PSI - Issue 78

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

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UPN100 sections to study cyclic performance [25]. The critical role of energy dissipation metrics in evaluating structural performance in seismic regions has been widely acknowledged, with research highlighting their importance in limit-state design [26]. This study leverages these advancements, using a GA to evolve brace topologies and address the combinatorial challenge of 12 potential locations (4 stories × 3 spans). The methodology integrates OpenSees for simulations [27] and MATLAB for GA implementation with an anticipated convergence curve showing a progressive increase in dissipated energy, culminating in an optimized configuration that enhances seismic resilience. 2. Methodology 2.1. Structural Model The KBF model comprises a 4-story frame with three spans; main frame, left span and right span, each featuring a story height of 2000 mm and a span width of 2000 mm [25]. This configuration builds on prior models by Piazzon et al., which reproduces the non-linear behavior of a knee bracing system equipped with a dissipative fuse, providing insights into the cyclic response using UPN100 sections as dissipators [25]. The OpenSees implementation employs columns (RHS 150×150×10, A = 5257mm 2 , I = 16525300 mm 4 ), beams (2×UPN100, A = 4800 mm 2 , I = 5300000 mm 4 ), and diagonal braces (same as columns), combining the lateral stiffness of braces with the ductility of knee elements [1]. Knee dissipators, modeled as UPN100 sections (A = 2700 mm 2 , F � = 120000N, K � = 21000N/mm ), operate via a dissipative fuse mechanism, yielding under seismic loads to protect beams and columns while absorbing energy through hysteresis [2], [25]. These fuse elements are calibrated per [25], with rotational springs at beam column joints to mimic the flexibility behavior (( k ��� = 6 × 10 � Nmm/rad ). Gravity loads follow Eurocode 8 guidelines [28], with nodal masses derived from structural weight and tributary area contributing to the total seismic mass distributed across top nodes. The tcl code facilitates topological optimization by defining knee-brace presence (0 = absent, 1 = present) and orientation (L = left oriented, R = right oriented) for each story and span, constrained to exactly six braces. Nodes and elements are dynamically generated or re-used based on the configuration, ensuring compatibility across spans. Simulations are performed under the L’Aquila 2009 earthquake. 2.2. Genetic Algorithm Optimization The GA, implemented in MATLAB, optimizes the topology of six knee braces to maximize hysteretic dissipated energy. The design space includes 12 locations (4 stories × 3 spans), with variables:  Presence: Binary vector (12 elements, each of value 0 or 1), constrained to sum to 6 (exactly six braces).  Orientation: Binary vector (6 elements, 0=L, 1=R) for the 6 active braces, constrained to exactly 3 L and 3 R for symmetry. The genetic algorithm (GA) was first proposed by Professor Holland in 1975 and is a globally optimal, self-adaptive probabilistic search method based on the principles of "survival of the fittest" and biological adaptation in nature [29]. GA is effective for optimization problems involving discrete variables and spaces, where traditional mathematical methods are ineffective or difficult to apply [30]. A key characteristic of GA is the coding of variables that describe the problem. The most common coding method transforms variables into binary strings of specific length, with a fitness function measuring individual fitness. In GA, a population evolves through successive generations via repeated application of genetic operators, including reproduction, crossover, and mutation [31–34]. As a new population is created, the performance index is evaluated for each new design to determine its fitness relative to others, continuing until no further improvement is observed in the best individual, yielding the optimal solution. The initial population (50 individuals) which is randomly generated includes a baseline with six braces (with mixed orientations: L L R R R L). The GA evolves through 20 generations, using a roulette wheel selection method, a crossover rate of 80% and a 5% probability custom mutation function that swaps knee brace locations and flips