Issue 78

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

Pinned Plate: effect of mesh size Mesh sensitivity is studied using element sizes of h = 10 mm, 7.5 mm and 15 mm with ER and r min kept fixed. Results are shown in Fig. 9 and the corresponding vertical displacements at the load node are listed in Tab. 1. All three mesh sizes produce the same primary load-carrying mechanism which is a symmetric inverted-V arch connecting the midspan load to the four pinned corners through two inclined compression struts. This consistency across discretization levels confirms that the main structural response is controlled by the geometry and boundary conditions rather than the mesh. The arch form is a natural outcome of the symmetric support arrangement and central loading which together favor a compression path of this type under large-displacement conditions. Differences appear in the secondary bracing outside the primary arch. The baseline (h = 10 mm, Fig. 9(b)) produces a distributed network of diagonal members that subdivide the lateral zones into triangular sub-cells. The coarse mesh (h = 15 mm, Fig. 9(c)) largely suppresses this secondary bracing leaving the arch as almost the only load-carrying element. Member boundaries are pixelated and the arch itself becomes thicker to compensate. The fine mesh (h = 7.5 mm, Fig. 9(a)) sharpens up the member definition and produces more slender diagonal struts with crisper solid-void boundaries suggesting that finer discretization captures secondary load paths that coarser meshes can only approximate.

Figure 9: Effect of mesh element size on the optimized topology of the pinned plate: (a) fine mesh (h = 7.5 mm); (b) baseline mesh (h = 10 mm); (c) coarse mesh (h = 15 mm). The vertical displacement at the load node gives a quantitative picture to go alongside the topology results. The baseline (h = 10 mm) gives U 2 = 0.051 mm, the coarse mesh (h = 15 mm) gives U 2 = 0.052 mm and the fine mesh (h = 7.5 mm) gives U 2 = 0.053 mm. The variation in the vertical displacement ଶ across the three investigated mesh sizes is less than 4%, indicating that the global stiffness of the optimized design is essentially mesh-independent within this range. This is consistent with the fact that the primary arch mechanism is the same in all three cases since it is this mechanism that contributes most to the overall stiffness. The slight increase in displacement for the fine mesh comes from the more slender secondary members it resolves which are collectively a little less stiff than the thicker members the coarser mesh produces. In short mesh refinement improves the geometric detail of secondary members without meaningfully changing the primary topology or the global stiffness response.

Variation from Baseline (%)

U 2 (mm)

Element Size (mm)

Mesh Type

7.5

Fine

0.053 0.051 0.052

+3.9%

10 15

Baseline Coarse

—

+2.0% Table 1: Effect of mesh element size on vertical displacement at the load node.

Pinned Plate: effect of evolutionary rate Three evolutionary rate settings are tested for the pinned plate: ER = 0.02, 0.01 and 0.04 with h and r min kept fixed. Results are shown in Fig. 10 and displacements are listed in Tab. 2. All three cases recover the same basic load-transfer idea with inclined struts connecting the load point to the corner supports. However the evolutionary rate has a noticeably stronger effect here than mesh size did. It affects not just the detail of the secondary bracing but also the completeness of the primary topology.

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