The inclusion of additive manufacturing (AM) offers a transformative shift in the construction and structural engineering industries, presenting significant potential for innovation, optimization, and sustainability. AM allows the production of complex geometries directly from digital models (Bos et al., 2016), significantly expanding the design space available to engineers and architects. In particular, Wire and Arc Additive Manufacturing (WAAM) has gained traction as a viable method for large-scale structural fabrication due to its high deposition rate, geometric flexibility, and cost-effectiveness (Shukla et al., 2020). The integration between AM and topology optimization made a generation of optimized structures with efficient material distribution possible with the aid of finite element applications (Craveiro et al., 2017). The use of AM in construction enables the production of unique components that are difficult to fabricate using traditional techniques (Labonnote et al., 2016). Recent high-profile applications—such as the Gaudí-inspired pavilion in Barcelona, Spain, and the 3D-printed office buildings in Dubai—demonstrate the architectural and structural capabilities of AM in producing complex forms that would be challenging, if not impossible, to achieve through conventional manufacturing methods (Lange et al., 2021).

This advancement aligns naturally with the field of topology optimization, a computational design approach that strategically redistributes material within a given domain to achieve maximum structural performance with minimum material use. Topology optimization, particularly using methods like Solid Isotropic Material with Penalization (SIMP), has proven effective in generating lightweight and structurally efficient components, often with non-intuitive geometries that require AM for physical realization ((Bendsøe & Sigmund, 2013); (Galjaard et al., 2014)). Previous studies have extended this methodology to various structural elements, including perforated beams (Tsavdaridis et al., 2015), trusses, and custom joints, with demonstrated benefits in both mechanical performance and material sustainability. The integration of AM with topology optimization not only enables highly efficient load paths but also supports sustainability goals by reducing material waste and embodied carbon in construction (Craveiro et al., 2017) (Wu et al., 2016).

In the context of seismic design, the application of topology optimization remains relatively underexplored but increasingly important. One of the most promising structural systems in seismic regions is the Eccentrically Braced Frame (EBF), which combines the ductility of moment-resisting frames with the stiffness and strength of concentrically braced frames. Central to the performance of EBFs is the shear link, a designated yielding component that dissipates energy during seismic events and protects the main structural members from inelastic deformation (Della Corte et al., 2013)(Bruneau et al., 2011). Conventional shear links are typically fabricated from rolled steel profiles such as HEB sections, chosen for their availability and standardized behavior. However, these standard profiles do not necessarily represent the most material-efficient or performance-optimized solutions, particularly in complex or high-seismic applications.

Recent research efforts have begun exploring the potential of topology-optimized shear links to improve the performance of EBFs. Notably, (Ramonell & Chacón, 2021) employed ABAQUS-based finite element modeling to design and assess topology-optimized horizontal links, reporting improvements in both yielding and ultimate strength compared to standard HEB sections. Similarly, (Saleh et al., 2024-08) extended this work to vertical shear links and cyclic loading conditions, further demonstrating the viability of optimization for enhancing seismic performance. These studies collectively highlight the potential of combining AM and topology optimization to create next-generation structural components that are both efficient and resilient.

However, the majority of existing research has focused on single-story frames, which do not fully capture the structural complexity or interaction effects present in multi-story buildings. As seismic demands and inter-story drift accumulate over height, the behavior of optimized shear links may differ significantly, necessitating further investigation into their scalability and effectiveness in multi-story contexts. This study aims to extend the current state of knowledge by applying topology optimization to horizontal shear links in multi-story EBFs and evaluating their performance under both monotonic (pushover) and cyclic loading conditions. Finite element models developed in Abaqus are used to simulate realistic boundary conditions and loading protocols, with performance metrics including base shear capacity, effective stiffness, energy dissipation, and buckling behavior. Comparisons between conventional HEB sections and their topology-optimized counterparts are made across one-, two-, and three-story frame configurations. This research also seeks to reduce structural material usage through computational topology optimization, thereby achieving volume-efficient structural components with improved seismic performance. This volume reduction directly translates into a lower demand for steel, which contributes to minimizing resource consumption and embodied carbon emissions-two core themes in environmental sustainability. As the steel industry is a major contributor to global CO₂ emissions, designing structural elements that require less material promotes more sustainable construction practices. In doing so, this research seeks to not only demonstrate the potential benefits of topology-optimized shear links in seismic design but also identify the limitations and considerations that must be addressed for their broader implementation.

Finite Element Models (FEM) within Abaqus were deployed to conduct pushover analyses on horizontal links in eccentric braced frames. The specifications of the link sections, including dimensions and material properties, were directly sourced from (Ramonell & Chacón, 2021), facilitating a rigorous validation of the resultant data. The sections utilized in this study are detailed in Table 1, with the material of choice being European steel grade S275. The material's plastic behavior is characterized by a nonlinear profile, delineated through two critical points: an initial yield point at zero strain and an ultimate strength of 430 MPa at a maximum strain of 0.2. The geometry and dimensions of the eccentric braced frame under investigation are illustrated in Figure 1. For this analysis, the entire frame is modeled using wire elements, whereas the link component is designated as a solid element to facilitate focused study.

The pushover analysis, conducted on each optimized link, was meticulously compared with the performance metrics of the conventional HEB links to evaluate enhancements or modifications in structural behavior. Notably, the analysis revealed that the performance improvements attributed to the optimized links were more pronounced in structures comprising two and three stories than in single-story configurations. This observation is particularly evident in the force-displacement curves, where, for single-story applications, the curves of optimized links closely approximated those of standard HEB sections, indicating a marginal performance differentiation. For the HEB 140 models, the comparative force-displacement curves are illustrated in Figure 8. Furthermore, a comprehensive comparison encapsulating the performance outcomes of both optimized and conventional links is presented in Table 2.

The cyclic loading protocol adheres to the specifications outlined in the (Steel Construction, 2016) guidelines, utilizing predefined link rotational angles. These angles are set at 0.0025, 0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, and 0.09. The protocol specifies that the first three angles undergo three loading cycles each, while the subsequent angles are subjected to two cycles. This approach ensures that the maximum rotational angle reaches 0.09, accommodating the typical range of shear link rotational angles, noted in the literature as spanning from 0.02 to 0.08. Given the known lengths of the link and the total beam for each model, a ratio—representing the division of the eccentric braced frame's length by the link's length—is calculated. Drift is then determined by dividing the link rotational angle by this ratio. Subsequently, displacement calculations are conducted by multiplying the height of the eccentric braced frame by the derived drift value. Furthermore, within the ABAQUS environment, the material's plastic hardening behavior is adjusted to a kinematic model. For each model, an amplitude is defined to facilitate the execution of the cyclic analysis, ensuring a rigorous and methodologically sound investigation into the structural dynamics of eccentric braced frames under cyclic loading conditions. The cyclic behavior was analyzed by obtaining the base shear for each model. From the base shear, an envelope is made to compare the behavior of the optimized shape and the normal HEB link. The energy dissipation coefficient is calculated using the area under the force-displacement curve and the two triangles OBE and ODF shown in Figure 9. The effective stiffness (ke) is obtained by knowing the maximum and minimum forces and their corresponding displacements (FEMA 356, 2000). A methodological detail is also illustrated in Fig. 9. The viscous damping coefficient (he) is obtained using Eq. 1 as follows:

The results show that while performance metrics such as effective stiffness and base shear capacity improved in optimized links. However, energy dissipation capacity and damping efficiency were reduced. Moreover, The cyclic analysis revealed a notable phenomenon where all optimized links exhibited a buckling effect, predominantly in one direction. This buckling, while not catastrophic, was consistently observed across various frame configurations and indicates a structural vulnerability introduced during the optimization process. The cause can be attributed to the redistribution of material away from regions that contribute to out-of-plane stiffness—a consequence of compliance-based topology optimization that does not inherently account for stability or local buckling resistance. While symmetry is often preserved in standard sections, the freedom allowed in topology optimization to remove material wherever deemed structurally redundant may lead to irregularities that, under dynamic conditions, act as triggers for instability. A sample of the force-displacement results for the HEB 140 links in the 2-storey model, illustrating this behavioral pattern, is graphically represented in Figure 10. Additionally, Table 3 consolidates the comprehensive outcomes derived from the cyclic analysis across all tested models.

The integration of additive manufacturing and topology optimization opens new avenues for research, design, and construction of complex steel elements. This synergy promotes the creation of novel, complex structural sections and contributes to material conservation and environmental sustainability. Comparative analysis through pushover analysis between conventional HEB links and their optimized counterparts reveals significant findings. The optimized shapes demonstrate an increase in effective yielding force and a substantial enhancement in the base shear ultimate force across all models, with the sole exception of the HEB 140 one-story model, which closely parallels the performance of the standard HEB link. This enhancement translates into an augmented effective stiffness for the optimized configurations. Furthermore, plastic energy dissipation analysis indicates a comparable performance between the optimized and conventional HEB links. Cyclic performance analysis of the optimized shapes underscores a notable increase in the base shear ultimate force, reaffirming the structural benefits of the optimization.

Despite the improved stiffness and strength observed in the optimized shear links, the study revealed limitations related to directional buckling and reduced energy dissipation capacity under cyclic loading. These issues highlight the need to explore multi-objective topology optimization that incorporates structural stability requirements, fatigue performance criteria, and energy dissipation capacity. Additionally, experimental validation of the optimized geometries, especially under dynamic loading, is recommended to support practical implementation and improve design robustness.

The abstract of this paper was presented at the Environmental Design, Material Science, and Engineering Technologies (EDMSET) Conference -2nd Edition, which was held on the 22 ^nd -24 ^th of April 2025.