“…This ring consists of two parts: intact part with original thickness t ( s ) = t 0 and corroded part where t ( s ) is the reduced thickness ( t ( s ) < t 0 ). The Timoshenko’s equation 12,20 reads (refer to Appendix F for a concise derivation)where E is elastic modulus, I is the moment of inertia, D is an unknown constant, ⋅ ′ = d ⋅/ ds and s ∈ [0, 2 π ] is angular coordinate in circumferential direction subject to periodicity conditions w (0) = w (2 π ), w ′(0) = w ′ (2 π ) and in extension conditions ∫02πw(s)ds=0. Note that in derivation of equation (1), the membrane inextensible assumption v ′ = w ( v is circumferential displacement) has been applied to simplify the solution.Figure 1.Schematic of a thin ring model with local thickness reduction due to corrosion.…”
Section: General Governing Equationmentioning
confidence: 99%
“…Xue and Fatt 18,19 used the same Timoshenko equation to analytically study the bifurcation pressure of corroded rings and used some perturbative WKB to derive some analytical approximations. Based on those previous attempts, Yan et al 20,21 extensively and analytically calculated the bifurcation pressure and collapse of corroded rings with some initial imperfection and showed that the analytical prediction by Timoshenko’s equation was accurate when numerical finite element analysis results were compared.…”
Section: Introductionmentioning
confidence: 99%
“…Only purely elastic collapse is considered in this paper and thus, the theoretical calculation directly applies for thin pipes. However, for thick-walled pipes for deep-sea applications, plasticity effect should be included (see some extensive discussions on this topic by our previous investigation 20 ).…”
This paper presents a perturbative analysis of bifurcation pressure of 2D corroded rings characterized by locally thinned regions under external pressure by asymptotically analyzing the Timoshenko differential equation and parametric analysis. First, for the case of one corrosion region, we formulate regular perturbative solution separately for anti-symmetric bifurcation and symmetric bifurcation cases. Concise formulation is presented by introducing a corrosion severity parameter and perturbative solution is presented. Second, we present a detailed analysis for the case where corrosion region has small angular extent by converting it into a singular perturbative problem and conduct various asymptotic analyses to illustrate the interesting interlacing behaviors. The derived explicit formula explains some numerical observation by Fatt in literature. Third, we conduct parametric analysis for the case of two interacting corrosion regions by classifying it into two cases: symmetric corrosion case and non-symmetric corrosion case. Finally, we present asymptotical analysis to investigate the extremely corroded case and show by Prufer transformation that anti-symmetric bifurcation pressure decreases when the distance of two corrosion regions is increasing. This paper serves to enhance the understanding of the collapse pressure of subsea pipes with local thickness reduction.
“…This ring consists of two parts: intact part with original thickness t ( s ) = t 0 and corroded part where t ( s ) is the reduced thickness ( t ( s ) < t 0 ). The Timoshenko’s equation 12,20 reads (refer to Appendix F for a concise derivation)where E is elastic modulus, I is the moment of inertia, D is an unknown constant, ⋅ ′ = d ⋅/ ds and s ∈ [0, 2 π ] is angular coordinate in circumferential direction subject to periodicity conditions w (0) = w (2 π ), w ′(0) = w ′ (2 π ) and in extension conditions ∫02πw(s)ds=0. Note that in derivation of equation (1), the membrane inextensible assumption v ′ = w ( v is circumferential displacement) has been applied to simplify the solution.Figure 1.Schematic of a thin ring model with local thickness reduction due to corrosion.…”
Section: General Governing Equationmentioning
confidence: 99%
“…Xue and Fatt 18,19 used the same Timoshenko equation to analytically study the bifurcation pressure of corroded rings and used some perturbative WKB to derive some analytical approximations. Based on those previous attempts, Yan et al 20,21 extensively and analytically calculated the bifurcation pressure and collapse of corroded rings with some initial imperfection and showed that the analytical prediction by Timoshenko’s equation was accurate when numerical finite element analysis results were compared.…”
Section: Introductionmentioning
confidence: 99%
“…Only purely elastic collapse is considered in this paper and thus, the theoretical calculation directly applies for thin pipes. However, for thick-walled pipes for deep-sea applications, plasticity effect should be included (see some extensive discussions on this topic by our previous investigation 20 ).…”
This paper presents a perturbative analysis of bifurcation pressure of 2D corroded rings characterized by locally thinned regions under external pressure by asymptotically analyzing the Timoshenko differential equation and parametric analysis. First, for the case of one corrosion region, we formulate regular perturbative solution separately for anti-symmetric bifurcation and symmetric bifurcation cases. Concise formulation is presented by introducing a corrosion severity parameter and perturbative solution is presented. Second, we present a detailed analysis for the case where corrosion region has small angular extent by converting it into a singular perturbative problem and conduct various asymptotic analyses to illustrate the interesting interlacing behaviors. The derived explicit formula explains some numerical observation by Fatt in literature. Third, we conduct parametric analysis for the case of two interacting corrosion regions by classifying it into two cases: symmetric corrosion case and non-symmetric corrosion case. Finally, we present asymptotical analysis to investigate the extremely corroded case and show by Prufer transformation that anti-symmetric bifurcation pressure decreases when the distance of two corrosion regions is increasing. This paper serves to enhance the understanding of the collapse pressure of subsea pipes with local thickness reduction.
“…The localised buckling initiated by initial imperfection and hydrostatic pressure plays a significant role in the pipeline collapse during lateral or upheaval buckling of a pipeline [17]. Various authors studied the effect of ovalisation and pipe diameter-to-thickness ratio on pipe collapse pressure [17,[106][107][108][109]. In Figure 17, fO represents the initial ovality of the pipeline, Pc is the collapse pressure of the pipeline, and Po is the yield pressure.…”
Section: Local Buckling Of An Initially Dented Pipelinementioning
The buckling analysis of an offshore pipeline refers to the analysis of temperature-induced uplift and lateral buckling of pipelines by analytical, numerical, and experimental means. Thus, the current study discusses different research performed on thermal pipe-buckling and the different factors affecting the pipeline’s buckling behaviour. The current study consists of the dependency of the pipe-buckling direction on the seabed features and burial condition; the pre-buckling and post-buckling load-displacement behaviour of the pipeline; the effect of soil weight, burial depth, axial resistance, imperfection amplitude, temperature difference, interface tensile capacity, and diameter-to-thickness ratio on the uplift and lateral resistance; and the failure mechanism of the pipeline. Moreover, the effect of external hydrostatic pressure, bending moment, initial imperfection, sectional rigidity, and diameter-to-thickness ratio of the pipeline on collapse load of the pipeline during buckling were also included in the study. This work highlights the existing knowledge on the topic along with the main findings performed up to recent research. In addition, the reference literature on the topic is given and analysed to contribute to a broad perspective on buckling analysis of offshore pipelines. This work provides a starting point to identify further innovation and development guidelines for professionals and researchers dealing with offshore pipelines, which are key infrastructures for numerous maritime applications.
“…His classical conclusion was derived under the elastic material and small deformation deformation assumption. Afterwards, many studies considering large deformation and more complicated loads have been investigated [22][23][24]. Smith [25] evaluated the buckling of a multisegment underwater hull.…”
This paper is the first to present the dynamic buckling behavior of spherical shell structures colliding with an obstacle block under the sea. The effect of deep water has been considered as a uniform external pressure by simplifying the effect of fluid–structure interaction. The calibrated numerical simulations were carried out via the explicit finite element package LS-DYNA using different parameters, including thickness, elastic modulus, external pressure, added mass, and velocity. The closed-form analytical formula of the static buckling criteria, including point load and external pressure, has been firstly established and verified. In addition, unprecedented parametric analyses of collision show that the dynamic buckling force (peak force), mean force, and dynamic force redistribution (skewness) during collisions are proportional to the velocity, thickness, elastic modulus, and added mass of the spherical shell structure. These linear relationships are independent of other parameters. Furthermore, it can be found that the max force during the collision is about 2.1 times that of the static buckling force calculated from the analytical formula. These novel insights can help structural engineers and designers determine whether buckling will happen in the application of submarines, subsea exploration, underwater domes, etc.
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