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海上单桩风机基础破碎波载荷及其动力响应
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作者 许莲 《广东造船》 2023年第2期100-103,95,共5页
破碎波冲击载荷是极浅水固定式风机基础设计中不可忽略的载荷,但工程实践中对其评估方法并不成熟。本文介绍了海上固定式单桩风机基础在破碎波作用下的准静力和时域冲击力的计算原理和方法,以实际案例为基础,对于不同规范方法计算的破... 破碎波冲击载荷是极浅水固定式风机基础设计中不可忽略的载荷,但工程实践中对其评估方法并不成熟。本文介绍了海上固定式单桩风机基础在破碎波作用下的准静力和时域冲击力的计算原理和方法,以实际案例为基础,对于不同规范方法计算的破碎波冲击力进行了对比,采用SACS软件进行破碎波冲击载荷下的动态响应分析,给出了若干结论和建议,可为同类型项目的结构设计提供借鉴。 展开更多
关键词 海上单桩风机基础 破碎波载荷 动力响应分析
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圆柱型结构内孤立波载荷实验及其理论模型 被引量:32
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作者 黄文昊 尤云祥 +1 位作者 王旭 胡天群 《力学学报》 EI CSCD 北大核心 2013年第5期716-728,共13页
在大型重力式密度分层水槽中,对内孤立波与圆柱型结构的相互作用特性开展了系列实验.基于两层流体中内孤立波的KdV,eKdV和MCC理论,建立了圆柱型结构内孤立波载荷的理论预报模型,给出了该载荷理论预报模型中3类内孤立波理论的适用性条件... 在大型重力式密度分层水槽中,对内孤立波与圆柱型结构的相互作用特性开展了系列实验.基于两层流体中内孤立波的KdV,eKdV和MCC理论,建立了圆柱型结构内孤立波载荷的理论预报模型,给出了该载荷理论预报模型中3类内孤立波理论的适用性条件.研究表明,圆柱型结构内孤立波水平载荷包括水平Froude--Krylov力、附加质量力和拖曳力3个部分,可以由Morison公式计算,而内孤立波垂向载荷主要为垂向Froude--Krylov力,可以由内孤立波诱导动压力计算.系列实验结果表明,附加质量系数可以取为常数1.0,拖曳力系数与内孤立波诱导速度场的雷诺数之间为指数函数关系,而且基于理论预报模型的数值结果与系列实验结果吻合. 展开更多
关键词 两层流体 内孤立 圆柱型结构 内孤立波载荷 Morison公式
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应力波载荷作用下材料断裂韧性测试技术研究进展 被引量:2
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作者 刘瑞堂 姜风春 刘殿魁 《实验力学》 CSCD 北大核心 2000年第2期137-146,共10页
本文对应力波载荷 (加载速率 KI 1 0 6MPa m / s)作用下 ,动态断裂韧性测试技术中的非光学方法进行了较全面和较系统的研究 ,比较了各自的优缺点 ,并对不同方法的可靠性和适用范围进行了分析 .
关键词 动态断裂韧性 测试技术 应力波载荷 材料
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应力波载荷作用下材料断裂韧性J_(Id)测试研究 被引量:2
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作者 刘瑞堂 姜风春 张晓欣 《兵工学报》 EI CAS CSCD 北大核心 2001年第1期115-119,共5页
本文建立了一个测定动态弹塑性断裂韧性 JId的方法。该方法利用改进的 Hopkinson压杆加载 Charpy冲击试样 ,利用压杆上应变片记录的入射应力波和反射应力波 ,由一维应力波理论得到试样所受的载荷和加载点位移。在建立的裂纹尖端张开位移... 本文建立了一个测定动态弹塑性断裂韧性 JId的方法。该方法利用改进的 Hopkinson压杆加载 Charpy冲击试样 ,利用压杆上应变片记录的入射应力波和反射应力波 ,由一维应力波理论得到试样所受的载荷和加载点位移。在建立的裂纹尖端张开位移 COD和裂纹扩展量Δa的关系中 ,令Δa =0 ,可得到裂纹起裂时的临界 ( COD) c从而确定裂纹的动态起裂点。与其它方法相比 ,本文的方法不需要昂贵的仪器来测试动态断裂参数 ;不需将应变片贴在试样上确定起裂时间 ,所以该方法可在较高或较低的温度下使用 ;在动态弹塑性断裂韧性 JId的计算中 ,考虑了材料的动态应力—应变行为 ,使测得的 JId 值能更好地反映材料在应力波载荷作用下的动态断裂性能。 展开更多
关键词 应力波载荷 动态弹塑性断裂韧性 Charpy冲击试样 材料
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应力波载荷作用下线弹性断裂过程的动态分析方法研究 被引量:5
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作者 沙桂英 刘殿魁 +1 位作者 刘瑞堂 姜风春 《爆炸与冲击》 EI CAS CSCD 北大核心 2002年第1期56-60,共5页
利用Hopkinson单压杆实验装置 ,对材料的线弹性动态断裂特性进行了研究 ,建立了应力波载荷作用下动态裂纹起裂及扩展过程的动态分析方法 ,采用该方法可同时测得材料的动态裂纹起裂时间、断裂韧性和裂纹扩展速度。 40Cr钢三点弯曲试样的... 利用Hopkinson单压杆实验装置 ,对材料的线弹性动态断裂特性进行了研究 ,建立了应力波载荷作用下动态裂纹起裂及扩展过程的动态分析方法 ,采用该方法可同时测得材料的动态裂纹起裂时间、断裂韧性和裂纹扩展速度。 40Cr钢三点弯曲试样的实验结果表明 :该钢的动态裂纹扩展过程主要是减速过程 ,在2 2 5TPam /s的加载速率下 ,起裂时间为 2 8 0 0 μs,最大裂纹扩展速度为 478 91m/s ,动态断裂韧性为6 3 12MPam。 展开更多
关键词 应力波载荷 线弹性断裂 动态断裂韧性 裂纹扩展速度 动态分析 材料 Hopkinson单压杆 40CR钢
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应力波载荷作用下弹塑性断裂全过程的动态分析
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作者 沙桂英 杨丽颖 +1 位作者 姜风春 刘瑞堂 《兵工学报》 EI CAS CSCD 北大核心 2003年第3期403-407,共5页
本文利用Hopkinson单压杆实验装置 ,对材料的弹塑性动态断裂特性进行了研究 ,建立了应力波载荷作用下动态裂纹起裂、扩展、止裂全过程的动态分析方法 ,采用该方法可同时测得材料的动态断裂韧性、裂纹扩展速度和止裂韧性。 90 7A钢三点... 本文利用Hopkinson单压杆实验装置 ,对材料的弹塑性动态断裂特性进行了研究 ,建立了应力波载荷作用下动态裂纹起裂、扩展、止裂全过程的动态分析方法 ,采用该方法可同时测得材料的动态断裂韧性、裂纹扩展速度和止裂韧性。 90 7A钢三点弯曲试样的实验结果表明 ,该钢的动态裂纹扩展是先加速后减速过程 ,在 1 4 9× 10 7MPam /s的加载速率下 ,最大裂纹扩展速度为 2 36 13m/s ,动态断裂韧性和止裂韧性分别为JⅠd=5 5 2 .4 2kJ/m2 ,JIa=4 14 .0 5kJ/m2 . 展开更多
关键词 应力波载荷 弹塑性断裂 动态断裂 裂纹 冲击响应 韧性 907A钢
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爆轰马赫波载荷特性及传播规律实验研究 被引量:1
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作者 曹兵 余志勇 陈惠武 《弹道学报》 CSCD 北大核心 2000年第2期78-83,共6页
利用相同装药品号 ,相同装药密度 ,不同装药直径 ,不同装药高度的园柱形装药 ,端面两点对称布置 ,同时起爆情况下的紫铜平板药型罩压痕实验 ,及对实验结果的数据处理 。
关键词 起爆 马赫 载荷特性 传播规律 实验
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应力波加载条件下907A钢-20℃时的动态断裂与止裂研究 被引量:15
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作者 沙桂英 刘瑞堂 +1 位作者 刘殿魁 姜风春 《哈尔滨工程大学学报》 EI CAS CSCD 2001年第1期96-101,共6页
在应力波加载 (SplitHopkinsonPressureBar)条件下 ,采用动态分析方法对 90 7A钢在 - 2 0℃时的裂纹起裂、扩展、止裂全过程进行了研究 .实验结果表明 :在 - 2 0℃时 ,90 7A钢的动态裂纹扩展过程是一先加速后减速的过程 ,其最大裂纹扩... 在应力波加载 (SplitHopkinsonPressureBar)条件下 ,采用动态分析方法对 90 7A钢在 - 2 0℃时的裂纹起裂、扩展、止裂全过程进行了研究 .实验结果表明 :在 - 2 0℃时 ,90 7A钢的动态裂纹扩展过程是一先加速后减速的过程 ,其最大裂纹扩展速度 V max  =2 16 .6 3m/s ;在 1.41× 10 7MPam12 ·s-1的加载速率下 ,90 7A钢的动态断裂韧性 KId =2 89.5 9MPam12 ,止裂韧性 KIA =2 6 2 .34MPam12 ,且二者相差不大 ,KId/KIA =1.1. 展开更多
关键词 应力波载荷 动态断裂韧性 裂纹扩展速度 止裂韧性 907A钢
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破碎波作用下单桩式海上风机水动力学数值分析 被引量:1
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作者 周林 施伟 +1 位作者 张松浩 张礼贤 《南方能源建设》 2020年第3期70-80,共11页
[目的]我国南汇、东海、大丰等海上风电场的设计波浪十分接近波浪破碎极限,需要探究浅水水域单桩式海上风机基础受破碎波载荷的动力响应。[方法]利用FAST耦合分析软件,考虑使用波浪拉伸的方式计算波浪力载荷,对单桩式风机在东海海况下... [目的]我国南汇、东海、大丰等海上风电场的设计波浪十分接近波浪破碎极限,需要探究浅水水域单桩式海上风机基础受破碎波载荷的动力响应。[方法]利用FAST耦合分析软件,考虑使用波浪拉伸的方式计算波浪力载荷,对单桩式风机在东海海况下的耦合动力响应特性进行分析。[结果]分析结果表明:使用波浪拉伸方式计算破碎波载荷更加接近实际海上风机所受到的载荷,且明显高于不使用拉伸方式计算的破碎波载荷。破碎波更容易激发塔筒的一阶固有频率,风浪联合作用下风机结构动力响应更加显著。[结论]研究成果为我国浅水非线性波浪区域单桩式海上风电的开发提供了一定的参考。 展开更多
关键词 海上风电 破碎波载荷 耦合分析 浪拉伸 动力响应
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海上隔水套管力学分析 被引量:7
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作者 施雷 张红 +3 位作者 冯定 马威 晏健 李志敏 《石油机械》 北大核心 2013年第11期65-69,共5页
国外文献对海上隔水套管的静态分析由于没有考虑波浪载荷对隔水管的作用而存在计算误差,国内对海上隔水套管的力学分析一般采用有限元软件进行模拟,缺乏与实际情况的参照对比。鉴于此,以一根断裂的海上隔水套管为例,对其进行力学分析。... 国外文献对海上隔水套管的静态分析由于没有考虑波浪载荷对隔水管的作用而存在计算误差,国内对海上隔水套管的力学分析一般采用有限元软件进行模拟,缺乏与实际情况的参照对比。鉴于此,以一根断裂的海上隔水套管为例,对其进行力学分析。分析结果表明,隔水套管所受最大应力在泥线上端附近,在此处易发生塑性变形;底层海流速度越大,隔水套管节点位移最大值越大,井口应力也越大;平台升沉值越大,隔水套管所受最大应力也越大,升沉对隔水套管弯曲变形时最大偏移位移影响较小;海流载荷、波载荷和浪载荷对隔水套管所受最大应力有较明显的影响,对隔水套管弯曲变形时最大偏移位移影响较大。 展开更多
关键词 海上隔水套管 海流载荷 波载荷 载荷 节点位移 最大应力 力学分析
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Deflection and stress of hollow CRCP slab under concentrated vehicle load 被引量:2
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作者 陈小兵 黄晓明 +1 位作者 丁建明 童金虎 《Journal of Southeast University(English Edition)》 EI CAS 2011年第2期213-216,共4页
Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement (CRCP) is translated into the equivalent half-wave sin... Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement (CRCP) is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness. 展开更多
关键词 concentrated vehicle load equivalence principle half-wave sine load elastic thin plates hollow continuouslyreinforced concrete pavement slab deflection and stressformulae slab thickness
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Mesh Size Effect in Numerical Simulation of Blast Wave Propagation and Interaction with Structures 被引量:24
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作者 师燕超 李忠献 郝洪 《Transactions of Tianjin University》 EI CAS 2008年第6期396-402,共7页
Numerical method is popular in analysing the blast wave propagation and interaction with structures.However,because of the extremely short duration of blast wave and energy trans-mission between different grids,the nu... Numerical method is popular in analysing the blast wave propagation and interaction with structures.However,because of the extremely short duration of blast wave and energy trans-mission between different grids,the numerical results are sensitive to the finite element mesh size.Previous numerical simulations show that a mesh size acceptable to one blast scenario might not be proper for another case,even though the difference between the two scenarios is very small,indicating a simple numerical mesh size convergence test might not be enough to guarantee accu-rate numerical results.Therefore,both coarse mesh and fine mesh were used in different blast scenarios to investigate the mesh size effect on numerical results of blast wave propagation and interaction with structures.Based on the numerical results and their comparison with field test re-sults and the design charts in TM5-1300,a numerical modification method was proposed to correct the influence of the mesh size on the simulated results.It can be easily used to improve the accu-racy of the numerical results of blast wave propagation and blast loads on structures. 展开更多
关键词 mesh size effect numerical simulation sensitivity blast wave propagation blast load STRUCTURES
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Time Domain Calculation of Connector Loads of a Very Large Floating Structure 被引量:3
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作者 Jiayang Gu Jie Wu +2 位作者 Enrong Qi Yifeng Guan Yubo Yuan 《Journal of Marine Science and Application》 CSCD 2015年第2期183-188,共6页
Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures (VLFSs) and create additional connector loads. In this study, the combined effects of ship collision... Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures (VLFSs) and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS 展开更多
关键词 very large floating structures (VLFSs) time domainmotion differential equation COLLISION CONNECTOR impact load hydrodynamic coefficient oscillation load impact load
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Influence of prolonged natural aging followed by artificial aging on tensile properties and compressive behavior of a thin-walled 6005 aluminum alloy tube 被引量:2
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作者 ZHANG Long LI Ke +1 位作者 HE Hong LI Luo-xing 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第9期2647-2659,共13页
The effects of aging treatments on the tensile properties and compressive behavior of a thin-walled 6005 aluminum alloy tube were studied.Samples after three natural aging(NA)conditions were subsequently aged at 180℃... The effects of aging treatments on the tensile properties and compressive behavior of a thin-walled 6005 aluminum alloy tube were studied.Samples after three natural aging(NA)conditions were subsequently aged at 180℃ for 0.5−12.0 h artificial aging(AA).Tensile and compressive tests were performed after AA.The results show that for samples with the same NA,the longer the AA time is,the higher the strengths alloy owns,and at the same time the material shows a much lower elongation and faster process from plastic deformation to fracture.However,with NA prolonging,the alloy exhibits much better plastic deformation ability after AA,though its strength is decreased.The major cause of strength and plasticity variation induced by changing NA time is that the size of the main strengtheningβ''precipitates is larger and the density is lower.This character is evaluated by the strain hardening exponent n.Compressive results show that the optimum energy absorption characteristics can be acquired at a moderate n(14<n<17).Large n(n≥18)results in the fracture of tube during axial compression while low n(n≤13)causes lower energy absorption. 展开更多
关键词 aluminum alloy aging PRECIPITATES energy absorption load fluctuation
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Finite Element Simplified Fatigue Analysis Method for a Non-tubular Joint of an Offshore Jacket Platform 被引量:2
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作者 Qinghua Bao Heng Feng 《Journal of Marine Science and Application》 2011年第3期321-324,共4页
This paper proposes the finite element simplified fatigue analysis method for fatigue evaluation of the composite non-tubular joint structure of an offshore jacket subjected to wave loads. The skirt pile sleeve of the... This paper proposes the finite element simplified fatigue analysis method for fatigue evaluation of the composite non-tubular joint structure of an offshore jacket subjected to wave loads. The skirt pile sleeve of the offshore jacket, which had been in service, was taken as an example of the non-tubular joint structure. SACS software was used for global analysis of multi-directional wave loads for the jacket platform, and ALGOR software was used to build a finite element model, perform finite element analysis, post-process stress results for acquiring the stress range, and perform fatigue evaluation. The analysis results indicate that the extreme stress range is within the allowable stress range and meets the requirements of DNV code. That means the simplified fatigue analysis method is effective and can be used in fatigue design for the non-tubular joint structure of an offshore jacket. 展开更多
关键词 offshore jacket platform skirt pile sleeve finite element fatigue evaluation
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Filtering Method of Aero⁃engine Load Spectrum Based on Rain Flow Counting 被引量:4
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作者 XU Cong SUN Zhigang +1 位作者 LU Qi SONG Yingdong 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第6期947-954,共8页
A filtering method of aero-engine load spectrum based on the rain flow counting is proposed in this paper.Firstly,the original load spectrum is counted through the rain flow method to get the peak and valley values.Th... A filtering method of aero-engine load spectrum based on the rain flow counting is proposed in this paper.Firstly,the original load spectrum is counted through the rain flow method to get the peak and valley values.Then,some data points in the original load spectrum are added between the peak and valley values.Finally,the filtering spectrum is obtained.The proposed method can reflect the path information of the original load spectrum.In addition,it can also eliminate the noise in the signal and improve the efficiency of signal processing,which is of practical significance for the research of aero-engine. 展开更多
关键词 load spectrum FILTERING rain flow counting AERO-ENGINE
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Dynamic strength characteristics and failure criteria of anisotropically consolidated silt under principal stress rotation 被引量:2
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作者 SHEN Yang ZHANG Peng-ju +1 位作者 XU Guo-jian LIU Han-long 《Journal of Central South University》 SCIE EI CAS 2013年第7期2025-2033,共9页
In order to identify the critical properties and failure criteria of in-situ silt under vehicle or wave loading, anisotropically consolidated silt under undrained cyclic principal stress rotation was studied with holl... In order to identify the critical properties and failure criteria of in-situ silt under vehicle or wave loading, anisotropically consolidated silt under undrained cyclic principal stress rotation was studied with hollow cylinder dynamic tests. The results show that for the slightly anisotropically consolidated samples with consolidation ratios no larger than 1.5, the structure collapses and the deviator strain and pore pressure increase sharply to fail after collapse. For the highly anisotropically consolidated samples with consolidation ratios larger than 1.5, the strain increases steadily to high values, which shows characteristics of ductile failure. 4% is suggested to be the threshold value of deviator stain to determine the occurrence of collapse. The normalized relationship between pore pressure and deviator strain can be correlated by a power fimction for all the anisotropically consolidated samples. Based on it, for the highly anisotropically consolidated samples, the appearance of inflection point on the power function curve is suggested to sign the failure. It can be predicted through the convex pore pressure at this point, whose ratio to the ultimate pore pressure is around linear with the consolidation ratio in spite of the dynamic shear stress level. And the corresponding deviator strain is between 3% and 6%. The strain failure criterion can also be adopted, but the limited value of stain should be determined according to engineering practice. As for the slightly anisotropically consolidated samples, the turning points appear after collapse. So, the failure is suggested to be defined with the occurrence of collapse and the collapse pore pressure can be predicted with the ultimate pore pressure and consolidation ratio. 展开更多
关键词 principal stress rotation anisotropic consolidation SILT COLLAPSE failure criterion
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Experimental Evaluation of the Post-ultimate Strength Behavior of a Ship's Hull Girder in Waves 被引量:6
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作者 Kazuhiro Iijima Ryota Wada Masahiko Fujikubo 《Journal of Marine Science and Application》 2012年第1期34-43,共10页
Experimental investigations into the collapse behavior of a box-shape hull girder subjected to extreme wave-induced loads are presented.The experiment was performed using a scaled model in a tank.In the middle of the ... Experimental investigations into the collapse behavior of a box-shape hull girder subjected to extreme wave-induced loads are presented.The experiment was performed using a scaled model in a tank.In the middle of the scaled model,sacrificial specimens with circular pillar and trough shapes which respectively show different bending moment-displacement characteristics were mounted to compare the dynamic collapse characteristics of the hull girder in waves.The specimens were designed by using finite element(FE)-analysis.Prior to the tank tests,static four-point-bending tests were conducted to detect the load-carrying capacity of the hull girder.It was shown that the load-carrying capacity of a ship including reduction of the capacity after the ultimate strength can be reproduced experimentally by employing the trough type specimens.Tank tests using these specimens were performed under a focused wave in which the hull girder collapses under once and repetitive focused waves.It was shown from the multiple collapse tests that the increase rate of collapse becomes higher once the load-carrying capacity enters the reduction path while the increase rate is lower before reaching the ultimate strength. 展开更多
关键词 post-ultimate strength collapse behavior experimental evaluation load-carrying capacity hull girder
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Modeling Loads Caused by Breaking Waves Striking Vertical Walls
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作者 康海贵 孙英伟 《Journal of Marine Science and Application》 2010年第2期163-167,共5页
Breaking waves can have tremendous destructive impact on vertical walls, yet they are poorly understood. By using particle imaging velocimetry (PIV) technology and high-precision pressure transducers, actual breakin... Breaking waves can have tremendous destructive impact on vertical walls, yet they are poorly understood. By using particle imaging velocimetry (PIV) technology and high-precision pressure transducers, actual breaking wave loads on vertical walls were studied. By simultaneously comparing the flow field structure and wave pressure, the mechanisms of breaking wave pressure could be analyzed. The probability distribution of the peak value of the first impact of a breaking wave was investigated. The results showed that the impact pressure p is mainly distributed in the range of 0.25-2.75 pv2, with the greatest possible probability at p/pv2 = 0.75. 展开更多
关键词 vertical breakwater breaking wave wave loads particle imaging velocimetry (PIV)
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Path-tracking Control of Underactuated Ships Under Tracking Error Constraints
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作者 Khac Duc Do 《Journal of Marine Science and Application》 CSCD 2015年第4期343-354,共12页
This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the dis... This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov's direct methods. The effectiveness of the proposed results is illustrated through simulations. 展开更多
关键词 underactuated ship path-tracking error constraint Lyapunov method backstepping method
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