Issue 75

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

Design scenario

Displacement constraint

Initial geometric imperfection

  0 Nmm p W









, Nmm p max W

, mm y max U

Setup

stab 

1.000 1.000

E1-OP1 E1-OP2

Elastic Elasto plastic Elasto plastic

NO NO

Automatically Automatically





 

28,311.08

7077.77

28,311.08

40.00 

7077.77

1.000

E1-OP3

YES

Automatically

Table 3: Key parameters of the optimization setups for the 37-bar truss. As a first aspect of the analysis, the convergence behavior of the three optimization setups is evaluated. As illustrated in Fig. 16, the evolution of the fitness function exhibits a similar overall trend across all configurations. In each case, a substantial drop in fitness values is observed within the initial generations, indicating rapid early improvements in the design solutions. This is followed by a stabilization phase between generations 10 and 15 , where convergence slows and the population saturates around near-optimal solutions. The shaded grey regions provide a qualitative illustration of the variability across the 10 independent optimization runs, highlighting the spread and consistency of the convergence process rather than representing a defined mathematical quantity.

(a) (c) Figure 16: Fitness evolution of (a) E1-OP1, (b) E1-OP2, and (c) E1-OP3, highlighting the best and worst performing runs among 10 independent optimization processes. The shaded area represents the distribution of the remaining runs. Corresponding to the minimum fitness values observed in each generation, the evolution of structural weight follows a similar trend across the optimization processes, as shown in Fig. 17. It is evident that E1-OP2 generally converges to a lower structural weight. This outcome results from the nature of the elasto-plastic design, in which a limited degree of plastic deformation is permitted. This flexibility enables additional material savings and guides the optimization toward lighter solutions. In contrast, E1-OP1 and E1-OP3 yield comparable final weights. This similarity arises because E1-OP3 includes a predefined maximum displacement constraint, which restricts the achievable load level and drives the optimization toward stiffer—and consequently heavier—configurations to satisfy the displacement limit. (b)

(a) (c) Figure 17: Structural weight evolution of (a) E1-OP1, (b) E1-OP2, and (c) E1-OP3, highlighting the best and worst performing runs among 10 independent optimization processes. The shaded area represents the distribution of the remaining runs. In terms of the complementary strain energy of residual forces, as shown in Fig. 18, low values are generally maintained throughout the optimization process for the best-performing configurations. Under the elastic design scenario (E1-OP1), (b)

143