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.

A new method for optimizing the design of nonlinear sinusoidal-web steel beams is introduced in this paper, focusing on reliability-based design principles. Utilizing a custom-written code with a reliability index as a key control factor, the study incorporates stochastic variables such as flange thickness, sinus wave width, sinusoidal-web plate thickness, and applied load magnitudes. Employing Finite Element Analysis (FEA) through ABAQUS software conducting experimental testing on sinusoidal HEA beams, this research showcases the successful application of reliability-based design in modifying beam design to meet the reliability requirements. The adoption of the suggested approach, which incorporates Monte Carlo simulation, is crucial in guiding the development of structural configurations that are robust to random nature in both load and manufacturing conditions. Results showcase improved structural integrity, and the successful convergence of optimized values, emphasizing the potential for enhanced steel structure design.

This study introduces an elasto-plastic topology optimization approach tailored for structural systems subjected to cyclic loading. By incorporating material nonlinearity, the method provides a robust framework for designing structures that withstand repetitive loading efficiently, avoiding excessive material use. This optimization approach integrates the effects of cyclic loading to enhance structural resilience while minimizing mean compliance. The proposed method is particularly applicable for optimizing structural components in steel frameworks where material efficiency and load-bearing capacity are critical. By emphasizing the elasto-plastic behavior of materials, this study aims to offer a practical tool for engineers seeking resilient structural designs that balance strength and sustainability. Potential applications extend to structural elements in earthquake-resistant buildings, where managing material use is essential for both environmental and economic impact.