PSI - Issue 78

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

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4. Discussion The optimized topology enhanced energy dissipation by strategically placing six knee braces across stories and spans. The GA allocated braces predominantly to lower stories and spans, aligning with higher seismic demands, as observed in [36]. Compared to the baseline, the optimized configuration improved energy dissipation by 7.27 %, consistent with topology optimization studies [4], [35]. The results align with [23], which emphasizes the role of brace configuration in energy distribution, and extend [24] by incorporating orientation symmetry (3 L and 3 R) to mitigate directional biases under seismic loading. The inclusion of three spans enabled asymmetric yet balanced configurations, enhancing flexibility compared to single span models in [25]. The optimized setup also showed varied interstory drifts, with lower values in lower stories (e.g., 0.16% in story 1 and 2) but higher in upper stories (up to 5%), suggesting potential for multi-objective optimization to balance energy and drift. It is noteworthy that while the energy improvement is measured from a random baseline configuration, the key result is the optimal configuration itself, which demonstrates repeatability across multiple runs despite varying initial populations, and is specific to the imposed constraints and the L’Aquila earthquake. Limitations include computational cost (due to repeated OpenSees calls) and convergence challenges, which could be addressed by parallel computing or increased population size/generations. Future work will explore multi-objective optimization (e.g., incorporating drift minimization) and taller frames to broaden applicability. 5. Conclusion This study optimized the topology of six knee braces in a 4-story, 3-span KBF using a GA to maximize hysteretic energy dissipation under the L’Aquila 2009 earthquake. The methodology, integrating OpenSees and MATLAB, achieved a 7.27% improvement in energy dissipation (5.095 × 10⁸ Nmm) compared to a chosen baseline (4.749 × 10⁸ Nmm), converging effectively by generation 8 to 20. The approach offers a simple, effective framework for optimal seismic layout, adaptable and repeatable for various configurations. Future research will extend this to taller frames, incorporate multi-objective optimization (e.g., drift minimization), and explore advanced algorithms [37].

Acknowledgements The authors acknowledge the University of Padova for supporting this research.

References

[1] J. D. Aristizabal-Ochoa, “Disposable knee bracing: Improvement in seismic design of steel frames,” J. Struct. Eng., vol. 112, no. 7, pp. 1544-1552, Jul. 1986, doi: 10.1061/(ASCE)0733-9445(1986)112:7(1544). [2] N. Bourahla, “Knee bracing system for earthquake resisting steel frames,” Doctoral thesis, https://research information.bris.ac.uk/en/studentTheses/knee-bracing-systemfor-earthquake-resisting-steel-frames. [3] K. C. Chang, M. L. Lai, T. T. Soong, D. S. Hao, and Y. C. Yeh, “Seismic behavior and design guidelines for steel frame structures with added viscoelastic damper,” NCEER 93-0009, National Center for Earthquake Engineering Research, Buffalo, NY, USA, 1993. [4] R. T. Haftka and H.M. Adelman, “Selection of actuator locations for static shape control of large space structures by heuristic integer programing,” Computers and Structures, vol. 20, no. 1–3, pp. 575–582, 1985. [5] S. A. Ashour and R. D. Hanson, “Elastic seismic response of buildings with supplemental damping,” Tech. Rep. UMCE 87-01, Department of Civil Engineering, University of Michigan, Ann Arbor, Mich, USA, 1987. [6] R. H. Zhang and T. T. Soong, “Seismic design of viscoelastic dampers for structural applications,” Journal of Structural Engineering, ASCE, vol. 118, no. 5, pp. 1375–1392, 1992. [7] M. Gürgöze and P. C. Müller, “Optimal positioning of dampers in multi-body systems,” Journal of Sound and Vibration, vol. 158, no. 3, pp. 517–530, 1992. [8] H. G. Natke and T. T. Soong, “Topological structural optimization under dynamic loads,” in Optimization of Structural systems and Applications, S. Hernandez and C. A. Brebbia, Eds., Computational Mechanics Publications, Southampton, UK, 1993.