A geometrically nonlinear topology optimization method is presented in this paper for steel I-section beams, incorporating large displacement analysis to capture realistic structural behavior under flexural loads. The developed framework aims to enhance structural performance and material efficiency by optimizing the web region while preserving critical load paths. The optimization process is driven by enhancing the Bi-directional Evolutionary Structural Optimization (BESO) algorithm implemented in MATLAB and coupled with ABAQUS. Three beam configurations are analyzed under identical boundary and loading conditions to compare the performance of the optimized layout against traditional designs. To further assess the robustness of the proposed algorithm, two additional load scenarios, including a four-point bending test and a uniformly distributed load, are investigated. The results demonstrate that the optimized beam configurations reduce web material by 60% (volume fraction = 0.40) under 45 kN mid-span load while sustaining 55% higher load than the circular-opening beam (45 kN vs. 29 kN) with mean stress of 203.1 MPa, achieving 20% less web material than the conventional design and 18% higher complementary work (1.89 × 10⁵ N mm) than the plain-web beam. The findings underline the value of incorporating geometric nonlinearity into topology optimization for producing high-performance, lightweight steel structures suitable for real-world engineering applications.

This study proposes a fatigue topology optimization approach for structural systems subjected to cyclic loading. Recognizing the impact of repeated loading on material endurance, the method incorporates fatigue considerations into the optimization process to enhance the durability and sustainability of load-bearing structures. By factoring in cyclic loading effects, this approach aims to reduce excessive material use while improving structural resilience, aligning with objectives for efficient and sustainable design. The proposed method is particularly useful in optimizing structural components in steel frameworks, where fatigue resistance and material efficiency are critical under dynamic loads. Emphasizing a balance between strength and durability, this study offers a practical tool for engineers aiming to design resilient structures that can endure cyclic stress without unnecessary material consumption. Furthermore, this framework is envisioned as a valuable solution for cyclic load environments, supporting more sustainable and resource-efficient engineering practices.