非粘合柔性立管截面特性的理论计算及BSR区域的疲劳分析
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摘要
随着海洋油气开发持续向深水推进,非粘合柔性软管的应用越来越广泛。与传统钢管相比,尤其当管体需要承受较大的弯曲变形时,柔性软管有着诸多优点。然而由于自身结构的复杂性,要确定其力学特性和结构响应从来都非易事。螺旋层的存在为此引入了诸多的不确定性,特别是对于弯曲响应。当用作海洋立管时,其与浮式平台的连接部位由于受到动力载荷的作用,极易发生过度弯曲或疲劳失效。弯曲刚度加强件(Bend Stiffener, BSR)则为其提供了一个弯曲刚度的过渡区域,以保证柔性立管的安全。
本文的主要任务是建立相应的理论模型来分析柔性立管-BSR这一系统的力学特性和结构响应,主要包括柔性立管的截面分析和BSR的非线性响应分析。此外,柔性立管的疲劳分析也是本文一个重要的研究内容。
非粘合柔性软管的截面分析可以分为轴对称响应分析和弯曲响应分析。本文建立了柔性软管在轴向力、扭矩以及内外压等轴对称载荷作用下的响应分析模型。首先基于能量法推导出软管各层的平衡方程并写成矩阵形式,得到其刚度矩阵；然后将各层刚度矩阵进行组装并考虑边界条件得到总刚度矩阵；进而通过迭代求解出所有变量。该模型可自行判断各层之间可能发生的分离并相应调整层间的接触压力,因而可以考虑轴向刚度与扭转刚度之间的耦合以及载荷施加的方向。Rough Bore型和Smooth Bore型的差别也通过调整载荷向量的方式进行了考虑。
通过将各层的弯曲响应函数相加,建立了柔性软管的弯曲响应分析模型。对于螺旋层,通过将其模拟为等效的圆管,推导出无滑移和完全滑移之间这一过渡段的弯矩-曲率关系以及弯曲刚度-曲率关系的显式表达,成功模拟了过渡段的非线性弯曲行为。正确考虑了螺旋条带局部弯曲和扭转的贡献,结果表明其对完全滑移刚度有较大影响,应在弯曲分析时予以考虑。此外,对初始接触压力的重要性也进行了讨论。该模型显式地描述了循环弯曲时柔性软管的弯曲迟滞行为。
截面分析的理论计算均与现有文献中实验测试的结果进行了比较,二者吻合良好。
给出一种BSR的锥形设计方法,并推导出其尖部转角的解析表达式。建立了柔性立管-BSR系统的非线性响应分析模型,首次同时考虑了几何非线性、材料非线性以及柔性立管非线性的弯矩-曲率关系等非线性因素。此外,给出一种确定BSR截面弯矩-曲率关系的理论方法,大大简化了其本构关系的计算。
柔性立管的疲劳性能一直是设计时需要考虑的重要因素之一,立管与浮式平台的连接部位则是一个容易发生疲劳失效的危险区域。基于Longuet-Higgins分布将表征长期海况的波浪散布图分解为单个规则波的散布图,以此进行柔性立管的疲劳分析,并与随机波法的计算结果进行了比较。结果表明：波浪散布图的离散应充分考虑系统响应的影响；若将波浪散布图离散得较为理想,则采用规则波法计算得到的疲劳寿命将和随机波法的结果较为接近。此外,通过参数敏感性分析讨论了诸多重要因素对疲劳寿命的影响。
As the offshore industry advances into deeper waters and harsher environments, the use of unbonded flexible pipes becomes increasingly essential. In many applications where high levels of bending deformations are expected flexible pipes have a distinct advantage over the conventional steel pipes. However, determination of various mechanical characteristics of flexible pipes has never been an easy task due to their complex structure. The presence of helical elements in a flexible pipe multilayered structure raises many uncertainties mainly associated with bending behavior. When flexible pipes are used as risers the upper connection of the riser to the floating production platform is highly affected by cyclic operational loadings and is recognized as one of the most vulnerable parts to failure from excessive bending or from accumulation of fatigue damage. Bend stiffeners (BSRs) are designed for the integrity of flexible risers, providing a gradual stiffness transition at the riser-vessel interface.
The objective of this thesis is to build analytical models to predict the structural behavior of the riser-BSR system, which involves cross-sectional analysis of the riser and non-linear analysis of the BSR. In addition, fatigue analysis of flexible risers is also an important issue of this work.
The analysis of an unbonded flexible pipe cross-section can be divided into axisymmetric and flexural or bending analysis. Theoretical model is developed for analyzing the response of flexible pipes to combined axisymmetric loads including axial force, torque and internal/external pressures. Equilibrium equations for flexible pipe components are derived and put into a matrix form based on energy approaches. A comprehensive guide for assembling the flexible pipe stiffness matrix is described. Equations for boundary conditions are incorporated into the stiffness matrix and with the help of small iterations the global equilibrium of the entire pipe can be achieved. The procedure automatically detects the tendency of layer separation and adjusts the interlayer contact pressures appropriately. Prediction of gap formations allows the model to account for coupling between the axial and torsional stiffnesses and the direction of load. The difference in construction of rough and smooth bore pipes is also accounted for using a rearranged load vector.
In bending, a flexural model is developed separately by superimposing the bending moment functions for each layer. The transition path from the upper (No-Slip) bound to the lower (Full-Slip) bound stiffness of the helical layer is modeled, by treating the helical layer as an equivalent thin tube. Explicit formulations are derived which describe the bending moment-curvature and the bending stiffness-curvature relationships within the transition mode. The influence of local bending and torsion of individual helical elements on the bending behavior of the entire pipe is evaluated. The findings imply that this local behavior significantly influences the full-slip bending stiffness and should be included in the bending analysis. The importance of the initial interlayer pressures is also investigated. The model explicitly determines the bending hysteresis in a pipe undergoing cyclic bending.
In the cross-sectional analysis, wherever possible, theoretical results are compared with experimental data from the available literature and encouraging correlations are found.
A methodology for the BSR taper design is outlined. The exact expression of the angle at the tip of the BSR required for the design is derived. In the analysis of the riser-BSR system, the formulation is extended taking non-linear properties into account both for the BSR material and for the flexible pipe bending behavior. An analytical procedure is also presented to calculate the bending moment versus curvature relationship for each BSR cross-section, which renders the prediction of the constitutive model much simpler.
Fatigue performance of flexible risers is an important design consideration. The top of the riser including the BSR is recognized as a critical region to fatigue failure. The Longuet-Higgins distribution is employed to decompose the wave scatter diagram into an individual regular wave scatter diagram, based on which various analyses are performed to estimate the fatigue life of a flexible riser. The resulting result is compared with that obtained from the stochastic analyses and rainflow counting technique. Comparative analysis shows that the system response should be fully considered in the decomposition process of sea states. Provided that the regular wave bin discretization is performed well, the predicted fatigue life from this method will generally agree well with that from the equivalent rainflow analysis. A parametric study is also conducted to assess the importance of several main aspects in the fatigue response of flexible risers.
本文的主要任务是建立相应的理论模型来分析柔性立管-BSR这一系统的力学特性和结构响应,主要包括柔性立管的截面分析和BSR的非线性响应分析。此外,柔性立管的疲劳分析也是本文一个重要的研究内容。
非粘合柔性软管的截面分析可以分为轴对称响应分析和弯曲响应分析。本文建立了柔性软管在轴向力、扭矩以及内外压等轴对称载荷作用下的响应分析模型。首先基于能量法推导出软管各层的平衡方程并写成矩阵形式,得到其刚度矩阵；然后将各层刚度矩阵进行组装并考虑边界条件得到总刚度矩阵；进而通过迭代求解出所有变量。该模型可自行判断各层之间可能发生的分离并相应调整层间的接触压力,因而可以考虑轴向刚度与扭转刚度之间的耦合以及载荷施加的方向。Rough Bore型和Smooth Bore型的差别也通过调整载荷向量的方式进行了考虑。
通过将各层的弯曲响应函数相加,建立了柔性软管的弯曲响应分析模型。对于螺旋层,通过将其模拟为等效的圆管,推导出无滑移和完全滑移之间这一过渡段的弯矩-曲率关系以及弯曲刚度-曲率关系的显式表达,成功模拟了过渡段的非线性弯曲行为。正确考虑了螺旋条带局部弯曲和扭转的贡献,结果表明其对完全滑移刚度有较大影响,应在弯曲分析时予以考虑。此外,对初始接触压力的重要性也进行了讨论。该模型显式地描述了循环弯曲时柔性软管的弯曲迟滞行为。
截面分析的理论计算均与现有文献中实验测试的结果进行了比较,二者吻合良好。
给出一种BSR的锥形设计方法,并推导出其尖部转角的解析表达式。建立了柔性立管-BSR系统的非线性响应分析模型,首次同时考虑了几何非线性、材料非线性以及柔性立管非线性的弯矩-曲率关系等非线性因素。此外,给出一种确定BSR截面弯矩-曲率关系的理论方法,大大简化了其本构关系的计算。
柔性立管的疲劳性能一直是设计时需要考虑的重要因素之一,立管与浮式平台的连接部位则是一个容易发生疲劳失效的危险区域。基于Longuet-Higgins分布将表征长期海况的波浪散布图分解为单个规则波的散布图,以此进行柔性立管的疲劳分析,并与随机波法的计算结果进行了比较。结果表明：波浪散布图的离散应充分考虑系统响应的影响；若将波浪散布图离散得较为理想,则采用规则波法计算得到的疲劳寿命将和随机波法的结果较为接近。此外,通过参数敏感性分析讨论了诸多重要因素对疲劳寿命的影响。
As the offshore industry advances into deeper waters and harsher environments, the use of unbonded flexible pipes becomes increasingly essential. In many applications where high levels of bending deformations are expected flexible pipes have a distinct advantage over the conventional steel pipes. However, determination of various mechanical characteristics of flexible pipes has never been an easy task due to their complex structure. The presence of helical elements in a flexible pipe multilayered structure raises many uncertainties mainly associated with bending behavior. When flexible pipes are used as risers the upper connection of the riser to the floating production platform is highly affected by cyclic operational loadings and is recognized as one of the most vulnerable parts to failure from excessive bending or from accumulation of fatigue damage. Bend stiffeners (BSRs) are designed for the integrity of flexible risers, providing a gradual stiffness transition at the riser-vessel interface.
The objective of this thesis is to build analytical models to predict the structural behavior of the riser-BSR system, which involves cross-sectional analysis of the riser and non-linear analysis of the BSR. In addition, fatigue analysis of flexible risers is also an important issue of this work.
The analysis of an unbonded flexible pipe cross-section can be divided into axisymmetric and flexural or bending analysis. Theoretical model is developed for analyzing the response of flexible pipes to combined axisymmetric loads including axial force, torque and internal/external pressures. Equilibrium equations for flexible pipe components are derived and put into a matrix form based on energy approaches. A comprehensive guide for assembling the flexible pipe stiffness matrix is described. Equations for boundary conditions are incorporated into the stiffness matrix and with the help of small iterations the global equilibrium of the entire pipe can be achieved. The procedure automatically detects the tendency of layer separation and adjusts the interlayer contact pressures appropriately. Prediction of gap formations allows the model to account for coupling between the axial and torsional stiffnesses and the direction of load. The difference in construction of rough and smooth bore pipes is also accounted for using a rearranged load vector.
In bending, a flexural model is developed separately by superimposing the bending moment functions for each layer. The transition path from the upper (No-Slip) bound to the lower (Full-Slip) bound stiffness of the helical layer is modeled, by treating the helical layer as an equivalent thin tube. Explicit formulations are derived which describe the bending moment-curvature and the bending stiffness-curvature relationships within the transition mode. The influence of local bending and torsion of individual helical elements on the bending behavior of the entire pipe is evaluated. The findings imply that this local behavior significantly influences the full-slip bending stiffness and should be included in the bending analysis. The importance of the initial interlayer pressures is also investigated. The model explicitly determines the bending hysteresis in a pipe undergoing cyclic bending.
In the cross-sectional analysis, wherever possible, theoretical results are compared with experimental data from the available literature and encouraging correlations are found.
A methodology for the BSR taper design is outlined. The exact expression of the angle at the tip of the BSR required for the design is derived. In the analysis of the riser-BSR system, the formulation is extended taking non-linear properties into account both for the BSR material and for the flexible pipe bending behavior. An analytical procedure is also presented to calculate the bending moment versus curvature relationship for each BSR cross-section, which renders the prediction of the constitutive model much simpler.
Fatigue performance of flexible risers is an important design consideration. The top of the riser including the BSR is recognized as a critical region to fatigue failure. The Longuet-Higgins distribution is employed to decompose the wave scatter diagram into an individual regular wave scatter diagram, based on which various analyses are performed to estimate the fatigue life of a flexible riser. The resulting result is compared with that obtained from the stochastic analyses and rainflow counting technique. Comparative analysis shows that the system response should be fully considered in the decomposition process of sea states. Provided that the regular wave bin discretization is performed well, the predicted fatigue life from this method will generally agree well with that from the equivalent rainflow analysis. A parametric study is also conducted to assess the importance of several main aspects in the fatigue response of flexible risers.
引文
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