, J.N.: Wave effect on deformable bodie. Applied Ocean Reearch, Vol. 16, 1994, Huang, L.L., Rigg, H.R.: The hydrotatic tiffne of flexible floating tructure for linear hydroelaticity. Marine Structure, Vol. 13, 000, Malenica, Š.: Some apect of hydrotatic calculation in linear eakeeping. Proceeding of the 14 th NAV Conference, Palermo, Italy, Senjanović, I., Vladimir, N., Tomić, M.: Formulation of conitent retoring tiffne in hip hydroelatic analyi. Journal of Engineering Mathematic, Vol. 7, No. 1, 01, Senjanović, I., Hadžić, N., Vladimir, N.: Retoring tiffne in the hydroelatic analyi of marine tructure. Brodogradnja, Vol. 6, No. 3, 011, Remy, F., Molin, B., Ledoux, A.: Experimental and numerical tudy of the wave repone of a flexible barge. Proceeding of the International Conference on Hydroelaticity in Marine Technology, Wuxi, China, 006, HYELACS. Uer' Manual. FAMENA, Zagreb, 011..STIFF. Uer' Manual. FAMENA, Zagreb, AMG. Uer' Manual. BV, Pari, DYANA. Uer' Manual. FAMENA, Zagreb, HYDROSTAR. Uer' Manual. Bureau Verita, Pari, MSC.NASTRAN 005. Intallation and Operation Guide, MSC.Software,