PSI - Issue 79

Abubakr E.S. Musa et al. / Procedia Structural Integrity 79 (2026) 206–216

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The second critical factor to consider for the equivalent geometric imperfection is its amplitude. The primary objective of this equivalent imperfection is to ensure that the base FE model is prepared to accommodate the additional geometric imperfection intended to simulate thickness reduction due to corrosion. To determine the appropriate amplitude, the experimental load-carrying capacities of the two specimens without thickness reduction (T1-1 and T1 2) are used as reference benchmarks. This calibration ensures that the FE model accurately represents the behavior of the tested specimens (T1-1 and T1-2). A similar methodology has been introduced in the work of Musa et al. (2021), where it was proven to be effective for modeling cylindrical shells with dent imperfections, demonstrating its applicability and reliability in capturing the effects of imperfections in shell structures. As shown in Table 2, the average load-carrying capacity of the two specimens without thickness reduction is 322.5 kN, while the perfect FE model predicts a significantly higher load of 417.6 kN. To address this discrepancy, FE models with the imperfection shape illustrated in Fig. 3 and varying amplitudes were developed and analyzed. The variation in the load-carrying capacity with respect to the equivalent imperfection amplitude is presented in Fig.4. The primary purpose of this figure is to identify the specific amplitude required for the FE model to reproduce the average experimental failure load of the intact specimens (the target load). Fig. 4 shows that an amplitude between 0.4t and 0.5t is sufficient to achieve this target. By interpolating between these two points, the required amplitude is determined to be 0.418t , which ensures that the FE model matches the experimental load-carrying capacity.

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P (kN)

Target (Experimental) Applying equivalent imperfections

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

Amp./t

Fig. 4. Determination of the required amplitude of equivalent geometric imperfections

In conclusion, the base FE model will utilize an equivalent geometric imperfection with the previously defined shape (Fig.3) and an amplitude of 0.418t . This model will then be modified to introduce the intended imperfection simulating thickness reduction due to corrosion, as described in the subsequent section. 3.2. Thickness Reduction Imperfections The introduced thickness reduction represents a form of imperfection intentionally incorporated to simulate corrosion damage, referred to as the intended imperfection. The base FE model with an equivalent geometric imperfection of 0.418t amplitude was used as the foundation to model this part of analysis. Utilizing the same mesh configuration as the base FE model, which consists of 10,100 nodes, a Mathematica code was employed to generate the node coordinates and assign the corresponding thickness at each node. Conditional statements were implemented within the code to specify whether each node retained the full thickness or transitioned to the reduced thickness based on the predefined corrosion pattern. An example of the generated nodes and their corresponding thickness values is illustrated in Fig. 5.