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This research focuses on the effects of stiffeners and architectural opening on the steel shear wall topology optimization. To this aim, four relevant issues have been considered. The first issue is the optimality Pattern of the shear wall without stiffeners. The second is the Optimality Pattern of the shear wall with stiffeners in two directions. The third is the investigation on the topology optimization of the shear walls with fixed opening and the fourth is the multi-material topology optimization of the above issues. In the optimize process, the level set method based on the shape sensitivity and the finite element analysis for two-dimensional linear elastic problems has been used. The level set function implicitly indicated the boundaries of the design domain. Several numerical examples are used to demonstrate the optimal paths in the steel shear walls. The results show that optimal values have been changed by replacing stiffeners and creating openings in the wall, but the optimal topologies almost have a shape like a concentric bracing. Also, in the conventional shear walls (one material) the horizontal stiffeners have a significant effect on their performance.

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The use of steel shear wall systems has increased significantly in recent years as an effective solution for resisting lateral loads in buildings. This study focuses on the seismic collapse safety assessment of steel frames with optimal positions of steel shear walls obtained through various metaheuristic optimization algorithms and concepts of performance-based design methodology. Due to potential irregularities and discontinuities in the lateral load-resisting system and the limitations of code-based linear analysis, nonlinear pushover analyses with multiple lateral load patterns are employed to estimate key structural responses during the optimization process. The seismic collapse performance of the optimized frames is further evaluated using the FEMA P-695 methodology, which involves nonlinear dynamic analysis to assess collapse capacity. The primary objective is to examine the influence of steel plate shear wall placement on the structural weight optimization of steel frames. To this end, two case studies, a 10-story and a 15-story steel frame equipped with steel shear walls, are presented. The results demonstrate the critical role of shear wall location in achieving optimal structural designs.
 

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The dual steel system comprising moment-resisting frames integrated with steel shear walls represents an advanced seismic-resistant solution in structural engineering. This system synergistically combines the high ductility and energy dissipation capacity of steel frames with the substantial lateral stiffness and strength provided by steel shear walls. Proper design of such systems requires precise determination of the optimal location, thickness, and mechanical properties of the shear walls parameters that critically govern seismic performance, structural safety, material efficiency, and construction cost. To achieve an optimal balance between performance and economy, the problem is formulated as a constrained optimization task. This study employs the recently developed Puma Optimizer (PO) and introduces a novel enhanced variant, termed the Upgraded Puma Optimizer (U-PO). The key novelty of this work lies in the integration of Lévy flight distribution into the PO framework, replacing conventional Brownian motion to significantly strengthen the exploration–exploitation balance, global search capability, and convergence speed. This modification enables more effective handling of complex, high-dimensional structural optimization problems. The performance of the proposed U-PO is rigorously evaluated through the optimal design of three benchmark steel frames (1-, 10-, and 20-story) equipped with shear walls. The primary objective is to minimize the total structural weight while satisfying strength, serviceability, and seismic design requirements according to relevant building codes. Decision variables include frame member cross-sections as well as the location and thickness of shear walls. Comparative results against several established metaheuristic algorithms (HHO, AOA, and GWO) demonstrate the superiority of the U-PO, confirming that the incorporation of Lévy flights leads to markedly improved convergence behavior and solution quality. The U-PO consistently yields superior designs featuring notable reductions in structural weight through more efficient sizing and strategic placement of steel shear walls.