PSI - Issue 81

Ahsan Anugrah Elbar et al. / Procedia Structural Integrity 81 (2026) 3–10

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3.3. Benchmark analysis and mesh convergence study

Table 3 summarizes the benchmarking results for analytical and numerical deflection predictions at three loading levels. The analytical deflections for 100%, 125%, and 150% fill were 2.6 mm, 3.25 mm, and 3.9 mm, respectively. Corresponding finite element results yielded 2.76 mm, 3.42 mm, and 4.15 mm, with an average deviation of 5.93%, indicating good overall agreement between analytical and numerical approaches. Fig.3 (a) illustrates the mesh convergence behavior of stress, where the stress values exhibit a clear stabilization trend beyond a mesh size of 10 mm, indicating that further refinement provides only marginal improvement. In contrast, Fig. 3(b) shows that deflection displays slightly higher sensitivity to mesh variation, with the most significant deviation from the analytical value occurring at a mesh size of 10 mm. Nevertheless, the deflection variation between 10 mm and finer meshes remains relatively small, and the stress convergence at 10 mm suggests that this mesh size already captures the dominant structural response. Therefore, the 10 mm mesh was selected as the final mesh configuration, offering an optimal balance between numerical accuracy and computational cost. As shown in Fig. 4, the selected mesh configuration employs S4R shell elements with a uniform element size of 10 mm, representing the ramp plate geometry with appropriate boundary conditions. This configuration ensures adequate accuracy for both stress and deformation predictions while maintaining reasonable computational efficiency, making it suitable for subsequent loading and corrosion analyses (Islami et al., 2025; Melnyk et al., 2025).

Table 3. Benchmarking result. Models

Deflection (mm)

Disparity (%)

Analytical calculation

Finite element analysis

100% fill 125% fill 150% fill

2.6 3.25

2.76 3.42 4.15

6.15 5.23 6.41 5.93

3.9

Average Error

a

Fig. 3. Mesh convergence results: (a) mesh size vs stress; (b) mesh size vs deflection.

Fig. 4. Mesh configuration for the finite element simulation.