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摘要: 海洋复合管缆是海洋能源开发的关键链接结构, 通常由金属增强层、聚合物护套、功能单元及界面层等多种组成部分构成, 具有多层复合、多种异质材料组合和细长柔性等结构特点, 在浪流、内压、温度、浮体运动及海床约束等复杂环境与载荷共同作用下, 表现出显著的材料非线性、几何非线性、界面非线性和接触非线性, 直接影响海洋复合管缆的结构分析、强度评估与服役安全. 本文围绕海洋复合管缆非线性问题的研究进展, 系统介绍了其多层复合结构特性与非线性诱因, 梳理了材料非线性中橡胶和聚合物材料的超弹性、黏弹性与金属材料的弹塑性本构理论; 对比介绍了细长杆理论、集中质量法、共旋坐标法和绝对节点坐标法等几何非线性建模方法及相应求解策略; 归纳总结了界面非线性中界面强度、界面摩擦以及界面疲劳非线性相关理论; 论述了接触非线性中管缆−海床相互作用经典理论及改进模型. 现有研究虽然已经取得较多进展, 但对复杂海洋环境下多非线性共同作用机制的认识仍存在不足, 未来应面向多场、多尺度和长期服役条件, 进一步开展多非线性问题耦合分析, 为海洋复合管缆的安全设计与长期服役评估提供更可靠的理论支撑.Abstract: Marine composite pipes and cables are critical connection structures in offshore energy development. They are typically composed of metallic reinforcement layers, polymer sheaths, functional units, and interfacial layers, and are characterized by multilayer composite configurations, heterogeneous material combinations, and slender flexible geometries. Under the combined effects of complex marine environments and loading conditions, including waves and currents, internal pressure, temperature, floater motions, and seabed constraints, these structures exhibit pronounced material nonlinearity, geometric nonlinearity, interfacial nonlinearity, and contact nonlinearity, which directly affect their structural analysis, strength assessment, and service safety. Focusing on the research progress on nonlinear problems in marine composite pipes and cables, this paper systematically introduces their multilayer composite structural characteristics and the underlying causes of nonlinearity. It reviews the constitutive theories associated with material nonlinearity, including the hyperelastic and viscoelastic behavior of rubber and polymer materials, as well as the elastoplastic constitutive models of metallic materials. The major modeling approaches for geometric nonlinearity, including slender-rod theory, the lumped-mass method, the co-rotational method, and the absolute nodal coordinate formulation, together with the corresponding solution strategies, are comparatively reviewed. The theoretical developments related to interfacial nonlinearity, including interfacial strength, interfacial friction, and interfacial fatigue nonlinearity, are summarized. In addition, the classical theories and improved models for pipe/cable–seabed interaction in contact nonlinearity are discussed. Although substantial progress has been made in existing studies, the understanding of the coupled mechanisms of multiple nonlinearities under complex marine environments remains insufficient. Future research should therefore focus on coupled analyses of multiple nonlinear behaviors under multiphysics, multiscale, and long-term service conditions, so as to provide more reliable theoretical support for the safe design and long-term integrity assessment of marine composite pipes and cables.
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图 2 非粘结型海洋复合管缆典型结构示意图. (a)柔性立管典型结构示意图(Hanonge et al. 2010), (b)脐带缆典型结构示意图(Lu et al. 2017), (c)海缆典型结构示意图(张玉 等 2024), (d)增强型金属波纹管典型结构示意图(Abbasi et al. 2016), (e)复合低温软管典型结构示意图(徐岸南 等 2015)
图 3 粘结型海洋复合管缆典型结构示意图. (a)漂浮软管结构示意图, (b)水下软管结构示意图, (c) RTP典型结构示意图, (d) TCP典型结构示意图(Okolie et al. 2023)
图 6 材料时间相关行为与长期结构响应评估研究链条示意图. (Liu et al. 2016, Shen et al. 2018)
图 8 共旋坐标法梁单元运动分解示意图.(孙晓旭 等 2025)
图 9 ANCF与集中质量法算例对比图. (a)静态构形, (b)轴向力, (c)弯矩, (d)规则波下端部力时程(Wang et al. 2023)
图 10 经典内聚力模型牵引−分离曲线. (a)双线性内聚力模型(Geubelle et al. 1998), (b)指数型内聚力模型(Xu et al. 1994), (c)多项式内聚力模型(Tvergaard et al. 1992)
图 13 摩擦系数随循环次数演化曲线.(Yin et al. 2021)
图 12 不同接触压力弯矩−曲率曲线.(Wang et al. 2021)
图 15 疲劳内聚力模型的牵引−分离曲线退化示意图.(Hofman et al. 2024)
图 17 AB模型. (Bridge et al. 2004)
图 18 RQ模型.(Randolph et al. 2009)
图 21 考虑土体刚度退化与海沟发展的钢悬链线立管触地区海床形态演化.(Chen et al. 2022)
表 1 海洋复合管缆材料非线性模型对比
代表模型 类别 适用对象 主要用途 适用限制 Arruda-Boyce 超弹性 橡胶; 短时大变形、近似可逆, 且速率、历史与永久变形可忽略 有限链伸展或宽变形区的橡胶响应; 用于层间传载、局部变形及整体承载分析 率无关; 模型未考虑蠕变、应力松弛、Mullins效应、老化及损伤演化 Mooney-Rivlin 超弹性 橡胶及部分弹性体; 有限变形范围的短时准静态分析 参数较少的工程拟合; 粘结型软管橡胶层、浮管和附件 低阶形式对高应变应变硬化的描述能力有限; 体积变化明显时需引入可压缩项 Yeoh、Ogden 超弹性 橡胶及弹性体; 需要调整高应变曲线形状, 或分析多种变形模式 Yeoh可基于单轴数据拟合; Ogden适于具有多类试验数据的宽变形区描述 应变能函数不显含第二应变不变量; 材料响应显著依赖该不变量时描述能力受限; 高阶形式参数较多, 参数相关性增强; 标定通常需要多种变形模式试验数据 Maxwell、Kelvin-Voigt、Prony级数等 线性黏弹性 聚合物内衬、护套或橡胶; 材料状态稳定, 小变形或低应力下的速率与历史响应 松弛、蠕变、动态耗能和阻尼; 广义模型可用于较宽时间谱 松弛或蠕变函数不随载荷幅值变化; 不能描述明显的应力水平相关非线性黏弹性; 单元数增加会增加待识别参数 Schapery
单积分模型非线性黏弹性 聚合物; 时间响应明显受应力水平、温度或载荷历史影响 非线性蠕变、恢复以及温度梯度/非稳态载荷下的内衬嵌入等问题 非线性函数和移位因子需由多应力水平蠕变恢复、松弛等试验确定; 经典形式不包含独立的损伤和永久变形演化 spring-pot、
分数阶
Kelvin-Voigt等分数阶黏弹性 具有幂律蠕变、松弛或宽频率黏弹响应的聚合物 以较少参数表征连续松弛谱、幂律蠕变及宽频动力响应 直接针对多层海洋复合管缆聚合物层的面向多层海洋复合管缆聚合物层的材料标定、构件试验与结构验证仍有限 理想弹塑性及
各向同性硬化弹塑性 压力铠装、拉伸铠装、金属管和波纹管; 单调加载下超过屈服 初始屈服、极限承载或一次性安装工况; 各向同性硬化保留单调塑性硬化 不描述屈服后硬化; 各向同性硬化不能表征屈服面平移及包辛格效应 随动硬化或
混合硬化循环塑性 存在卸载再加载、循环弯拉/扭转、制造预变形或残余应力的金属铠装件 反向屈服、安定、棘轮与残余应力预测 参数通常依赖循环应力−应变试验; 线性随动硬化难以描述复杂循环硬化/软化和棘轮演化 Hill型各向异性屈服模型 各向异性塑性 具有方向相关屈服和塑性流动的延性各向异性材料 描述不同材料方向上的屈服及不可恢复变形 需要方向相关的屈服/塑性参数; 属于塑性模型, 不等同于纤维复合材料失效准则 Tsai-Wu等失效准则和渐进
损伤模型复合材料
失效与损伤RTP或TCP等纤维增强层; 关注纤维、基体或层内失效 判断失效起始, 并通过损伤变量描述刚度退化和损伤扩展 Tsai-Wu等强度准则本身只判定失效起始; 失效后的刚度退化需要独立的损伤演化规律 
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表 2 海洋复合管缆几何非线性建模方法对比
方法 变形描述思路 适用范围 截面特性表征方式 主要局限 简化索/杆/梁
模型以中心线描述整体构形; 根据具体模型保留轴向伸缩和弯曲, 部分简化形式忽略剪切或扭转 高柔性细长管缆的整体构形、张力、弯曲及动力响应 管缆多层截面通常压缩为等效轴向、弯曲和扭转等线刚度 截面局部变形及层间行为需另行建模; 具体适用范围受所采用的杆/梁假设限制 几何精确杆梁模型 采用中心线位置与截面姿态描述有限运动, 根据具体理论考虑伸缩、剪切、弯曲、扭转及有限转动 低张力、三维弯扭、大转动及需要保留较完整截面运动学的管缆分析 以轴向、剪切、弯曲、扭转等截面刚度进入一维模型; 多层截面通常先作等效 复杂多层截面的局部细节、层间接触与局部失稳通常需结合更精细模型分析 集中质
量法将连续管缆离散为质量节点及连接单元, 通过节点运动近似整体动力学行为 长细柔性管缆的整体构形、动力响应、安装分析及大位移运动问题 单位长度质量、轴向刚度, 按需要引入弯曲/扭转刚度及水动力参数 结果对离散尺度、连接单元和阻尼/接触模型较敏感, 对局部弯曲、扭转和截面运动的描述能力有限 共旋有
限元将单元整体刚体运动与局部变形分离, 在随单元运动的局部坐标系中计算结构变形 整体大位移、大转动而局部应变较小的梁/管缆动力问题及流固耦合分析 截面轴向、剪切、弯曲和扭转性质由所配梁单元提供; 共旋列式本身不确定截面等效模型 适用能力与所配梁单元及局部变形假设相关 绝对节点坐标法 以节点绝对位置及位置梯度/斜率作为广义坐标, 通过有限元插值描述柔性体大运动 海洋柔性缆线、立管和系泊线等大位移、大转动及复杂动力响应分析 截面/材料特性通过单元本构关系和截面参数输入, 可表征轴向、弯曲、剪切等效应 自由度较多, 计算规模较大; 对截面参数、数值积分、接触处理和边界条件设置要求较高
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表 3 海洋管缆几何非线性静态与准静态问题的求解策略比较
求解策略 核心步骤 适用情形 主要限制 Newton-Raphson
类迭代根据当前构形更新残差向量和切线刚度, 在给定载荷或位移增量内迭代求解非线性平衡方程 整体静态构形、张力、曲率和弯矩等常规非线性平衡问题; 载荷增量可与其组合 收敛受初始状态、载荷增量及非线性程度影响; 极限点附近常规载荷控制可能难以继续跟踪平衡路径 弧长法 同时修正位移和载荷参数, 将位移和载荷参数共同作为未知量, 通过弧长约束跟踪极限点附近及后屈曲阶段的平衡路径 极限承载、局部屈曲、压溃及后屈曲等需要获得完整平衡路径的问题 需合理设置弧长增量等路径控制参数; 所得结果描述平衡路径, 不直接表征动态失稳过程 HAM等半解析近似
方法构造非线性控制方程的近似解析表达, 用于特定边值问题的近似解析求解与参数分析 控制方程可适当简化或降维的安装与构形问题, 尤其适用于重复参数计算 代表案例主要为一般SCR和海底管道; 适用范围受方程简化、边界条件及级数收敛影响
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表 4 海洋复合管缆动力响应时域求解方法对比
方法分类 求解方法 核心原理与特点 应用场景 隐式求解方法 Newmark-β法 经典隐式积分格式; 当β ≥ 1/4、γ ≥ 1/2时无条件稳定; 平均加速度法 (γ = 1/2, β = 1/4) 最常用, 无数值阻尼, 二阶精度 集成于OrcaFlex、Riflex等商业软件及自研程序, 广泛用于立管、系泊缆的非线性动力方程求解; 适用于非粘结柔性立管、脐带缆和动态缆等结构的整体长时程动力分析; 一般立管和隔水管中的相关应用可作为算法稳定性与适用性的参考 HHT法与
广义-α法引入算法阻尼参数, 保持无条件稳定和二阶精度的同时滤除虚假高频响应; 广义-α法通过优化谱半径, 在保证低频精度下提供最优高频耗散 流−固耦合全局非线性运动方程求解; 质量随张力变化的失稳问题; 脐带缆在船舶升沉及三维海流作用下的动态响应; 圆柱振动方程; 基于共旋坐标法的随机波浪下管缆动力响应 Wilson-θ法 假设在[t, t + θΔt]内加速度线性变化; 当θ ≥ 1.37时无条件稳定; 由线性加速度法改进而来 深海采矿扬矿管纵向振动及升沉补偿研究; 适用于细长结构的时域分析 显式求解方法 中心差分法 显式递推格式, 利用前一时间步状态直接计算下一时间步响应, 无需迭代求解方程组, 具有二阶精度, 但受CFL条件制约需采用极小时间步长 较少用于千米级整体时域模拟, 常用于局部精细化分析; 非粘结柔性立管截面内部螺旋铠装层与聚合物层的复杂接触、滑移、“鸟笼”失效等极度非线性行为; 浮式风机动态缆多层缠绕结构的接触分离问题 显示Runge-Kutta方法 通过在单个时间步内计算多个中间阶段斜率的加权平均, 实现对微分方程的高阶精度数值积分; 常用显式Runge-Kutta格式通过多个中间阶段斜率加权实现时间推进 适用于自由度规模较小或中等的非线性动力系统时域求解, 在一般立管及输流结构中应用较多, 可为复合管缆动力响应分析提供算法参考 广义积分变
换技术基于特征函数展开的半解析/混合数值−解析方法; 将偏微分方程降阶为常微分方程组, 有限截断后数值求解再反演 主要用于流致振动和输流结构的动力响应分析, 在一般立管及柔性管道研究中应用较多, 可为复合管缆简化动力模型的求解提供方法参考
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