Issue 78

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

Figure 3: Baseline optimization results for the L-shaped beam: (a) evolution histories of mean compliance and volume fraction; (b) final optimized topology (red: solid elements; red: void elements).

Figure 4: Effect of mesh element size on the optimized topology of the L-shaped beam: (a) fine mesh (h = 2 mm); (b) baseline mesh (h = 3 mm); (c) coarse mesh (h = 6 mm). L-Shaped Beam: effect of evolutionary rate Three evolutionary rate settings are tested: ER = 0.01, 0.02 and 0.04 with h and r min kept fixed. Results are shown in Fig. 5. All three cases produce the same primary load-carrying scheme confirming that the main structural response is not sensitive to the evolutionary rate within this range. The differences appear in the secondary bracing. The conservative rate (ER = 0.01, Fig. 5(a)) gives the most well-defined internal structure with clean diagonal struts and uniform triangulation in the lower arm. Slow incremental updates give the sensitivity field time to settle between iterations which helps maintain regularity. The baseline (ER = 0.02, Fig. 5(b)) produces a similar layout with slightly thicker diagonals. At the aggressive rate (ER = 0.04, Fig. 5(c)) the internal bracing becomes noticeably less regular. The diagonal members lose their uniform distribution and the triangulated substructure breaks down. This happens because large simultaneous material changes cause sensitivity oscillations that the algorithm cannot resolve properly under large-displacement conditions. The overall finding is that the evolutionary rate has a stronger effect on secondary load path stability in nonlinear BESO than it does in the linear case.

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