Issue 78

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

Figure 5: Effect of evolutionary rate on the optimized topology of the L-shaped beam: (a) conservative evolutionary rate ( ER = 0.01); (b) baseline case ( ER = 0.02); (c) aggressive evolutionary rate ( ER = 0.04). L-Shaped Beam: effect of filter radius Filter radii of r min = 18 mm, 21 mm and 24 mm are tested with h and ER kept fixed. Results are shown in Fig. 6. In all three cases the primary structure consisting of the vertical web and curved corner strut remains unchanged confirming that the global load-transfer requirement dominates over the regularizing effect of the filter in this range. Differences appear only in the secondary bracing of the lower arm. The baseline ( r min = 18 mm, Fig. 6(a)) produces the most detailed internal layout with multiple diagonal members forming a well-distributed triangulated system. Increasing to r min = 21 mm (Fig. 6(b)) smooths out the sensitivity field over a wider area which suppresses some of the finer branching and strengthens a smaller number of load paths. The junction near the re entrant corner becomes more pronounced and the diagonal system in the lower arm simplifies. At r min = 24 mm (Fig. 6(c)) this effect goes further. Secondary features are largely suppressed and the topology settles into a compact layout with a few thick dominant struts. This progression makes sense given what the filter does: larger radii enforce a coarser minimum feature size and trade structural detail for smoother more regularized geometry.

Figure 6: Effect of filter radius on the optimized topology of the L-shaped beam: (a) baseline case ( r min = 18 mm); (b) ( r min = 21 mm); (c) ( r min = 24 mm). Pinned plate The second example is a pinned plate which is structurally quite different from the L-shaped beam. The design domain is a 720 mm by 477 mm rectangular plate pinned at all four corners with a concentrated downward load of 15 kN applied at the midpoint of the top edge as shown in Fig. 7. This setup produces a predominantly biaxial stress state with tension and compression competing across the domain which creates a very different optimization landscape compared to the L-shaped

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