Issue 78

M. Habashneh et alii, Fracture and Structural Integrity, 78 (2026) 409-431; DOI: 10.3221/IGF-ESIS.78.24

diagonal ribs and well-defined triangular regions within the arms. The intermediate mesh (h=2 mm, Fig. 14(b)) retains the same overall pattern but with fewer secondary members and a simpler internal layout. In the case of the coarse mesh (h=2 mm, Fig. 14(c)), the topology becomes more simplified. The number of diagonal ribs decreases, the internal cells become larger, and the members appear thicker. Despite these differences, the primary spoke like structure and the horizontal bridging strut remain clearly visible in all cases, demonstrating that the global structural response is largely independent of mesh size within the investigated range.

Figure 13: Baseline optimization results for the U-shaped plate: (a) final optimized topology (black: solid elements; red: void elements); (b) evolution histories of mean compliance and volume fraction.

Figure 14: Effect of mesh element size on the optimized topology of the U-shaped plate: (a) baseline mesh (h = 2 mm); (b) medium mesh (h = 3 mm); (c) coarse mesh (h = 4 mm). The displacement results support the observed topological trends. The baseline case (h = 2 mm) gives a displacement of 0.0375 mm, while the values increase to 0.0390 mm and 0.041 mm for mesh sizes of 3 mm and 4 mm, respectively. This corresponds to an overall increase of about 9.3% between the finest and coarsest meshes. The variation is larger than that observed for the L-shaped beam and pinned plate examples. This higher sensitivity is mainly due to the more complex geometry of the U-shaped plate. Features such as the notch corners, the narrow connecting region, and the multiple diagonal load paths create a stress field that requires a finer discretization to be captured accurately. As a result, the structural stiffness is more affected by mesh size. Despite this, all mesh levels recover the same main load-transfer mechanism. This confirms that the baseline mesh of 2 mm is adequate for capturing the overall structural response, while further refinement mainly improves the representation of secondary members and local details.

Variation from Baseline (%)

U 2 (mm)

Element Size (mm)

Mesh Type

2 3 4

Baseline Medium

0.0375 0.0390

—

+4.0%

Coarse +9.3% Table 4: Effect of mesh element size on vertical displacement at the load node. 0.041

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