# Effect of Corrugated Sheet Diameter on Structural Behavior under Cryogenic Temperature and Hydrodynamic Load

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## Abstract

**:**

## 1. Introduction

## 2. Finite Element Analysis

#### 2.1. Scenario and Material Properties

^{−1}, respectively.

#### 2.2. Loading and Boundary Conditions

#### 2.3. Mesh Convergence Study

## 3. Result and Discussion

#### 3.1. Validation

#### 3.2. Overall Structural Behavior

#### 3.3. Effect of Corrugation Shape under Pressure

#### 3.3.1. Effect of Corrugation Radius

#### 3.3.2. Effect of Fillet Angle

#### 3.4. Effect of Corrugated Dimension under Temperature Gradient

#### 3.4.1. Effect of Corrugation Radius

#### 3.4.2. Effect of Fillet Angle

## 4. Conclusions

- In the pressure analysis, the maximum stress occurs at the intersection of the fillet along the middle of the longitudinal direction. In addition, the maximum deformation occurs at the center of the corrugation for different heights based on the load conditions.
- In the hydrodynamic pressure analysis, the maximum stress and deformation increase as the radius of the corrugation increases. In particular, the corrugation radius should not exceed 0.11 L because it would induce severe deformation compared to that of the 0.1 L corrugation radius.
- In the pressure load condition, the maximum stress and deformation decrease with increasing fillet angle. The sensitivity is greater in the symmetric pressure analysis, where the maximum deformation decreases by 15% to 25% based on the fillet angle.
- In the thermal contraction condition, the effect of the fillet angle on the structural behavior is less than 1%. However, there exists an inflection point at which the maximum deformation increases or decreases depending on the corrugation radius. Furthermore, a short corrugation radius induces more residual stress in the corrugation.
- From the analysis results, the optimum corrugation radius and fillet angle were determined as 0.09 L and 82.4°, respectively. The fillet angle is a more important factor under hydrodynamic loading than thermal contraction conditions. Therefore, a larger fillet angle is recommended for reducing corrugation deformation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Photograph of the primary barrier. (

**b**) Simplified primary barrier without knot area for FEA. (

**c**) Schematic of hydrodynamic loading caused by ship motion. The black arrow represents the flow direction. (

**d**) Schematic of the membrane-type LNG CCS [9].

**Figure 2.**(

**a**) Detailed SPB drawing: (

**b**) front view of SPB, (

**c**) half-length model, and (

**d**) quarter model.

**Figure 3.**(

**a**) Stress–strain curve of AISI 304L tensile test at −163 °C; (

**b**) thermal expansion coefficient of AISI 304L at room and cryogenic temperature.

**Figure 4.**Loading and boundary conditions in (

**a**) symmetric hydrodynamic pressure, (

**b**) thermal shrinkage, and (

**c**) asymmetric hydrodynamic pressure analysis. The red rectangles represent the flat bottom of the SPB, and each line represents a side of the SPB. Furthermore, the gray arrows indicating the pressure direction do not cross the yellow pressure limit line.

**Figure 5.**Schematic of mesh size distribution in (

**a**) symmetric and asymmetric hydrodynamic pressure analysis and (

**b**) thermal shrinkage analysis.

**Figure 6.**Maximum deformation according to the number of elements in (

**a**) pressure tests and (

**b**) thermal shrinkage analysis. The red dashed line connotes deformation convergence.

**Figure 7.**Photographs of the (

**a**) experimental apparatus and (

**b**) strain measurement points at the primary barrier; graphs depicting the (

**c**) tensile properties of AISI 304L at room temperature and (

**d**) experimental and FEA time–strain histories [9].

**Figure 8.**Stress distribution for case No. 32 in (

**a**) symmetric pressure analysis, (

**b**) thermal shrinkage analysis, and (

**c**) asymmetric pressure analysis. The black dashed rectangle and purple dot represent the points under maximum stress. Side view 1 (pressure) represents the pressure side, and side view 2 (nonpressure) represents the opposite case.

**Figure 9.**Deformed shapes for case No. 32 in (

**a**) symmetric pressure analysis, (

**b**) thermal shrinkage analysis, and (

**c**) asymmetric pressure analysis. The black dashed rectangle represents the area of maximum deformation; side view 1 (pressure) shows the face exposed to pressure, and side view 2 (nonpressure) represents the opposite case.

**Figure 10.**Deformation direction of the SPB on the length–middle section in the (

**a**) symmetric pressure analysis, (

**b**) asymmetric pressure analysis, and (

**c**) thermal shrinkage analysis. The black arrows represent the deformation direction of the node from the red line to the blue dashed line.

**Figure 11.**Deformed SPB shapes of 82.8° fillet angle under asymmetric pressure in (

**a**) case No. 12, (

**b**) case No. 22, (

**c**) case No. 32, and (

**d**) case No. 42.

**Figure 12.**Maximum SPB stress and deformation according to the fillet angle in each test (

**a**,

**c**) symmetric pressure analysis and (

**b**,

**d**) asymmetric pressure analysis.

**Figure 13.**Maximum (

**a**) stress, stress on the center corrugation, and (

**b**) deformation of SPB according to the fillet angle in thermal shrinkage analysis. The dashed line represents the enlarged region of the graphs.

R/L | Case No. | θ (°) |
---|---|---|

0.08 | 11 | 82.4 |

12 | 82.8 | |

13 | 83.2 | |

14 | 83.6 | |

0.09 | 21 | 82.4 |

22 | 82.8 | |

23 | 83.2 | |

24 | 83.6 | |

0.10 | 31 | 82.4 |

32 | 82.8 | |

33 | 83.2 | |

34 | 83.6 | |

0.11 | 41 | 82.4 |

42 | 82.8 | |

43 | 83.2 | |

44 | 83.6 |

**Table 2.**The tensile properties of AISI 304L at room temperature [30].

Yield Stress $({\mathit{\sigma}}_{\mathit{y}},\text{}\mathbf{MPa})$ | Young’s Modulus (E, MPa) | Strength Coefficient (H, MPa) | Strain Hardening Exponent (n) |
---|---|---|---|

331.3 | 206,387 | 1678.8 | 0.46 |

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**MDPI and ACS Style**

Park, J.-S.; Kim, J.-H.; Jeong, Y.-C.; Kim, H.-T.; Kim, S.-K.; Lee, J.-M.
Effect of Corrugated Sheet Diameter on Structural Behavior under Cryogenic Temperature and Hydrodynamic Load. *Metals* **2022**, *12*, 521.
https://doi.org/10.3390/met12030521

**AMA Style**

Park J-S, Kim J-H, Jeong Y-C, Kim H-T, Kim S-K, Lee J-M.
Effect of Corrugated Sheet Diameter on Structural Behavior under Cryogenic Temperature and Hydrodynamic Load. *Metals*. 2022; 12(3):521.
https://doi.org/10.3390/met12030521

**Chicago/Turabian Style**

Park, Jin-Seok, Jeong-Hyeon Kim, Yong-Cheol Jeong, Hee-Tae Kim, Seul-Kee Kim, and Jae-Myung Lee.
2022. "Effect of Corrugated Sheet Diameter on Structural Behavior under Cryogenic Temperature and Hydrodynamic Load" *Metals* 12, no. 3: 521.
https://doi.org/10.3390/met12030521