Issue 75

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

which were compared in the following. In this example as well, the prescribed maximum displacement limit of ,max 12.70mm y U  is defined in accordance with Eurocode standards, considering a total structural height of 5080mm H  and the corresponding serviceability limit of /400 H .

(a) (b) Figure 24 : Results for the initial configuration of the 25-bar truss: (a) load–plastic deformation response of the entire structure; (b) load– displacement response at node J2.

Design scenario

Displacement constraint

Initial geometric imperfection

  0 Nmm p W









, Nmm p max W

, mm y max U

stab 

Setup

10.85 10.85

43.40 43.40

1.000 1.000

E2-OP2 Elasto-plastic E2-OP3 Elasto-plastic

NO YES

Automatically Automatically



12.70

Table 9: Key parameters of the optimization setups for the 25-bar truss.

As a first step in the analysis, Fig. 25 compares the convergence histories of the generation-wise minimum fitness for E2 OP1 and E2-OP2. In both cases, the sequence drops sharply in the early generations and then transitions to a slower, monotonic approach to a plateau. The gray band—the gap between the best and worst individuals—visually indicates the population variance, as in the previous example. By the final generations, both setups reach nearly identical fitness levels, demonstrating comparable convergence behavior and overall performance.

(a) (b) Figure 25: Fitness evolution of (a) E2-OP1 and (b) E2-OP3, highlighting the best and worst performing runs among 5 independent optimization processes. The shaded area represents the distribution of the remaining runs. Consistent with the minimum-fitness history, the generation-wise structural weight follows a similar trend, as shown in Fig. 26. This suggests that, near convergence, the weight component dominates the objective function. The final structural weights for E2-OP1 and E2-OP2 are essentially identical, indicating comparable solutions across the two setups. In this numerical example as well, the complementary plastic work of the residual forces p W for the best-fitness solutions remains small, although not strictly zero in every case, as shown in Fig. 27. Moreover, all final designs across the runs satisfy the prescribed limit , p max W , demonstrating that the proposed formulation effectively controls plastic deformations.

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