Abstract
This paper presents an analytical investigation of elastic collapse of asymmetrically corroded rings under external pressure when both internal corrosion and external corrosion exist. Governing equations are derived for membrane inextensible and membrane extensible cases; a full continuity condition is rigorously derived by the Euler-Bernoulli beam assumption. Comparison with finite element analysis (FEA) shows good agreement for load-displacement curves but membrane extensibility should be included to accurately predict the initial deformation phase, although the discrepancy for both the inextensible and extensible models vanishes for larger deformation phases. By the perturbation technique, the initial load-displacement slope is calculated, and extensive parametric analysis shows complicated dependency of this slope on the misalignment parameter and the angular extent of corrosion. We also present an infallible semi-analytical perturbation solution for both homogeneous and inhomogeneous cases by the Lyapunov arbitrary small-parameter method and show that the resulting power series always converges; then a mathematical argument of analyticity has been presented to illustrate that the so-called homotopy analysis method in the literature converges when the convergence controlling parameter is lying in (−2, 0). This paper serves to enhance the understanding of asymmetrically corroded rings and it is mainly relevant to offshore engineering.
摘要
目的
腐蚀缺陷削弱管道的极限承载外压。本文旨在探讨非对称腐蚀形态下管道极限外压的理论计算方法。
创新点
1. 建立非对称腐蚀管道在外压下垮塌的非齐次微分控制方程;2. 通过摄动法技巧,给出初始变形的显式表达;3. 深入讨论薄膜可压缩性对垮塌压力的影响。
方法
1. 通过理论推导,构建非对称腐蚀缺陷下管道变形的控制方程;2. 采用摄动法和对称算子方法,分析变形和压力的关系;3. 通过任意小李雅普诺夫半解析方法,求解齐次和非齐次微分控制方程,对任意壁厚分布具有一定的适用性。
结论
1. 理论计算结果和有限元计算结果基本一致;2. 不对称参数对变形有较大影响;3. 基于欧拉-伯努利假设的连续性条件较为复杂,但是简化连续性条件是可行的;4. 薄膜拉伸性严重影响初始变形;5. 半解析方法总是收敛的,同时同伦分析法中收敛控制参数应该在(−2, 0)取值。
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Acknowledgments
This work is supported by the Natural Science Foundation of Zhejiang Province (No. LQ21E050001), the Science and Technology Plan Project of Zhejiang Bureau of Quality and Technical Supervision (No. 20200307), and Eyas Program Incubation Project of Zhejiang Provincial Administration for Market Regulation (No. CY2022221) China.
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Sun-ting YAN acquired the fund for this research, designed the research, derived the equations and theories, conducted FEA, wrote the draft, and made the revision. Ping TANG, Zhang-wei LING, and Yong-gui CHEN reviewed the manuscript and provided advice on writing and data analysis.
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Sun-ting YAN, Ping TANG, Zhang-wei LING, and Yong-gui CHEN declare that they have no conflict of interest.
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ESMs A—G; Figs. S1–S18; Tables S1 and S2
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Yan, St., Tang, P., Ling, Zw. et al. An analytical investigation of the collapse of asymmetrically corroded pipes under external pressure. J. Zhejiang Univ. Sci. A 23, 358–374 (2022). https://doi.org/10.1631/jzus.A2100487
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DOI: https://doi.org/10.1631/jzus.A2100487