PSI - Issue 41

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Ilham Widiyanto et al. / Procedia Structural Integrity 41 (2022) 274–281 Widiyanto et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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Cylinder shell material considered for FE analysis follows industry practice API 5L grade X65. This material also plays a vital role in the oil and gas exploration industry, applied to pipelines. API 5L grade X65 material belongs to high-strength, low carbon steel. Material is an elastic-perfectly plastic material model is adapted to simulate the constitutive behavior of the outer pipe. Young's modulus, Poisson ratio, Yield stress are taken as 211330 N/mm 2 , 0.3, and 552 MPa, respectively, as reported by Fatoba and Akid (2014). 3.2. Boundary Condition In this study, the model is assumed to be under external pressure. The incremental external pressure in this FE analysis was 1 MPa over the entire surface of the cylindrical shell in all analyses. At one end of the cylinder, the shell is completely fixed. While at one end, only axial movement is allowed. The Boundary condition model can be seen in Fig 4a. In the nonlinear buckling step, the arc length method used is 0.1 mm, the minimum arc length was 0.00001 mm, the maximum arc length was 1E+36 mm, and the number of iterative steps of the total arc length was 100. This is implemented by turning on the NLGEOM (non-linear-geometry) switch in the Step module in ABAQUS. In this study, the cylindrical shell model was varied in geometry and cylinder dimensions. The distribution of variations can be seen in Table 3. The meshing size is varied into 3, namely the size of 20 mm, 30 mm, and 40 mm, which are symbolized by the code 1, 2, and 3. This meshing aims to get a convergence value. The mesh element used in the shell cylinder is S4R which is called the 4-node quadrilateral finite membrane strain linear reduction integral shell element. The meshing model can be seen in Fig 4b. The diameter of the cylinder used in this simulation uses the size of the offshore pipe product. The diameters are, among others, measuring 711.2 mm, 762 mm, and 812.8 mm, which are symbolized by the code sequentially A, B, and C. While the geometry types are unstiffened cylinder shell, stringer-stiffened cylinder shell, and ring-stiffened cylinder shell are symbolized by the code sequentially, namely S1, S2, and S3.

(a) (b) Fig. 4 FEA configurations: (a) Boundary condition modelling; and (b) Meshing model S1-1-A

This nonlinear buckling analysis uses ABAQUS/CAE software with the finite element method. In this analysis, there are 2 stages, namely linear buckling and nonlinear buckling. Linear buckling is the beginning of the simulation of nonlinear buckling. In linear buckling, initial imperfections and material nonlinearity are not considered. The result of the analysis of linear buckling is the eigenvalue. The input used in nonlinear buckling is the eigenvalue first mode. The first eigenmode of linear buckling is often introduced as the worst imperfection to study the buckling characteristics of shells.

Table 3. Variations of modelling cylinder shell No

Variation

Geometry

Diameter

1 2 3 4 5 6 7 8 9

S1 S2 S3 S2 S2 S2 S3 S3 S3

A A A B B B A B C