船冰相互作用研究方法综述
|
摘要
船舶在冰区航行以及海洋结构物在冰区的运营中,结构物与海冰的相互作用是一个关键问题。由于海冰的材料特性复杂,目前对于相关问题的了解有限,开发有效的本构模型以及对数值方法应用的改进是船冰作用研究的关键。文章对近年来船冰作用问题的研究方法进行了总结。船冰作用的主要研究方法包括试验法、有限元法、离散元法和概率法。通过试验能够获得最直接的数据,同时也是建立海冰本构模型的基础,但试验成本高昂;有限元法理论基础扎实,商业软件较多,方便实现,但在模拟冰的脆性破碎和碎冰大尺度移动方面能力有限;离散元法能够更好地模拟冰的破碎与离散的特点,但目前该方法的开发应用不够完善;由于冰的某些特性如内部缺陷大小和方向具有随机性,因此概率法也被认为适于研究冰的部分问题。
The problem of ship-ice interaction is the critical issue in ships' navigation and marine operation in the arctic area. Since the material properties of sea ice are complex and related to superficial knowledge,developing effective material constitutive models and improving numerical methods are of crucial importance in ice-ship interaction analysis. This paper summarizes the main investigating methods for ship-ice interaction analysis, which are testing method, FEM(finite element method), DEM(discrete element method)and probabilistic method. Direct data can be obtained through on-site measurement tests, and it is also the basis for sea ice material constitutive models, but tests are always high-cost. FEM has a profound theoretical foundation and is easy to implement, but is limited in simulation of brittle crush behavior and fragments' large-scale movement. Nevertheless, DEM has better abilities in simulating these characteristics, but DEM still needs further development. Owing to the randomness of some features of ice, such as size and orientation of inner flaws, probabilistic method is also considered to be suitable for the research on ship-ice interaction.
The problem of ship-ice interaction is the critical issue in ships' navigation and marine operation in the arctic area. Since the material properties of sea ice are complex and related to superficial knowledge,developing effective material constitutive models and improving numerical methods are of crucial importance in ice-ship interaction analysis. This paper summarizes the main investigating methods for ship-ice interaction analysis, which are testing method, FEM(finite element method), DEM(discrete element method)and probabilistic method. Direct data can be obtained through on-site measurement tests, and it is also the basis for sea ice material constitutive models, but tests are always high-cost. FEM has a profound theoretical foundation and is easy to implement, but is limited in simulation of brittle crush behavior and fragments' large-scale movement. Nevertheless, DEM has better abilities in simulating these characteristics, but DEM still needs further development. Owing to the randomness of some features of ice, such as size and orientation of inner flaws, probabilistic method is also considered to be suitable for the research on ship-ice interaction.
引文
[1]Bergan P G,Cammaert G,Skeie G,et al.On the potential of computational methods and numerical simulation in ice mechanics[C]//IOP Conference Series:Materials Science and Engineering.IOP Publishing,2010,10(1):012102.
[2]Liu Z.Analytical and numerical analysis of iceberg collisions with ship structures[D].Doctor thesis,Norwegian University of Science and Technology,2011.
[3]Jordaan I J.Mechanics of ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17-18):1923-1960.
[4]Michel B,Toussaint N.Mechanisms and theory of indentation of ice plates[J].Journal of Glaciology,1978,19:285-300.
[5]Sodhi D S.Crushing failure during ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17):1889-1921.
[6]Li C,Barrette P,Jordaan I.High pressure zones at different scales during ice-structure indentation[C]//ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering.American Society of Mechanical Engineers,2004:887-894.
[7]Browne T,Taylor R,Jordaan I,et al.Small-scale ice indentation tests with variable structural compliance[J].Cold Regions Science&Technology,2013,88(88):2-9.
[8]Taylor R S,Jordaan I J.Damage and fracture during contact between a spherical indenter and ice:experimental results and finite element simulations[J].Key Engineering Materials,2014,577-578:609-612.
[9]Kim E,Golding N,Schulson E M,et al.Mechanisms governing failure of ice beneath a spherically-shaped indenter[J].Cold Regions Science&Technology,2012,78(4):46-63.
[10]Wells J,Jordaan I.Small-scale laboratory experiments on the indentation failure of polycrystalline ice in compression:Main results and pressure distribution[J].Cold Regions Science&Technology,2011,65(3):314-325.
[11]Sopper R,Daley C,Colbourne B,et al.The influence of external boundary conditions on ice loads in ice-structure interactions[C].ASME 2016,International Conference on Ocean,Offshore and Arctic Engineering,2016:V008T07A007.
[12]Sopper R,Daley C,Colbourne B,et al.The influence of water,snow and granular ice on ice failure processes,ice load magnitude and process pressure[J].Cold Regions Science&Technology,2017,139.
[13]O’Rourke B J,Jordaan I J,Taylor R S,Gürtner A.Experimental investigation of oscillation of loads in ice high-pressure zones,part 1:Single indentor system[J].Cold Regions Science and Technology,2016,124:25-39.
[14]Timco G W,Weeks W F.A review of the engineering properties of sea ice[J].Cold Regions Science&Technology,2010,60(2):107-129.
[15]Timco G W,Frederking R M W.Confined compression tests:Outlining the failure envelope of columnar sea ice[J].Cold Regions Science&Technology,1986,12(1):13-28.
[16]Riska K,Frederking R M W.Ice load penetration modelling[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,1987:317-327.
[17]马健钧.海冰弯曲破坏的数值模拟方法研究[D].天津:天津大学,2013.Ma Jianjun.Methodology research on the numerical simulation of the bending failure of sea ice[D].Tianjin:Tianjin University,2013.
[18]Jones S J.High strain-rate compression tests on ice[J].The Journal of Physical Chemistry B,1997,101(32):6099-6101.
[19]Jones S J,Gagnon R E,Derradji A,et al.Compressive strength of iceberg ice[J].Canadian Journal of Physics,2003,81(1-2):191-200.
[20]Barrette P D,Jordaan I J.Pressure-temperature effects on the compressive behavior of laboratory-grown and iceberg ice[J].Cold Regions Science&Technology,2003,36(1-3):25-36.
[21]Sinha N K,Cai B.Elasto-delayed-elastic simulation of short-term deflection of fresh-water ice covers[J].Cold Regions Science&Technology,1996,24(2):221-235.
[22]Gagnon R E,Gammon P H.Triaxial experiments on iceberg and glacier ice[J].Journal of Glaciology,1995,41(139):528-540.
[23]Gratz E T,Schulson E M.Brittle failure of columnar saline ice under triaxial compression[J].Journal of Geophysical Research Solid Earth,1997,102(B3):5091-5107.
[24]Weiss J,Schulson E M.The failure of fresh-water granular ice under multiaxial compressive loading[J].Acta Metallurgica Et Materialia,1995,43(6):2303-2315.
[25]Timco G W,Frederking R M W.An investigation of the failure envelope of granular/discontinuous-columnar sea ice[J].Cold Regions Science&Technology,1984,9(1):17-27.
[26]Schulson E M,Nickolayev O Y.Failure of columnar saline ice under biaxial compression:Failure envelopes and the brittle-to-ductile transition[J].Journal of Geophysical Research Solid Earth,1995,100(B11):22383-22400.
[27]Smith T R,Schulson E M.The brittle compressive failure of fresh-water columnar ice under biaxial loading[J].Acta Metallurgica Et Materialia,1993,41(1):153-163.
[28]Smith T R,Schulson E M.Brittle compressive failure of salt-water columnar ice under biaxial loading[J].Journal of Glaciology,1994,40(135):265-276.
[29]Schwarz J,Weeks W F.Engineering properties of sea ice[J].Journal of Glaciology,1977,19(81):499-531.
[30]von Bock R U F,Polach.Numerical analysis of the bending strength of model-scale ice[J].Cold Regions Science&Technology,2015,118:91-104.
[31]Han H,Jia Q,Huang W,et al.Flexural strength and effective modulus of large columnar-grained freshwater ice[J].Journal of Cold Regions Engineering,2015,30(2):04015005.
[32]Svec O J,Frederking R M W.Cantilever beam tests in an ice cover:Influence of plate effects at the root[J].Cold Regions Science and Technology,1981,4(2):93-101.
[33]Timco G W,Frederking R M W.Comparative strengths of fresh water ice[J].Cold Regions Science and Technology,1982,6(1):21-27.
[34]Frederking R M W,Svec O J.Stress-relieving techniques for cantilever beam tests in an ice cover[J].Cold Regions Science and Technology,1985,11(3):247-253.
[35]Gagnon R E,Gammon P H.Characterization and flexural strength of iceberg and glacier ice[J].Journal of Glaciology,1995,41(137):103-111.
[36]Barrette P,Jordaan I.Beam bending and fracture behaviour of iceberg ice[C].National Research Council Program on Energy Research and Development(PERD),2001:4-78.
[37]季顺迎,王安良,苏洁,等.环渤海海冰弯曲强度的试验测试及特性分析[J].水科学进展,2011,22(2):266-272.Ji Shunying,Wang Anliang,Su Jie,et al.Experimental studies and characteristics analysis of sea ice flexural strength around the Bohai Sea[J].Advances in Water Science,2011,22(2):266-272.
[38]季顺迎,刘宏亮,许宁,等.渤海海冰断裂韧度试验[J].水科学进展,2013,24(3):386-391.Ji Shunying,Liu Hongliang,Xu Ning,et al.Experiments on sea ice fracture toughness in the Bohai Sea[J].Advances in Water Science,2013,24(3):386-391.
[39]Ralph F,Mckenna R,Gagnon R.Iceberg characterization for the bergy bit impact study[J].Cold Regions Science&Technology,2008,52(1):7-28.
[40]Gagnon R,Cumming D,Ritch R,et al.Overview accompaniment for papers on the bergy bit impact trials[J].Cold Regions Science&Technology,2008,52(1):1-6.
[41]Johnston,M,Timco,et al.Measuring global impact forces on the CCGS Terry Fox with an inertial measurement system called MOTAN[J].Cold Regions Science&Technology,2008,52(1):67-82.
[42]Johnston M,Ritch R,Gagnon R,et al.Comparison of impact forces measured by different instrumentation systems on the CCGS Terry Fox during the Bergy Bit Trials[J].Cold Regions Science&Technology,2008,52(1):83-97.
[43]Gagnon R.Analysis of data from bergy bit impacts using a novel hull-mounted external impact panel[J].Cold Regions Science&Technology,2008,52(1):50-66.
[44]Timco G W.Isolated ice floe impacts[J].Cold Regions Science&Technology,2011,68(1):35-48.
[45]M覿覿tt覿nen M,Marjavaara P,Saarinen S,et al.Ice crushing tests with variable structural flexibility[J].Cold Regions Science&Technology,2011,67(3):120-128.
[46]史庆增,徐继祖,宋安.海冰作用力的模拟试验[J].海洋工程,1991(1):16-22.Shi Qingzeng,Xu Jizu,Song An.The modeling test of the sea ice forces[J].Ocean Engineering,1991(1):16-22.
[47]黄焱.冰激海洋平台振动的动力模型试验研究[D].天津:天津大学,2004.Huang Yan.The study of ice induced vibration on marine platforms by dynamic model test[D].Tianjin:Tianjin University,2004.
[48]Sinha N K.Rheology of columnar-grained ice[J].Experimental Mechanics,1978,18(12):464-470.
[49]Karr D G,Choi K.A three-dimensional constitutive damage model for polycrystalline ice[J].Mechanics of Materials,1989,8(1):55-66.
[50]Ralston T D.Yield and plastic deformation in ice crushing failure[C].Proceeding of the Arctic Ice Dynamics Joint Experiment International Commission on Snow and Ice Symposium,1980:234-245.
[51]Jordaan I J,Stone B M,Mckenna R F,et al.Effect of microcracking on the deformation of ice[J].Canadian Geotechnical Journal,2011,29(1):143-150.
[52]Lade P V.Characterization of the mechanical behavior of sea ice as a frictional material[J].Journal of Geophysical Research Atmospheres,2002,107(B12):ECV 10-1-ECV 10-10.
[53]Lade P V.Modeling sea ice as an elasto-plastic frictional material[C]//IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics.Springer Netherlands,2001:227-238.
[54]Singh S K,Jordaan I J.Constitutive behaviour of crushed ice[J].International Journal of Fracture,1999,97(1):171-187.
[55]Keller A,Hutter K.A viscoelastic damage model for polycrystalline ice,inspired by Weibull-distributed fiber bundle models.Part I:Constitutive models[J].Continuum Mechanics&Thermodynamics,2014,26(6):879-894.
[56]Jordaan I J.Mechanics of ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17-18):1923-1960.
[57]Derradji-Aouat A,Sinha N K,Evgin E.Mathematical modelling of monotonic and cyclic behaviour of fresh water columnar grained S-2 ice[J].Cold Regions Science&Technology,2000,31(31):59-81.
[58]Polach R V B U,Ehlers S.Model scale ice-Part B:Numerical model[J].Cold Regions Science&Technology,2013,94(10):53-60.
[59]Kolari K.A complete three-dimensional continuum model of wing-crack growth in granular brittle solids[J].International Journal of Solids&Structures,2017.
[60]Wong Chee K,Brown T G.A three-dimensional model for ice rubble pile-ice sheet-conical structure interaction at the piers of confederation bridge,Canada[J].Journal of Offshore Mechanics and Arctic Engineering,2018,140(5):051501.
[61]Liu Z,Amdahl J.A new formulation of the impact mechanics of ship collisions and its application to a ship-iceberg collision[J].Marine Structures,2010,23(3):360-384.
[62]Liu Z,Amdahl J,L覬set S.Integrated numerical analysis of an iceberg collision with a foreship structure[J].Marine Structures,2011,24(4):377-395.
[63]Gagnon R E.A numerical model of ice crushing using a foam analogue[J].Cold Regions Science&Technology,2011,65(3):335-350.
[64]Metrikin I,Lu W,Lubbad R,et al.Numerical simulation of a floater in a broken-ice field:Part I-Model description[C].ASME 2012,International Conference on Ocean,Offshore and Arctic Engineering,2012:579-588.
[65]Drover E,Kenny S.Finite element modeling of iceberg interaction with subsea protection structures[C].OTC Arctic Technology Conference.Offshore Technology Conference,2012,1:468-478.
[66]Ralph F,Soper S,Stuckey P,et al.Impact loads and protection of subsea structures on the seabed from floating iceberg keels[C].OTC Arctic Technology Conference.Offshore Technology Conference,2012,2:738-750.
[67]Ren Huilong,Wang Chuan,Li Hui,et al.Research of vertical bending moment in amidships calculation method caused by the crash-breaking way[J].Journal of Ship Mechanics,2014,18(9):1109-1116.
[68]翟帅帅,李辉,王川,等.不同本构模型对船冰相互作用的影响[J].舰船科学技术,2014(6):20-25.Zhai Shuaishuai,Li Hui,Wang Chuan,et al.The effect of different constitutive modeling on ship-ice interaction[J].Ship Science and Technology,2014(6):20-25.
[69]武文华,于佰杰,岳前进,等.JZ20-2NW平台抗冰性能的有限元分析[J].中国海洋平台,2007,22(6):25-28.Wu Wnhua,Yu Baijie,Yue Qianjin,et al.FEM analysis for ice-induced vibration of JZ20-2NW platform[J].China Offshore Platform,2007,22(6):25-28.
[70]韩雷,李锋,岳前进.冰-锥相互作用破坏全过程的有限元模拟[J].中国海洋平台,2007,22(2):22-27.Han Lei,Li Feng,Yue Qianjin,et al.Simulation of the whole failure process by FEM during ice-conical structures interaction[J].China Offshore Plarform,2007,22(2):22-27.
[71]Zhang D,Wang G,Yue Q.Evaluation of ice-induced fatigue life for a vertical offshore structure in the Bohai Sea[J].Cold Regions Science and Technology,2018,154:103-110.
[72]Shi C,Hu Z,Ringsberg J,et al.Validation of a temperature-gradient-dependent elastic-plastic material model of ice with finite element simulations[J].Cold Regions Science&Technology,2016,133(1):15-25.
[73]宋安,卢海,汪震宇,等.斜面结构上冰载荷的模型试验与有限元分析[J].天津大学学报,2006,39(B06):393-397.Song An,Lu Hai,Wang Zhenyu,et al.Model test and finite element analysis of ice load on sloping structure[J].Journal of Tianjin University,2006,39(B06):393-397.
[74]宋艳平,张爱锋.舷侧结构与冰碰撞的有限元仿真方法[J].大连海事大学学报,2013(4):42-46.Song Yanping,Zhang Aifeng.Finite element simulation method based ship side structure collision with ice[J].Journal of Dalian Maritime University,2013(4):42-46.
[75]Golding N,Schulson E M,Renshaw C E.Shear faulting and localized heating in ice:The influence of confinement[J].Acta Materialia,2010,58(15):5043-5056.
[76]Schulson E M.Compressive shear faults in ice:plastic vs.Coulombic faults[J].Acta Materialia,2002,50(13):3415-3424.
[77]Renshaw C E,Golding N,Schulson E M.Maps for brittle and brittle-like failure in ice[J].Cold Regions Science&Technology,2014,97:1-6.
[78]Derradji-Aouat A.A unified failure envelope for isotropic fresh water ice and iceberg ice[C].Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering,2000.
[79]Derradji-Aouat A,Sarzynski M,Cordes R.Iceberg ice constitutive modeling and FEA validation[C].OTC Arctic Technology Conference.Offshore Technology Conference,2015.
[80]Derradji-Aouat A.Multi-surface failure criterion for saline ice in the brittle regime[J].Cold Regions Science&Technology,2003,36(1-3):47-70.
[81]Martonen P,Derradji-Aouat A,M覿覿tt覿nen M,et al.Non-linear finite elements simulations of level ice forces on offshore structures using a multi surface failure criterion[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2003.
[82]Schulson E M.Brittle failure of ice[J].Engineering Fracture Mechanics,2001,68(17-18):1839-1887.
[83]Kolari K,Kuutti J,Kurkela J.FE-simulation of continuous ice failure based on model update technique[C]//Power and Energy Engineering Conference,2009.APPEEC 2009.Asia-Pacific.IEEE,2009:1-4.
[84]Jordaan I,Li C,Barrette P,et al.Mechanisms of ice softening under high pressure and shear[C].Proceedings of the International Conference on Port and Ocean Engineering Under Arctic Conditions,2005:249-260.
[85]Goldstein R V,Osipenko N M.On an ice failure model with a large contact region[J].Mechanics of Solids,2011,46(1):109-122.
[86]Gürtner A.Ice model tests as a basis for calibrating numerical ice-structure interaction models[C]//Proceedings of the HY-DRALAB III Joint User Meeting.Hannover,2010,1.
[87]Hilding D,Forsberg J,Gürtner A.Simulation of ice action loads on offshore structures[C]//8th European LS-DYNAUsers Conference.Strasbourg,France,2011:1-12.
[88]Lu W,Lubbad R,L覬set S.Simulating ice-sloping structure interactions with the cohesive element method[J].Journal of Offshore Mechanics and Arctic Engineering,2014,136(3):031501.
[89]Wang F,Zou Z J,Zhou L,et al.A simulation study on the interaction between sloping marine structure and level ice based on cohesive element model[J].Cold Regions Science&Technology,2018,149.
[90]Gribanov I,Taylor R,Sarracino R.Cohesive zone micromechanical model for compressive and tensile failure of polycrystalline ice[J].Engineering Fracture Mechanics,2018.
[91]Selvadurai A P S,Sepehr K.Two-dimensional discrete element simulations of ice-structure interaction[J].International Journal of Solids&Structures,1999,36(31-32):4919-4940.
[92]Dorival O,Metrikine A,Simone A.A lattice model to simulate ice-structure interaction[C].ASME,International Conference on Offshore Mechanics and Arctic Engineering.2008:989-996.
[93]Riikil覿T I,Tallinen T,魡str觟m J,et al.A discrete-element model for viscoelastic deformation and fracture of glacial ice[J].Computer Physics Communications,2015,195:14-22.
[94]Tuhkuri J,Poloj覿rvi A.A review of discrete element simulation of ice-structure interaction[J].Philosophical Transactions,2018,376(2129).
[95]Ranta J,Poloj覿rvi A,Tuhkuri J.Limit mechanisms for ice loads on inclined structures:Buckling[J].Cold Regions Science&Technology,2017,147.
[96]Ranta J,Poloj覿rvi A,Tuhkuri J.Ice loads on inclined marine structures-Virtual experiments on ice failure process evolution[J].Marine Structures,2018,57:72-86.
[97]Poloj覿rvi A,Tuhkuri J A.Pustogvar.DEM simulations of direct shear box experiments of ice rubble:Force chains and peak loads[J].Cold Regions Science&Technology,2015,116:12-23.
[98]Gong H,Poloj覿rvi A,Tuhkuri J.Preliminary 3D DEM simulations on ridge keel resistance on ships[C].POAC,2017.
[99]Sun S,Shen H H.Simulation of pancake ice load on a circular cylinder in a wave and current field[J].Cold Regions Science&Technology,2012,78(4):21-4.
[100]Hansen E H,L覬set S.Modelling floating offshore units moored in broken ice:Model description[J].Cold Regions Science&Technology,1999,29(2):97-106.
[101]Lau M,Lawrence K P,Rothenburg L.Discrete element analysis of ice loads on ships and structures[J].Ships&Offshore Structures,2011,6(3):211-221.
[102]Yulmetov R,Lubbad R,L覬set S.Planar multi-body model of iceberg free drift and towing in broken ice[J].Cold Regions Science&Technology,2015,121:154-166.
[103]Hopkins M A.Discrete element modeling with dilated particles[J].Engineering Computations,2004,21(2/3/4):422-430.
[104]Hopkins M A,Shen H H.Simulation of pancake-ice dynamics in a wave field[J].Annals of Glaciology,2000,33(1):355-360.
[105]L覬set S.Discrete element modelling of a broken ice field-Part I:Model development[J].Cold Regions Science&Technology,1994,22(4):339-347.
[106]季顺迎,李春花,刘煜.海冰离散元模型的研究回顾及展望[J].极地研究,2012,24(4):315-330.Ji Shunying,Li Chunhua,Liu Yu.A review of advances in sea-ice discrete element models[J].Chinese Journal of Polar Research,2012,24(4):315-330.
[107]季顺迎,李紫麟,李春花,等.碎冰区海冰与船舶结构相互作用的离散元分析[J].应用力学学报,2013(4):520-526.Ji Shunying,Li Zilin,Li Chunhua,et al.The study of ice induced vibration on marine platforms by dynamic model test[J].Chinese Journal of Applied Mechanics,2013(4):520-526.
[108]季顺迎,狄少丞,李正,等.海冰与直立结构相互作用的离散单元数值模拟[J].工程力学,2013(1):463-469.Ji Shunying,Di Shaocheng,Li Zheng,et al.Discrete element modeling of interaction between sea ice and vertical offshore structures[J].Engineering Mechnics,2013(1):463-469.
[109]Ji S,Di S,Liu S.Analysis of ice load on conical structure with discrete element method[J].Engineering Computations,2015,32(4):1121-1134.
[110]Jordaan I,Li C,Sudom D,et al.Principles for local and global ice design using pressure-area relationships[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2005:375-386.
[111]Jordaan I,Frederking R,Li C.Mechanics of ice compressive failure,probabilistic averaging and design load estimation[C].Proceedings 18th International Symposium on Ice.IAHR’06,2006,1:223-230.
[112]Jordaan I,Li C,Frederking R.Simulation of probabilistic averaging in ice load estimation[C].IAHA’06,2006,2:215-222.
[113]Kujala P,Suominen M,Riska K.Statistics of ice loads measured on MT Uikku in the Baltic[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2009:PAOC09-51.
[114]Suyuthi A,Leira B J,Riska K.A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields[J].Cold Regions Science&Technology,2014,97(10):7-20.
[115]Stuckey P,Ralph F,Jordaan I.Iceberg design load methodology[C].International Conference and Exhibition on Performance of Ships and Structures in Ice 2008.ICETECH,2008:225-232.
[116]Taylor R S,Jordaan I J.Probabilistic fracture mechanics analysis of spalling during edge indentation in ice[J].Engineering Fracture Mechanics,2014,134:242-266.
[117]Thijssen J,Fuglem M,Richard M,et al.Implementation of ISO 19906 for probabilistic assessment of global sea ice loads on offshore structures encountering first-year sea ice[C].Oceans-St.John’s.IEEE,2014:1-8.
[118]Paavilainen J,Tuhkuri J.Parameter effects on simulated ice rubbling forces on a wide sloping structure[J].Cold Regions Science&Technology,2012,81(5):1-10.
[119]Paavilainen J,Tuhkuri J.Pressure distributions and force chains during simulated ice rubbling against sloped structures[J].Cold Regions Science&Technology,2013,85:157-174.
[120]Paavilainen J,Tuhkuri J,Poloj覿rvi A.2D numerical simulations of ice rubble formation process against an inclined structure[J].Cold Regions Science&Technology,2011,68(1-2):20-34.
[121]Paavilainen J,Tuhkuri J,Poloj覿rvi A.2D combined finite-discrete element method to model multi-fracture of beam structures[J].Engineering Computations,2009,26(6):578-598.
[122]邵帅,周国丰,王帅霖,等.基于离散元-有限元模型的冰激锥体海洋平台结构振动分析[J].计算力学学报,2015,32(5):662-667.Shao Shuai,Zhou Guofeng,Wang Shuailin,et al.Ice induced vibration of concial offshore platform structure based on discrete element model-finite element model[J].Chinise Journal of Computational Mechanics,2015,32(5):662-667.
[123]王帅霖,邵帅,季顺迎.冰激海洋平台结构振动的离散元-有限元耦合分析[C].2014颗粒材料计算力学会议论文集,2014:241-245.Wang Shuailin,Shao Shuai,Ji Shunying.DEM-FEM analysis of ice-induced vibration of offshore platform structure[C].2014 Proceedings of Conference of Computational Mechanics of Granular Materials,2014:241-245.
[124]Ehlers S,Tabri K.A combined numerical and semi-analytical collision damage assessment procedure[J].Marine Structures,2012,28(1):101-119.
[125]薛彦卓,陆锡奎,王庆,等.冰三点弯曲试验的近场动力学数值模拟[J].哈尔滨工程大学学报,2018,39(4):607-613.Xue Yanzhuo,Lu Xikui,Wang Qing.Simulation of three-point bending test of ice based on peridynamic[J].Journal of Harbin Engineering University,2018,39(4):607-613.
[126]Liu R W,Xue Y Z,Lu X K,et al.Simulation of ship navigation in ice rubble based on peridynamics[J].Ocean Engineering,2018,148:286-298.
[127]Wang Qing,Wang Yi,Yuan Lihao,et al.Simulation of brittle-ice contacting with stiffened plate with peridynamics[J].Journal of Ship Mechanics,2018,22(3):339-352.
[128]Ye L Y,Wang C,Chang X,et al.Propeller-ice contact modeling with peridynamics[J].Ocean Engineering,2017,139:54-64.
[129]Robb D M,Gaskin S J,Marongiu J C.SPH-DEM model for free-surface flows containing solids applied to river ice jams[J].Journal of Hydraulic Research,2016,54(1):27-40.
[2]Liu Z.Analytical and numerical analysis of iceberg collisions with ship structures[D].Doctor thesis,Norwegian University of Science and Technology,2011.
[3]Jordaan I J.Mechanics of ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17-18):1923-1960.
[4]Michel B,Toussaint N.Mechanisms and theory of indentation of ice plates[J].Journal of Glaciology,1978,19:285-300.
[5]Sodhi D S.Crushing failure during ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17):1889-1921.
[6]Li C,Barrette P,Jordaan I.High pressure zones at different scales during ice-structure indentation[C]//ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering.American Society of Mechanical Engineers,2004:887-894.
[7]Browne T,Taylor R,Jordaan I,et al.Small-scale ice indentation tests with variable structural compliance[J].Cold Regions Science&Technology,2013,88(88):2-9.
[8]Taylor R S,Jordaan I J.Damage and fracture during contact between a spherical indenter and ice:experimental results and finite element simulations[J].Key Engineering Materials,2014,577-578:609-612.
[9]Kim E,Golding N,Schulson E M,et al.Mechanisms governing failure of ice beneath a spherically-shaped indenter[J].Cold Regions Science&Technology,2012,78(4):46-63.
[10]Wells J,Jordaan I.Small-scale laboratory experiments on the indentation failure of polycrystalline ice in compression:Main results and pressure distribution[J].Cold Regions Science&Technology,2011,65(3):314-325.
[11]Sopper R,Daley C,Colbourne B,et al.The influence of external boundary conditions on ice loads in ice-structure interactions[C].ASME 2016,International Conference on Ocean,Offshore and Arctic Engineering,2016:V008T07A007.
[12]Sopper R,Daley C,Colbourne B,et al.The influence of water,snow and granular ice on ice failure processes,ice load magnitude and process pressure[J].Cold Regions Science&Technology,2017,139.
[13]O’Rourke B J,Jordaan I J,Taylor R S,Gürtner A.Experimental investigation of oscillation of loads in ice high-pressure zones,part 1:Single indentor system[J].Cold Regions Science and Technology,2016,124:25-39.
[14]Timco G W,Weeks W F.A review of the engineering properties of sea ice[J].Cold Regions Science&Technology,2010,60(2):107-129.
[15]Timco G W,Frederking R M W.Confined compression tests:Outlining the failure envelope of columnar sea ice[J].Cold Regions Science&Technology,1986,12(1):13-28.
[16]Riska K,Frederking R M W.Ice load penetration modelling[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,1987:317-327.
[17]马健钧.海冰弯曲破坏的数值模拟方法研究[D].天津:天津大学,2013.Ma Jianjun.Methodology research on the numerical simulation of the bending failure of sea ice[D].Tianjin:Tianjin University,2013.
[18]Jones S J.High strain-rate compression tests on ice[J].The Journal of Physical Chemistry B,1997,101(32):6099-6101.
[19]Jones S J,Gagnon R E,Derradji A,et al.Compressive strength of iceberg ice[J].Canadian Journal of Physics,2003,81(1-2):191-200.
[20]Barrette P D,Jordaan I J.Pressure-temperature effects on the compressive behavior of laboratory-grown and iceberg ice[J].Cold Regions Science&Technology,2003,36(1-3):25-36.
[21]Sinha N K,Cai B.Elasto-delayed-elastic simulation of short-term deflection of fresh-water ice covers[J].Cold Regions Science&Technology,1996,24(2):221-235.
[22]Gagnon R E,Gammon P H.Triaxial experiments on iceberg and glacier ice[J].Journal of Glaciology,1995,41(139):528-540.
[23]Gratz E T,Schulson E M.Brittle failure of columnar saline ice under triaxial compression[J].Journal of Geophysical Research Solid Earth,1997,102(B3):5091-5107.
[24]Weiss J,Schulson E M.The failure of fresh-water granular ice under multiaxial compressive loading[J].Acta Metallurgica Et Materialia,1995,43(6):2303-2315.
[25]Timco G W,Frederking R M W.An investigation of the failure envelope of granular/discontinuous-columnar sea ice[J].Cold Regions Science&Technology,1984,9(1):17-27.
[26]Schulson E M,Nickolayev O Y.Failure of columnar saline ice under biaxial compression:Failure envelopes and the brittle-to-ductile transition[J].Journal of Geophysical Research Solid Earth,1995,100(B11):22383-22400.
[27]Smith T R,Schulson E M.The brittle compressive failure of fresh-water columnar ice under biaxial loading[J].Acta Metallurgica Et Materialia,1993,41(1):153-163.
[28]Smith T R,Schulson E M.Brittle compressive failure of salt-water columnar ice under biaxial loading[J].Journal of Glaciology,1994,40(135):265-276.
[29]Schwarz J,Weeks W F.Engineering properties of sea ice[J].Journal of Glaciology,1977,19(81):499-531.
[30]von Bock R U F,Polach.Numerical analysis of the bending strength of model-scale ice[J].Cold Regions Science&Technology,2015,118:91-104.
[31]Han H,Jia Q,Huang W,et al.Flexural strength and effective modulus of large columnar-grained freshwater ice[J].Journal of Cold Regions Engineering,2015,30(2):04015005.
[32]Svec O J,Frederking R M W.Cantilever beam tests in an ice cover:Influence of plate effects at the root[J].Cold Regions Science and Technology,1981,4(2):93-101.
[33]Timco G W,Frederking R M W.Comparative strengths of fresh water ice[J].Cold Regions Science and Technology,1982,6(1):21-27.
[34]Frederking R M W,Svec O J.Stress-relieving techniques for cantilever beam tests in an ice cover[J].Cold Regions Science and Technology,1985,11(3):247-253.
[35]Gagnon R E,Gammon P H.Characterization and flexural strength of iceberg and glacier ice[J].Journal of Glaciology,1995,41(137):103-111.
[36]Barrette P,Jordaan I.Beam bending and fracture behaviour of iceberg ice[C].National Research Council Program on Energy Research and Development(PERD),2001:4-78.
[37]季顺迎,王安良,苏洁,等.环渤海海冰弯曲强度的试验测试及特性分析[J].水科学进展,2011,22(2):266-272.Ji Shunying,Wang Anliang,Su Jie,et al.Experimental studies and characteristics analysis of sea ice flexural strength around the Bohai Sea[J].Advances in Water Science,2011,22(2):266-272.
[38]季顺迎,刘宏亮,许宁,等.渤海海冰断裂韧度试验[J].水科学进展,2013,24(3):386-391.Ji Shunying,Liu Hongliang,Xu Ning,et al.Experiments on sea ice fracture toughness in the Bohai Sea[J].Advances in Water Science,2013,24(3):386-391.
[39]Ralph F,Mckenna R,Gagnon R.Iceberg characterization for the bergy bit impact study[J].Cold Regions Science&Technology,2008,52(1):7-28.
[40]Gagnon R,Cumming D,Ritch R,et al.Overview accompaniment for papers on the bergy bit impact trials[J].Cold Regions Science&Technology,2008,52(1):1-6.
[41]Johnston,M,Timco,et al.Measuring global impact forces on the CCGS Terry Fox with an inertial measurement system called MOTAN[J].Cold Regions Science&Technology,2008,52(1):67-82.
[42]Johnston M,Ritch R,Gagnon R,et al.Comparison of impact forces measured by different instrumentation systems on the CCGS Terry Fox during the Bergy Bit Trials[J].Cold Regions Science&Technology,2008,52(1):83-97.
[43]Gagnon R.Analysis of data from bergy bit impacts using a novel hull-mounted external impact panel[J].Cold Regions Science&Technology,2008,52(1):50-66.
[44]Timco G W.Isolated ice floe impacts[J].Cold Regions Science&Technology,2011,68(1):35-48.
[45]M覿覿tt覿nen M,Marjavaara P,Saarinen S,et al.Ice crushing tests with variable structural flexibility[J].Cold Regions Science&Technology,2011,67(3):120-128.
[46]史庆增,徐继祖,宋安.海冰作用力的模拟试验[J].海洋工程,1991(1):16-22.Shi Qingzeng,Xu Jizu,Song An.The modeling test of the sea ice forces[J].Ocean Engineering,1991(1):16-22.
[47]黄焱.冰激海洋平台振动的动力模型试验研究[D].天津:天津大学,2004.Huang Yan.The study of ice induced vibration on marine platforms by dynamic model test[D].Tianjin:Tianjin University,2004.
[48]Sinha N K.Rheology of columnar-grained ice[J].Experimental Mechanics,1978,18(12):464-470.
[49]Karr D G,Choi K.A three-dimensional constitutive damage model for polycrystalline ice[J].Mechanics of Materials,1989,8(1):55-66.
[50]Ralston T D.Yield and plastic deformation in ice crushing failure[C].Proceeding of the Arctic Ice Dynamics Joint Experiment International Commission on Snow and Ice Symposium,1980:234-245.
[51]Jordaan I J,Stone B M,Mckenna R F,et al.Effect of microcracking on the deformation of ice[J].Canadian Geotechnical Journal,2011,29(1):143-150.
[52]Lade P V.Characterization of the mechanical behavior of sea ice as a frictional material[J].Journal of Geophysical Research Atmospheres,2002,107(B12):ECV 10-1-ECV 10-10.
[53]Lade P V.Modeling sea ice as an elasto-plastic frictional material[C]//IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics.Springer Netherlands,2001:227-238.
[54]Singh S K,Jordaan I J.Constitutive behaviour of crushed ice[J].International Journal of Fracture,1999,97(1):171-187.
[55]Keller A,Hutter K.A viscoelastic damage model for polycrystalline ice,inspired by Weibull-distributed fiber bundle models.Part I:Constitutive models[J].Continuum Mechanics&Thermodynamics,2014,26(6):879-894.
[56]Jordaan I J.Mechanics of ice-structure interaction[J].Engineering Fracture Mechanics,2001,68(17-18):1923-1960.
[57]Derradji-Aouat A,Sinha N K,Evgin E.Mathematical modelling of monotonic and cyclic behaviour of fresh water columnar grained S-2 ice[J].Cold Regions Science&Technology,2000,31(31):59-81.
[58]Polach R V B U,Ehlers S.Model scale ice-Part B:Numerical model[J].Cold Regions Science&Technology,2013,94(10):53-60.
[59]Kolari K.A complete three-dimensional continuum model of wing-crack growth in granular brittle solids[J].International Journal of Solids&Structures,2017.
[60]Wong Chee K,Brown T G.A three-dimensional model for ice rubble pile-ice sheet-conical structure interaction at the piers of confederation bridge,Canada[J].Journal of Offshore Mechanics and Arctic Engineering,2018,140(5):051501.
[61]Liu Z,Amdahl J.A new formulation of the impact mechanics of ship collisions and its application to a ship-iceberg collision[J].Marine Structures,2010,23(3):360-384.
[62]Liu Z,Amdahl J,L覬set S.Integrated numerical analysis of an iceberg collision with a foreship structure[J].Marine Structures,2011,24(4):377-395.
[63]Gagnon R E.A numerical model of ice crushing using a foam analogue[J].Cold Regions Science&Technology,2011,65(3):335-350.
[64]Metrikin I,Lu W,Lubbad R,et al.Numerical simulation of a floater in a broken-ice field:Part I-Model description[C].ASME 2012,International Conference on Ocean,Offshore and Arctic Engineering,2012:579-588.
[65]Drover E,Kenny S.Finite element modeling of iceberg interaction with subsea protection structures[C].OTC Arctic Technology Conference.Offshore Technology Conference,2012,1:468-478.
[66]Ralph F,Soper S,Stuckey P,et al.Impact loads and protection of subsea structures on the seabed from floating iceberg keels[C].OTC Arctic Technology Conference.Offshore Technology Conference,2012,2:738-750.
[67]Ren Huilong,Wang Chuan,Li Hui,et al.Research of vertical bending moment in amidships calculation method caused by the crash-breaking way[J].Journal of Ship Mechanics,2014,18(9):1109-1116.
[68]翟帅帅,李辉,王川,等.不同本构模型对船冰相互作用的影响[J].舰船科学技术,2014(6):20-25.Zhai Shuaishuai,Li Hui,Wang Chuan,et al.The effect of different constitutive modeling on ship-ice interaction[J].Ship Science and Technology,2014(6):20-25.
[69]武文华,于佰杰,岳前进,等.JZ20-2NW平台抗冰性能的有限元分析[J].中国海洋平台,2007,22(6):25-28.Wu Wnhua,Yu Baijie,Yue Qianjin,et al.FEM analysis for ice-induced vibration of JZ20-2NW platform[J].China Offshore Platform,2007,22(6):25-28.
[70]韩雷,李锋,岳前进.冰-锥相互作用破坏全过程的有限元模拟[J].中国海洋平台,2007,22(2):22-27.Han Lei,Li Feng,Yue Qianjin,et al.Simulation of the whole failure process by FEM during ice-conical structures interaction[J].China Offshore Plarform,2007,22(2):22-27.
[71]Zhang D,Wang G,Yue Q.Evaluation of ice-induced fatigue life for a vertical offshore structure in the Bohai Sea[J].Cold Regions Science and Technology,2018,154:103-110.
[72]Shi C,Hu Z,Ringsberg J,et al.Validation of a temperature-gradient-dependent elastic-plastic material model of ice with finite element simulations[J].Cold Regions Science&Technology,2016,133(1):15-25.
[73]宋安,卢海,汪震宇,等.斜面结构上冰载荷的模型试验与有限元分析[J].天津大学学报,2006,39(B06):393-397.Song An,Lu Hai,Wang Zhenyu,et al.Model test and finite element analysis of ice load on sloping structure[J].Journal of Tianjin University,2006,39(B06):393-397.
[74]宋艳平,张爱锋.舷侧结构与冰碰撞的有限元仿真方法[J].大连海事大学学报,2013(4):42-46.Song Yanping,Zhang Aifeng.Finite element simulation method based ship side structure collision with ice[J].Journal of Dalian Maritime University,2013(4):42-46.
[75]Golding N,Schulson E M,Renshaw C E.Shear faulting and localized heating in ice:The influence of confinement[J].Acta Materialia,2010,58(15):5043-5056.
[76]Schulson E M.Compressive shear faults in ice:plastic vs.Coulombic faults[J].Acta Materialia,2002,50(13):3415-3424.
[77]Renshaw C E,Golding N,Schulson E M.Maps for brittle and brittle-like failure in ice[J].Cold Regions Science&Technology,2014,97:1-6.
[78]Derradji-Aouat A.A unified failure envelope for isotropic fresh water ice and iceberg ice[C].Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering,2000.
[79]Derradji-Aouat A,Sarzynski M,Cordes R.Iceberg ice constitutive modeling and FEA validation[C].OTC Arctic Technology Conference.Offshore Technology Conference,2015.
[80]Derradji-Aouat A.Multi-surface failure criterion for saline ice in the brittle regime[J].Cold Regions Science&Technology,2003,36(1-3):47-70.
[81]Martonen P,Derradji-Aouat A,M覿覿tt覿nen M,et al.Non-linear finite elements simulations of level ice forces on offshore structures using a multi surface failure criterion[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2003.
[82]Schulson E M.Brittle failure of ice[J].Engineering Fracture Mechanics,2001,68(17-18):1839-1887.
[83]Kolari K,Kuutti J,Kurkela J.FE-simulation of continuous ice failure based on model update technique[C]//Power and Energy Engineering Conference,2009.APPEEC 2009.Asia-Pacific.IEEE,2009:1-4.
[84]Jordaan I,Li C,Barrette P,et al.Mechanisms of ice softening under high pressure and shear[C].Proceedings of the International Conference on Port and Ocean Engineering Under Arctic Conditions,2005:249-260.
[85]Goldstein R V,Osipenko N M.On an ice failure model with a large contact region[J].Mechanics of Solids,2011,46(1):109-122.
[86]Gürtner A.Ice model tests as a basis for calibrating numerical ice-structure interaction models[C]//Proceedings of the HY-DRALAB III Joint User Meeting.Hannover,2010,1.
[87]Hilding D,Forsberg J,Gürtner A.Simulation of ice action loads on offshore structures[C]//8th European LS-DYNAUsers Conference.Strasbourg,France,2011:1-12.
[88]Lu W,Lubbad R,L覬set S.Simulating ice-sloping structure interactions with the cohesive element method[J].Journal of Offshore Mechanics and Arctic Engineering,2014,136(3):031501.
[89]Wang F,Zou Z J,Zhou L,et al.A simulation study on the interaction between sloping marine structure and level ice based on cohesive element model[J].Cold Regions Science&Technology,2018,149.
[90]Gribanov I,Taylor R,Sarracino R.Cohesive zone micromechanical model for compressive and tensile failure of polycrystalline ice[J].Engineering Fracture Mechanics,2018.
[91]Selvadurai A P S,Sepehr K.Two-dimensional discrete element simulations of ice-structure interaction[J].International Journal of Solids&Structures,1999,36(31-32):4919-4940.
[92]Dorival O,Metrikine A,Simone A.A lattice model to simulate ice-structure interaction[C].ASME,International Conference on Offshore Mechanics and Arctic Engineering.2008:989-996.
[93]Riikil覿T I,Tallinen T,魡str觟m J,et al.A discrete-element model for viscoelastic deformation and fracture of glacial ice[J].Computer Physics Communications,2015,195:14-22.
[94]Tuhkuri J,Poloj覿rvi A.A review of discrete element simulation of ice-structure interaction[J].Philosophical Transactions,2018,376(2129).
[95]Ranta J,Poloj覿rvi A,Tuhkuri J.Limit mechanisms for ice loads on inclined structures:Buckling[J].Cold Regions Science&Technology,2017,147.
[96]Ranta J,Poloj覿rvi A,Tuhkuri J.Ice loads on inclined marine structures-Virtual experiments on ice failure process evolution[J].Marine Structures,2018,57:72-86.
[97]Poloj覿rvi A,Tuhkuri J A.Pustogvar.DEM simulations of direct shear box experiments of ice rubble:Force chains and peak loads[J].Cold Regions Science&Technology,2015,116:12-23.
[98]Gong H,Poloj覿rvi A,Tuhkuri J.Preliminary 3D DEM simulations on ridge keel resistance on ships[C].POAC,2017.
[99]Sun S,Shen H H.Simulation of pancake ice load on a circular cylinder in a wave and current field[J].Cold Regions Science&Technology,2012,78(4):21-4.
[100]Hansen E H,L覬set S.Modelling floating offshore units moored in broken ice:Model description[J].Cold Regions Science&Technology,1999,29(2):97-106.
[101]Lau M,Lawrence K P,Rothenburg L.Discrete element analysis of ice loads on ships and structures[J].Ships&Offshore Structures,2011,6(3):211-221.
[102]Yulmetov R,Lubbad R,L覬set S.Planar multi-body model of iceberg free drift and towing in broken ice[J].Cold Regions Science&Technology,2015,121:154-166.
[103]Hopkins M A.Discrete element modeling with dilated particles[J].Engineering Computations,2004,21(2/3/4):422-430.
[104]Hopkins M A,Shen H H.Simulation of pancake-ice dynamics in a wave field[J].Annals of Glaciology,2000,33(1):355-360.
[105]L覬set S.Discrete element modelling of a broken ice field-Part I:Model development[J].Cold Regions Science&Technology,1994,22(4):339-347.
[106]季顺迎,李春花,刘煜.海冰离散元模型的研究回顾及展望[J].极地研究,2012,24(4):315-330.Ji Shunying,Li Chunhua,Liu Yu.A review of advances in sea-ice discrete element models[J].Chinese Journal of Polar Research,2012,24(4):315-330.
[107]季顺迎,李紫麟,李春花,等.碎冰区海冰与船舶结构相互作用的离散元分析[J].应用力学学报,2013(4):520-526.Ji Shunying,Li Zilin,Li Chunhua,et al.The study of ice induced vibration on marine platforms by dynamic model test[J].Chinese Journal of Applied Mechanics,2013(4):520-526.
[108]季顺迎,狄少丞,李正,等.海冰与直立结构相互作用的离散单元数值模拟[J].工程力学,2013(1):463-469.Ji Shunying,Di Shaocheng,Li Zheng,et al.Discrete element modeling of interaction between sea ice and vertical offshore structures[J].Engineering Mechnics,2013(1):463-469.
[109]Ji S,Di S,Liu S.Analysis of ice load on conical structure with discrete element method[J].Engineering Computations,2015,32(4):1121-1134.
[110]Jordaan I,Li C,Sudom D,et al.Principles for local and global ice design using pressure-area relationships[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2005:375-386.
[111]Jordaan I,Frederking R,Li C.Mechanics of ice compressive failure,probabilistic averaging and design load estimation[C].Proceedings 18th International Symposium on Ice.IAHR’06,2006,1:223-230.
[112]Jordaan I,Li C,Frederking R.Simulation of probabilistic averaging in ice load estimation[C].IAHA’06,2006,2:215-222.
[113]Kujala P,Suominen M,Riska K.Statistics of ice loads measured on MT Uikku in the Baltic[C].Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions,2009:PAOC09-51.
[114]Suyuthi A,Leira B J,Riska K.A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields[J].Cold Regions Science&Technology,2014,97(10):7-20.
[115]Stuckey P,Ralph F,Jordaan I.Iceberg design load methodology[C].International Conference and Exhibition on Performance of Ships and Structures in Ice 2008.ICETECH,2008:225-232.
[116]Taylor R S,Jordaan I J.Probabilistic fracture mechanics analysis of spalling during edge indentation in ice[J].Engineering Fracture Mechanics,2014,134:242-266.
[117]Thijssen J,Fuglem M,Richard M,et al.Implementation of ISO 19906 for probabilistic assessment of global sea ice loads on offshore structures encountering first-year sea ice[C].Oceans-St.John’s.IEEE,2014:1-8.
[118]Paavilainen J,Tuhkuri J.Parameter effects on simulated ice rubbling forces on a wide sloping structure[J].Cold Regions Science&Technology,2012,81(5):1-10.
[119]Paavilainen J,Tuhkuri J.Pressure distributions and force chains during simulated ice rubbling against sloped structures[J].Cold Regions Science&Technology,2013,85:157-174.
[120]Paavilainen J,Tuhkuri J,Poloj覿rvi A.2D numerical simulations of ice rubble formation process against an inclined structure[J].Cold Regions Science&Technology,2011,68(1-2):20-34.
[121]Paavilainen J,Tuhkuri J,Poloj覿rvi A.2D combined finite-discrete element method to model multi-fracture of beam structures[J].Engineering Computations,2009,26(6):578-598.
[122]邵帅,周国丰,王帅霖,等.基于离散元-有限元模型的冰激锥体海洋平台结构振动分析[J].计算力学学报,2015,32(5):662-667.Shao Shuai,Zhou Guofeng,Wang Shuailin,et al.Ice induced vibration of concial offshore platform structure based on discrete element model-finite element model[J].Chinise Journal of Computational Mechanics,2015,32(5):662-667.
[123]王帅霖,邵帅,季顺迎.冰激海洋平台结构振动的离散元-有限元耦合分析[C].2014颗粒材料计算力学会议论文集,2014:241-245.Wang Shuailin,Shao Shuai,Ji Shunying.DEM-FEM analysis of ice-induced vibration of offshore platform structure[C].2014 Proceedings of Conference of Computational Mechanics of Granular Materials,2014:241-245.
[124]Ehlers S,Tabri K.A combined numerical and semi-analytical collision damage assessment procedure[J].Marine Structures,2012,28(1):101-119.
[125]薛彦卓,陆锡奎,王庆,等.冰三点弯曲试验的近场动力学数值模拟[J].哈尔滨工程大学学报,2018,39(4):607-613.Xue Yanzhuo,Lu Xikui,Wang Qing.Simulation of three-point bending test of ice based on peridynamic[J].Journal of Harbin Engineering University,2018,39(4):607-613.
[126]Liu R W,Xue Y Z,Lu X K,et al.Simulation of ship navigation in ice rubble based on peridynamics[J].Ocean Engineering,2018,148:286-298.
[127]Wang Qing,Wang Yi,Yuan Lihao,et al.Simulation of brittle-ice contacting with stiffened plate with peridynamics[J].Journal of Ship Mechanics,2018,22(3):339-352.
[128]Ye L Y,Wang C,Chang X,et al.Propeller-ice contact modeling with peridynamics[J].Ocean Engineering,2017,139:54-64.
[129]Robb D M,Gaskin S J,Marongiu J C.SPH-DEM model for free-surface flows containing solids applied to river ice jams[J].Journal of Hydraulic Research,2016,54(1):27-40.