Reliability Evaluation of Jacket-type Offshore Platforms Subjected to Wind, Wave, and Current Loads

Transcription

1 IOP Conference Seres: Earth and Envronmental Scence PAPER OPEN ACCESS Relablty Evaluaton of Jacket-type Offshore Platforms Subected to Wnd, Wave, and Current Loads To cte ths artcle: Z F Song 2017 IOP Conf. Ser.: Earth Envron. Sc Related content - Determnaton of current loads of floatng platform for specal purposes Guang-yng Ma, Yun-long Yao and Chenyao Zhao - Bayesan-Networks-Based Rsk Evaluaton Approach of Offshore Platform Xaobng Yuan, Baopng Ca, Xaoyan Shao et al. - Strength Analyss and Relablty Evaluaton for Speed Reducers Yuo-Tern Tsa and Yung-Yuan Hsu Vew the artcle onlne for updates and enhancements. Ths content was downloaded from IP address on 03/09/2018 at 12:30

2 Relablty Evaluaton of Jacket-type Offshore Platforms Subected to Wnd, Wave, and Current Loads Z F Song School of Cvl Engneerng, North Chna Unversty of Technology, Beng , Chna Abstract: The am of ths study s to evaluate the relablty and senstvty of acket-type offshore platforms under wnd, wave, and current loads. The relablty of the platforms are comprehensvely determned based on the deformaton and energy of the acket platform. The Young s Modulus; the yeld strength; the stran hardenng rate; the dameter and thckness of members; the water depth; the wave heght and perod; the wave veloctes on the surface, mddle, and base of the platform; the drag coeffcent; the nertal coeffcent; and the horzontal concentrated scaled loads are defned n the study as random varables. The senstvty of the performance functons to the above-mentoned varables s determned, and the varables that most nfluence the performance of the platform are dentfed. Man conclusons are drawn as follows: the ncreasng mean and decreasng standard devaton of wall thckness n Type-1, Type-4, and Type-2 acket members can effectvely reduce the deformaton and total stran energy of platform structures. For acket structures n the plastc state, ncreasng the mean and decreasng the standard devaton of yeld strength s a reasonable method for reducng deformaton. Maxmum deformaton and stran energy are hghly correlated whether the load level s hgh or low, and the correlaton of these ndcators wth the varables consdered gradually ncreases wth the load level. Preface An offshore platform possesses many features of a complcated structure, a large bulk, a hgh constructon cost, and s located n the complex and harsh marne envronment. The structure of an offshore platform s constantly subect to the forces of wnd, waves, current, sea ce, and tdes. Adverse factors, such as envronmental corroson, adheson of marne creatures, the washng away of subsol, basc dynamc softenng, and materal agng can weaken the structural members and the overall resstance of a platform, affectng ts servce, safety, and durablty [1]. There have been a number of offshore platform accdents both domestcally and overseas (see Fg. 1) that have resulted n sgnfcant economc losses and adverse socal mpact. For example, n the wnter of 1964, two new drllng platforms located n the Unted States at Cook Inlet, Alaska, were severely damaged by sea ce. After hurrcanes Hlda and Betsy, 22 of Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, ournal ctaton and DOI. Publshed under lcence by Ltd 1

3 around 1000 platforms n the Gulf of Mexco collapsed or were otherwse damaged, becomng non-operatonal. After Hurrcane Andrew n 1992, 19 of around 3850 platforms n the Gulf of Mexco were damaged and non-operatonal. On December 18, 2011, a Russan ol platform sank after mpact wth sea ce. The relablty of offshore platforms has been an mportant subect upon whch both domestc and overseas researchers and engneers are focused. Many domestc and overseas researchers have studed the relablty of offshore platform structures. Freze [2] compared dfferent regulatons dctatng the relablty level of offshore platform acket structures n procedures API RP 2A-LRFD and SNAME T&R Bulletn 5-5A, and conducted an n-depth dscusson of ther reasonng. Zhu [3] dscussed the man problems of relablty analyss of offshore platform acket structures, and provded a general analyss procedure for the safety factor method. Deng [4] presented a relablty estmaton method for offshore platform acket structures, takng nto account punchng falure and bucklng falure of members. Ths method can determne the man falure modes of the structural system of the platform. Salau [5] derved a tme-dependent relablty equaton for offshore platform acket structures, and accurately ascertaned the relablty of corroded acket members. Jn [6] consdered the couplng effect between offshore platform acket members, ples, and sol, and evaluated the acket relablty under extreme load. Hezararb [7] combned the nonlnear pushover method wth the wave load ncremental method to evaluate the nonlnear response of the offshore platform acket-ple-sol system under the acton of waves through senstvty analyss. Lera [8] studed the relablty of the offshore platform feld-related response. Fg.1 Collapse of offshore platform However, prevous studes have been lmted to the relablty of the platform structural members and acket systems, and do not take nto account the senstvty and correlaton of acket behavor to dfferent loads. Therefore, the relablty and senstvty of offshore platform acket systems under the acton of wnd, wave, and current loads were selected as the obect of ths study, wth the ntent of comprehensvely evaluatng platform relablty from the perspectve of maxmum deformaton and total stran energy n the platform acket members. The senstvty of the acket structure deformaton and stran energy to varable physcal parameters, geometrc parameters, and wnd, wave, and current loads were studed, and the most nfluental varable s dentfed. Fnally, the correlaton between performance functons s dscussed. 1. Relablty theory 1.1 Latn Hypercube samplng method In order to accurately measure the relablty of offshore platform acket structures under the acton of wnd, wave, and current, the Monte Carlo method s used for relablty computaton n ths study. The Latn Hypercube samplng method can effcently generate multvarate samples and greatly reduce the number of smulatons wthout compromsng accuracy. The mean s estmated as 2

4 The m th value s estmated as 1 N N = 1 Y = Y = y (1) Y 1 N m N = 1 The cumulatve dstrbuton functon (CDF) s estmated as y y y的次数 y FY ( y) = N = ( y ) (2) 1.2 Senstvty A senstvty coeffcent represents the relatve mportance of a random varable to the falure probablty, whch satsfes the followng relaton: α1 + α2 + L + α n = 1 (4) where α ( = 1, 2, L, n) represents the senstvty coeffcent of the th random varable to the falure probablty, whch ndcates the relatve contrbuton of each random varable to the falure probablty. The senstvty coeffcent to the relablty ndex s expressed as β u = u1 + u2 + L + un = = α (5) u u β where u represents the random varable n standard normal space. The senstvty coeffcent to the falure probablty P f s expressed as Pf β = Φ ( β) = f( β) (6) u u u where Φ ( β ) represents a standard normal dstrbuton functon, and φ( β) represents a standard normal densty functon. 1.3 Correlaton between performance functons n structural system Performance functons Z and Z correspond to falure modes and, respectvely, expressed here as Z, Z. The performance functons contan only two statstcally ndependent varables, R and S. The standard errors of the mean for R and S are m R, m S and σ R, σ S, respectvely. The performance functons Z, Z can be respectvely expressed as: Z = ar bs (7) Z = ar bs (8) The correlaton coeffcent of Z, Z can be expressed as: ρ Z, Z 2 2 COV ( Z, Z ) aa σr + bb σs = = (9) σ σ σ σ Z Z Z Z If the performance functon s nonlnear, t can be expanded by a Taylor seres at the check pont X, the approxmate value of the correlaton coeffcent s calculated by a smple equaton (assumng the basc varables are not related), and the correlaton coeffcent of Z, Z s expressed as: ρ Z, Z COV ( Z, Z ) = = σ σ Z ' ' k xk ' k ' X x X 2 2 Z Z Z ' ' k xk ' k xk ' X X Z Z (3) (10) 2. Computaton of wave force The computaton of wave force s generally dvded nto the computaton of small scale wave force and the computaton of large scale wave force, based on the rato of the structural scale to the wavelength (D/L) where D s the characterstc length of the obect (such as dameter for a cylnder), and L ndcates 3

5 the wavelength. When D/L 0.2, the obect under consderaton s consdered to be small scale. When D/L > 0.2, the obect under consderaton s consdered to be large scale, for whch the free surface effect and the relatve scale effect, namely the dffracton effect, should be consdered. For the calculaton of wave force on small-scale slender columns, the famous Morson Equaton s wdely used n engneerng desgn [9]: where: 1 y y fwy = CDρw u u + 2 t t (11) 2 2 π D u y CMρw 2 4 t t f s the wave force per unt length vertcally actng on the ppe column n kn m ; ρ s the wyd seawater densty n 3 kg m ; D s the ppe column dameter n m ; u s the horzontal velocty of water partcle on axs of ppe column n ms; C D s the resstance coeffcent; C M s the nerta force coeffcent [10]. As Stokes wave theory can accurately descrbe the actual wave moton, standards for classfcaton of marne platforms lke ABS and DNV also suggest usng three-order or fve-order Stokes wave theory to conduct strength checks and structural desgn for marne structures. The Stokes wave theory can also be used for small-szed acket parts [11]. Ths study used the ANSYS software, whch can accommodate four dfferent wave theores: the mcro-ampltude wave theory wth deep fadng and emprcal correcton, the Ary wave theory, the fve-order Stokes wave theory, and the stream functon wave theory. If the fve-order Stokes wave theory s selected, only wave heght, perod, and phase angle are requred as nputs. If structural statc analyss s performed, before nputtng the phase angle, the phase angle of the maxmum wave current couplng force must be determned, and ths should be taken as the parameter for statc analyss. 3. Relablty and senstvty analyss of offshore platform ackets 3.1 Model parameters The parameters of an offshore platform acket structure were taken from Reference [10]. The platform conssted of an upper platform and a lower acket structure (see Fg. 2), wth the acket bottom fxed by a ple foundaton. The upper platform supports the frame and the deck, wth external dmensons of 30 m 20 m, and the heght from the water surface to the top deck was 15 m. The maorty of the lower acket structure conssted of 4 man ducts usng slm tubes for support, formng a spatal tower frame structure. The ple foundaton was drven nto the seabed sol through the man ducts. The sze of man duct n the acket structure above the mud lne was Φ m; the sze of man duct n the acket structure below the mud lne was Φ m; the sze of man ppe used n the deck was Φ m; the sze of nter-story horzontal bracng n the acket system was Φ m; the sze of dagonal braces n the acket system was Φ m; the secton area of the deck beams was 0.16 m 2, wth a heght of 0.4 m and a wdth of 0.4 m; the deck was m thck, 30 m long, and 20 m wde; the water depth was 45 m, wth a wnd velocty of 43.6 m/s, an effectve wave heght of 14.8 m, an effectve wave perod of 10.8 s, a surface flow rate of 2.35 m/s, a central flow rate of 1.96 m/s, and a bottom flow rate of 1.60 m/s. In order to smplfy the computaton, the nfluence of ple and sol on the behavor of the acket structure was not consdered, and the lower part of the acket was assgned a fxed constrant. The entre acket platform model used four element types: PIPE20, PIPE59, BEAM4 and SHELL43 (see Fg. 2). The PIPE20 element was used for the man vertcal supportng members of the deck framework above the water surface, as well as for members below the mud lne. Because the 4

6 hydrodynamc effect and the wave-current nteracton can be consdered n the PIPE59 element, t was used for acket members below water surface but above mud lne. The BEAM4 element was used for deck level frame beams, and the SHELL43 element used to model the horzontal deck. The steel materal used was D36, wth an elastc modulus of Pa, a Posson's rato of 0.3, a densty of 7850 kg/m 3, a yeld strength of 360 MPa, and a stran hardenng rate of The b-lnear elastc-plastc hardenng model was adopted for the steel. When the fve-order Stokes wave theory s used, the value of the phase angle ϕ has a sgnfcant mpact on the wave load actng on the structure. Before startng the statc analyss, t was necessary to determne the phase angle ϕ from 0 to 360 at whch the wave current couplng force s at ts maxmum. The authors determned that the phase angle correspondng to the maxmum wave current couplng force was 46 [10]. Based on the characterstcs of the acket-type offshore platform, Jnpng Ou proposed the whole advancement method [1], an approxmate method for lmt analyss that s essentally a pushover analyss method, whch treats the platform structure as resstng the horzontal force as a whole to calculate the bearng capacty of entre structure. Based on ths, for the convenence of computaton, the wnd loads were equally concentrated at the eght nodes where platform and acket structure ntersect, and were amplfed by dfferent multples to study the elastc-plastc mechancal propertes of the acket structure under the acton of the three dfferent appled horzontal loads. From the pont of vew of deformaton and energy, the relablty and senstvty of the acket platform under wnd, wave, and current loads were studed. The acket physcal parameters (elastc modulus, yeld strength, and stran hardenng rate), geometrc parameters (ppe dameter and wall thckness) for four classes of sectons (A D), the water depth, the wave heght and perod, the surface, central, and bottom flow rate, the drag coeffcent, the nerta force coeffcent, and the amplfed wnd load were defned as random varables. The statstcal characterstcs of each random varable are shown n Table 1. See references [12] and [13] for parameter selecton rules. 7m Shell63 Beam4 8m Y Z Y X X 10m 10m 10m Z Ppe16 一类截面二类截面三类截面四类截面 Ppe59 10m 5m 5m Ppe16 (a) Whole model (b) Unt types Fg.2 Model of offshore platform Table 1 Statstcal parameters of random varables Random Probablty Mean Standard Random Probablty Mean Standard Descrpton Descrpton varable dstrbuton value error varable dstrbuton value error DW/m Water depth Normal D1 Class A Truncated dameter /m Gauss HW/m Wave heght Normal T1 Class A wall Truncated thckness/m Gauss TW/s Wave perod Normal D2 Class B Truncated dameter /m Gauss VS/(m/s) Surface flow Class B wall Truncated Normal T2 rate thckness/m Gauss VM/(m/s) Central flow Class C Truncated Normal D3 rate dameter /m Gauss VB/(m/s) Bottom flow Class C wall Truncated Normal T3 rate dameter /m Gauss CD Resstance Normal D4 Class D Truncated

7 coeffcent dameter /m Gauss CE Inerta force Class D wall Truncated Normal T4 coeffcent thckness/m Gauss E/MPa Elastc modulus Log normal Load level 1/kN f y/mpa Yeld strength Normal LOAD Load level 2/kN Normal b Stran hardenng rate Normal Load level 3/kN Relablty analyss Frst, the relablty of offshore platform acket structures under the acton of the three dfferent horzontal loads consdered was studed. Defnng the maxmum deformaton and the total stran energy as performance functons, the CDF curves of probablty for the maxmum deformaton and the total stran energy under three load levels are shown n Fg. 3 and Fg. 4, respectvely. As can be seen from Fg. 3a, for Load Level 1, the average maxmum deformaton was m, wth a standard error of m; the probablty for deformaton beyond a threshold of 0.12 m was %, and the probablty for deformaton beyond a threshold of 0.15 m was 4.34 %. Wth the ncrease n load level, the mean and the standard error of the maxmum deformaton also ncreased. Accordng to Fg. 3b, for Load Level 2, the mean of maxmum deformaton reached m wth a standard error of m, and accordng to Fg. 3c for Load Level 3, the mean of maxmum deformaton was m wth a standard error of m. Probablty Probablty Probablty Dsplacement /m Dsplacement /m Dsplacement /m (a) Load level 1 (b) Load level 2 (c) Load level 3 Fg.3 CDF curves of maxmum deformaton Probablty Probablty Probablty Energy /J( 10 6 ) Energy /J( 10 6 ) Energy /J( 10 6 ) (a) Load level 1 (b) Load level 2 (c) Load level 3 Fg.4 CDF curves of total stran energy Fg. 4 shows the CDF curve of probablty for the total stran energy. As shown n Fg. 4a, for Load Level 1, whch s relatvely lght, the mean of total stran energy was only J, wth a standard error of J. As the load level ncreased, a number of members n the acket entered nto the plastc state, and the total stran energy ncreased as well. From Fg. 4b, t can be seen that when Load Level 2 was appled, the total stran reached J, a two-fold ncrease compared to Load Level 1. As can be seen from Fg. 4c, for Load Level 3, the acket has been sgnfcantly deformed and a large number of members have entered nto the plastc state, wth the mean of total stran energy reachng J, 6

8 whch s a two-fold ncrease over Load Level Senstvty and correlaton analyss In ths secton, the senstvty of the maxmum deformaton and total stran energy to each random varable was analyzed by applyng dfferent load levels to the acket platform. All calculaton results are shown n Table 2 to Table 4, whle Fg. 5 and Fg. 6 show the pe dagrams llustratng the senstvty of the maxmum deformaton and total stran energy to each random varable under the three load levels appled. From Table 2 and Fg. 5a, t can be seen that for Load Level 1, the maxmum deformaton s mostly senstve to changes n horzontal concentrated loads, whch exhbt a senstvty coeffcent of a postve value, ndcatng that the maxmum deformaton ncreases as the value of the horzontal concentrated load ncreases. The senstvty coeffcent for the elastc modulus was a negatve value, ndcatng that the maxmum deformaton decreases as the elastc modulus ncreases. The senstvty coeffcents for the wall thckness of Class A, D, and B members were , , and , respectvely, ndcatng that an ncrease n mean wall thckness and reducton of ther standard error can effectvely reduce acket deformaton. The senstvty coeffcents for the dameter of Class D, A, and C members were , , and , respectvely, ndcatng that an ncrease n mean external dameter and reducton n ther standard error can also reduce the acket deformaton to some extent. The senstvty coeffcents for water depth, wave heght, wave perod, central flow velocty, bottom flow velocty, resstance coeffcent, nerta force coeffcent, and yeld strength were all so low that they can be neglected. Wth ncreasng load levels, there were some members enterng the plastc state, and thus the senstvty of structure to changes n yeld strength ncreases. As dsplayed n Table 3 and Fg. 5b, for Load Level 2 the senstvty of the maxmum deformaton to changes n yeld strength ncreased from to , whle the senstvty of other random varables remaned unchanged. It can be seen from Table 4 and Fg. 5c that for Load Level 3, there are more members enterng the plastc state, and the senstvty of the maxmum deformaton to changes n yeld strength was ncreased to Therefore, t can be seen that for ackets n the plastc state, ncreasng the mean yeld strength and decreasng ts standard error can effectvely reduce the maxmum deformaton. Accordng to the nformaton n Table 2 to Table 4 and Fg. 6, for the three load levels, the total stran energy ndcates the hghest senstvty to changes n the horzontal concentrated load, followed by changes n the elastc modulus. The data suggests smlar hgh senstvty to the wall thckness of the Class D, A, and B members, whch s smlar to the senstvtes of maxmum deformaton. In case of a low load level, the senstvty of total stran energy to the yeld strength can be gnored. As the load level ncreases, the senstvty coeffcent of the yeld strength ncreases from , frst to , then to , whch s caused by the gradual enterng of the members nto the plastc state. Table 2 Senstvty of maxmum deformaton and total stran energy to each random varable (Load Level 1) Performance functon DW HW TW VS VM VB CD CE E fy D E Performance functon B D1 T1 D2 T2 D3 T3 D4 T4 LOAD D E Table 3 Senstvty of maxmum deformaton and total stran energy to each random varable (Load Level 2) Performance functon DW HW TW VS VM VB CD CE E fy D E Performance functon B D1 T1 D2 T2 D3 T3 D4 T4 LOAD D E

9 Table 4 Senstvty of maxmum deformaton and total stran energy to each random varable (Load Level 3) Performance functon DW HW TW VS VM VB CD CE E fy D E Performance functon B D1 T1 D2 T2 D3 T3 D4 T4 LOAD D E Unmportant: Unmportant: Senstvty coeffcent Senstvty coeffcent (a) Load level 1 (b) Load level 2 Senstvty coeffcent Unmportant: (c) Load level 3 Fg.5 Senstvty pe dagrams of the maxmum deformaton to each random varable Unmportant: Senstvty coeffcent Senstvty coeffcent Unmportant: (a) Load level 1 (b) Load level 2 Unmportant: Senstvty coeffcent (c) Load level 3 Fg.6 Senstvty pe dagrams of total stran energy to each random varable 8

10 Senstvty coeffcent Senstvty coeffcent Load level Load level (a) Maxmum deformaton (b) Total stran energy Fg.7 Trend curves of senstvty coeffcent of each random varable under dfferent load level Fg. 7 shows the senstvty coeffcent curve for the man random varables of the acket assembly when subected to the three load levels. It can be seen that as the load level ncreases, the maxmum deformaton and total stran energy gradually grow less and less senstve to changes n the elastc modulus, and exhbt sgnfcantly ncreased senstvty to changes n the yeld strength and wall thckness of Class B members. The senstvty of the deformaton and stran energy to changes n the wall thckness of Class A and D members also decreases wth ncreasng load, whle ther senstvty to other random varables dd not show sgnfcant change. There s a correlaton between the performance functons defned by the maxmum deformaton and the total stran energy of the platform. Ths secton quantfes the extent of ths correlaton. The correlaton coeffcents under three load levels are shown n Table 5, whle Fg. 8 shows the scatter plots of ther correlaton under Load Level 1, whch s qute hgh. Accordng to Table 5, the correlaton coeffcents are for both Load Levels 1 and 2, and for Load Level 3, the correlaton coeffcent reaches Therefore, wth the ncrease n load level, the correlaton between the maxmum deformaton and the total stran energy ncreases gradually. Ths s because as the load ncreases, more members approach the yeld state, resultng n the ncreased mpact of yeld strength on the two performance functons. It can also be seen that regardless of the load level, the two performance functons consdered n ths study exhbt sgnfcant correlaton n excess of Table 5 Correlaton between performance functons Load level 1 Load level 2 Load level 3 Item D E D E D E D E Energy /J( 10 6 ) Dsplacement /m Fg.8 Scatter plots between maxmum deformaton and total stran energy (load level 1) 9

11 4 Conclusons (1) In order to comprehensvely evaluate the relablty of offshore platform acket structures, a varety of performance functons can be consdered for dfferent research obectves. Ths study consders the two performance functons of maxmum deformaton and total stran energy for the acket system, and quanttatvely determnes the structural relablty for each performance functon. (2) The extent of the senstvty of the two performance functons to changes n each random varable was determned, and the random varables most affectng the performance functons were dentfed. It was observed that the relablty of the offshore platform acket structure can be enhanced by ratonally controllng the probablty parameter of these random varables. Increasng the mean wall thckness of Class A, D, and B members, and reducng ther standard error can effectvely reduce the deformaton and total stran energy of the overall acket structure. Wth the ncrease n load level, the senstvty of the structure to changes n the yeld strength ncreases steadly. For acket members n the plastc state, mprovng the mean yeld strength and reducng the standard error can effectvely control the maxmum deformaton of the acket structure. Wth the ncrease n load level, the senstvty of the maxmum deformaton and total stran energy to changes n the elastc modulus gradually decreases, and ther senstvty to changes n the yeld strength sgnfcantly ncreases. (3) Regardless of the load level, there s strong correlaton between the maxmum deformaton and the total stran energy, whch s an advanced correlaton. Wth an ncrease n load level, the correlaton between the maxmum deformaton and the total stran energy mproves gradually, caused by more members enterng nto the yeld state, ncreasng the nfluence of yeld strength on the two performance functons REFERENCE [1] Ou J P, Duan Z D, Xao Y Q. Safety evaluaton of offshore platform structures: theory, method, applcaton [M]. Beng: Scence Press, 2003,1-9. [2] Freze P. A., Morand A. C., Brknshaw M, etc. Fxed and ack-up platforms: bass for relablty assessment [J]. Marne Structures, 1997,10(2-4): [3] Zhu Q X. Optmum desgn for offshore platform structural relablty [J]. Chna ocean Engneerng, 1992, 6(3): [4] Deng H Z, Sun Q. Relablty analyss for offshore platform structural systems [J]. Chna Ocean Engneerng, 1997,11(1):1-10. [5] Salau M. A., Esezobor D. E., Omotoso M. F. Relablty assessment of offshore acket structures n Nger Delta [J]. Petroleum & Coal, 2011,53(4): [6] Jn W L. Relablty-based desgn for acket platform under extreme loads [J]. Chna Ocean Engneerng, 1996,10(2): [7] Mona Hezararb, Bahaar M. R., Vahd Bagher, etc. Senstvty analyss of acket-type offshore platforms under extreme waves [J]. Journal of Constructonal Steel Research, 2013,83(3): [8] Bernt J. Lera, Danel Karunakaran. Ste-dependent relablty of a moble ack-up platform [J]. Marne Structures, 1995,8(2): [9] Morson J. R., O. Bren M. P., Johnson J.W., et al. The force exerted by surface wave on ples [J]. Petroleum Transactons, AIME, 1950,2(5): [10] Yang J, Lu S J, Xe R J. Applcaton of ANSYS n offshore ol engneerng [M]. Beng: Petroleum Industry Press, 2010,10-15,182. [11] Skelbrea, L., Hendrckson, J. A., Ffth order gravty wave theory [C]//Proceedngs, Seventh Conference on Coastal Engneerng, Ch. 10, 1961: [12] Jang Y B. Relablty calculaton and dscusson of desgn method of cable-stayed double-layer cylndrcal lattced shells[d]. Nanng: Southeast Unversty, 2006, [13] Du C. System relablty analyss of ocean acket platforms [D]. Dalan: Dalan Unversty of Technology, 2006,