PSI - Issue 41

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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In the nonlinear buckling stage, material nonlinearity and geometric imperfections are considered. Shapes and sizes of geometric imperfections are automatically included in the model. However, in this simulation, cylinder caps are omitted to simplify the model and reduce complex computations. The output of this nonlinear buckling analysis is load proportionally factor (LPF). This LPF is used in calculating critical buckling load. In addition, this LPF also produces arc length values. This arc length can be used to find the value of the displacement. The critical buckling load and displacement values can be calculated using the following equations: = . 0 (3) = . (4) Where P is the critical buckling load in the form of pressure. P 0 is the initial load input, in this case, the value of the first eigenmode, which is used as input for nonlinear buckling analysis. S is the arc length, and R is the radius of the cylinder shell while is the displacement of the shell cylinder 4. Result and Discussion This section describes the simulation results, namely the critical buckling load on the shell cylinder. The cylinder shell is pressured from the outside and axial compression. Each geometry has a different critical buckling load. The simulation results for critical buckling load are shown in Table 4. In Fig. 5, the vertical axis shows pressure while the horizontal axis shows the displacement. Variations in the cylindrical shell mainly affect the type of geometry, diameter size, and meshing size.

Table 4. Results of critical buckling load Model

Value (MPa)

S1-1-A S2-1-A S3-1-A S2-1-B S2-2-B S2-3-B S3-2-A S3-2-B S3-2-C

0.55 0.36 1.11 0.29 0.29 0.30 0.93 0.72 0.55

From these results, on various types of geometry, the ring-stiffened cylinder S3-1-A shell has a critical buckling load of 1.110 MPa higher than that of the unstiffened cylinder shell and stringer-stiffened cylinder shell. Meanwhile, stringer-stiffened cylinder shell S2-1-A has 0.367 MPa lower yield when compared to ring-stiffened cylinder shell and unstiffened cylinder shell. The equilibrium path of the cylindrical shell is shown in Fig 5.

Fig. 5 Equilibrium path comparing result