# Numerical Simulation of Local Buckling of Submarine Pipelines under Combined Loading Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Critical Load of Local Buckling of Pipeline

#### 2.1. Pipeline Buckling under External Pressure

#### 2.2. Pipeline Buckling under Combined Action of Bending Moment and External Pressure

## 3. Finite Element Analysis

#### 3.1. Finite Element Model

#### 3.2. Pipe Material Parameters

#### 3.3. Unit Selection

#### 3.4. Boundary Conditions

## 4. Result Analysis and Discussion

#### 4.1. Sensitivity Analysis of Local Buckling Defects of Submarine Pipelines

#### 4.1.1. Comparison of Simulation Results with Measured Values

#### 4.1.2. Effect of Depression on Critical Pressure

#### 4.1.3. Sensitivity of Different Radius-Thickness Ratio to Defects

#### 4.2. Nonlinear Local Buckling of Submarine Pipelines under Combined Axial Force, Bending Moment, and External Pressure

#### 4.2.1. Analysis Model

#### 4.2.2. Pressure-Displacement Curves of Pipelines Subjected to Different Bending Moments

#### 4.2.3. Effect of Bending on Critical Pressure

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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${\mathbf{D}}_{0}\mathbf{}$ $\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{t}$ $\left(\mathbf{m}\mathbf{m}\right)$ | $\frac{{\mathbf{D}}_{0}}{\mathbf{t}}$ | $\mathbf{E}$ $\left(\mathbf{GPa}\right)$ | ${\mathbf{E}}_{\mathbf{t}}\mathbf{}$ $\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ | ${\mathbf{\sigma}}_{\mathbf{y}}\mathbf{}$ $\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ | $\frac{{\mathbf{\sigma}}_{\mathbf{y}}}{\mathbf{E}}$ | ${\mathbf{P}}_{\mathbf{y}}\mathbf{}$ $\left(\mathbf{K}\mathbf{N}\right)$ | ${\mathbf{M}}_{\mathbf{p}}\mathbf{}$ $\left(\mathbf{K}\mathbf{N}\cdot \mathbf{m}\mathbf{m}\right)$ |
---|---|---|---|---|---|---|---|---|

42 | 1 | 42 | 69 | 1500 | 90 | 0.0013 | 11.59 | 151.29 |

28 | 1 | 28 | 69 | 1500 | 90 | 0.0013 | 7.91 | 70.56 |

M = 0 | M = 0.2 Mp | M = 0.4 Mp | M = 0.6 Mp | M = 0.8 Mp | |
---|---|---|---|---|---|

critical buckling pressure ${P}_{I}$ | 2.12 MPa | 2.07 MPa | 1.90 MPa | 1.83 MPa | 1.73 MPa |

reduction rate | 0 | 2.36% | 10.38% | 13.68% | 18.40% |

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**MDPI and ACS Style**

Su, W.; Ren, J.
Numerical Simulation of Local Buckling of Submarine Pipelines under Combined Loading Conditions. *Materials* **2022**, *15*, 6387.
https://doi.org/10.3390/ma15186387

**AMA Style**

Su W, Ren J.
Numerical Simulation of Local Buckling of Submarine Pipelines under Combined Loading Conditions. *Materials*. 2022; 15(18):6387.
https://doi.org/10.3390/ma15186387

**Chicago/Turabian Style**

Su, Wenxian, and Jie Ren.
2022. "Numerical Simulation of Local Buckling of Submarine Pipelines under Combined Loading Conditions" *Materials* 15, no. 18: 6387.
https://doi.org/10.3390/ma15186387