PSI - Issue 78

Riccardo Piazzon et al. / Procedia Structural Integrity 78 (2026) 230–236

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orientations while maintaining the 6 – brace and symmetry constraint. Elitism preserves the top 5 individuals. Additional constraints ensure at least one brace per story to ensure balanced dissipation and to prevent soft story effect. The fitness function computes the total energy dissipated via trapezoidal integration of force-displacement data from OpenSees outputs, caching results for efficiency. The GA writes presence/orientation configurations to an input file, runs OpenSees, and updates the population based on fitness, drawing on principles from genetic optimization in seismic design [6]. A custom output function logs the best configuration per generation, including presence matrix, orientations, total energy, and per-story energy exported for post-analysis. 3. Results The GA evaluated 1000 configurations (50 per generation × 20 generations), converging after 20 generations. The optimal topology placed knee braces at: main frame story 1 (L-oriented), left span story 1 (L-oriented), right span story 1 (R-oriented), left span story 2 (L-oriented), right span story 3 (R-oriented), and left span story 4 (R-oriented), dissipating 5.095 × 10⁸ Nmm of hysteretic energy - a 7.27% improvement over the baseline 4.749 × 10⁸ Nmm. Table 1 summarizes the optimized configuration.

Table 1. Optimized Knee-Brace Topology Story Main Frame (Presence, Orientation)

Left Span (Presence, Orientation)

Right Span (Presence, Orientation)

Energy (Nmm)

1 2 3 4

1, L 0, - 0, - 0, -

1, L 1, R

1, R

2.36×10 8 1.13×10 8 8.24×10 7 7.81×10 7 5.095×10 8

0, -

0, -

1, R

1, L

0, -

Total

-

-

-

The optimized configuration dissipated the highest energy in the first story (2.36 × 10⁸ Nmm), approximately 2.1 times that of the second story and significantly more than the upper stories, as visually depicted in Fig. 1(b), which presents energy dissipation per story. Fig. 1(a) shows the convergence curve, and Fig. 2(a) presents energy dissipation per story/span with the corresponding optimal configuration displayed at Fig. 2(b). Fig. 3. Presents the hysteretic response of dissipators in the optimal configuration (Generation 20). a b

Fig. 1. (a) GA Convergence Curve; (b) Energy dissipated per story per spans.