Issue 75

P. Grubits et alii, Fracture and Structural Integrity, 75 (2026) 124-156; DOI: 10.3221/IGF-ESIS.75.10

domain—exhibits low sensitivity to buckling. However, in problems involving more slender structures, this parameter may become critical for achieving convergence and maintaining structural stability. Furthermore, the results of the three optimization setups are summarized in Tabs. 4, 5, and 6, which present the mean values and standard deviations calculated from the 10 independent runs. Overall, E1-OP2 achieves the lowest average fitness value of 0.2082. Consequently—and as also reflected in the structural weight evolution—E1-OP2 yields the lowest mean structural weight of 451.54kg, while maintaining an average complementary strain energy of only 0.000725Nmm. In comparison, E1-OP1 and E1-OP3 result in higher mean weights of 525.99kg and 560.08kg, corresponding to increases of approximately 16.5% and 24.0%, respectively, relative to E1-OP2. These findings further confirm the efficiency of the elasto-plastic design scenario in enabling material-efficient solutions with minimal inelastic deformation. In addition, the highest observed standard deviation in structural weight is only 30.22kg (in the case of E1-OP1), which is relatively small considering the range of possible solutions. This demonstrates the reliability and robustness of the developed optimization framework. Finally, as shown consistently in Tabs. 4–6, all three design constraints associated with the penalty function are satisfied in every optimization run, highlighting the effectiveness of the proposed methodology in achieving compliant and high-performing structural designs.

  Nmm p W

  0 / m  P P

  kg s G 525.96 533.67 517.15 513.56 502.66 597.67 550.70 503.44 492.64 522.48 525.99

   

fitness

Run

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000

4.289 3.988 3.774

0.2545 0.2593 0.2490 0.2467 0.2399 0.2995 0.2700 0.2404 0.2336 0.2523 0.2545 0.0190

1 2 3 4 5 6 7 8 9

12.874 6.804 10.749 9.872 6.106 5.696 6.141 7.029

10

Mean

Std. dev.

30.22

3.107

Table 4: The summary of the optimization outcomes for E1-OP1.

  Nmm p W

  0 / m  P P

  kg s G 447.37 449.00 452.18 453.68 446.04 470.50 423.63 458.97 449.30 464.70 451.54

    5.043 6.431 8.787 3.754 4.898 6.686 6.302 5.964 5.418 4.554 5.784

fitness

Run

0.000000 0.000004 0.000893 0.000000 0.000418 0.000000 0.005305 0.000000 0.000627 0.000000 0.000725 0.001642

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000

0.2052 0.2071 0.2107 0.2091 0.2043 0.2197 0.1909 0.2124 0.2064 0.2160 0.2082

1 2 3 4 5 6 7 8 9

10

Mean

Std. dev.

12.61

1.400

0.0078

Table 5: The summary of the optimization outcomes for E1-OP2.

145