This work presents an innovative framework for thermoelastic-plastic reliability-based topology optimization, tackling challenges related to material uncertainties, geometric imperfections, and variations in volume fractions. An enhanced Bi-directional Evolutionary Structural Optimization (BESO) method is developed. It integrates thermoelastic-plastic finite element analysis with stochastic reliability constraints to achieve robust and efficient structural designs under combined thermal and mechanical loading. The framework incorporates advanced modeling techniques, including temperature-dependent material properties, elasto-plastic behavior, and eigenmode-based imperfection modeling. A key innovation lies in formulating reliability constraints by treating volume fraction as a random variable to model material usage uncertainty. This ensures compliance with target safety indices. The proposed methodology is verified through detailed numerical examples, including steel beam and shell structures subjected to temperatures up to 800 °C. Results show that the probabilistic designs achieved up to 30% higher load-bearing capacity compared to deterministic ones and demonstrated improved stress distribution and thermal resilience. These enhancements confirm the method’s effectiveness in achieving optimal layouts that balance material efficiency, structural stability, and reliability.

The growing demand for concrete in tropical regions faces two unresolved challenges: the high carbon footprint of ordinary Portland cement (OPC) and limited understanding of how supplementary cementitious materials affect the mechanical performance of laterite rock aggregates concrete. Although metakaolin (MK) is a highly reactive pozzolan, its combined use with laterite rock aggregates concrete and its influence on strength development and microstructure have not been sufficiently clarified. This study investigates the mechanical behavior and sustainability potential of laterite rock aggregate concrete in which OPC is partially replaced by MK at 0%, 5%, 10%, 15%, and 20% by weight. All mixes were prepared at a constant water–binder ratio of 0.50 and tested for workability, compressive strength, split-tensile strength, and flexural strength at 7, 14, and 28 days, with and without a polycarboxylate-based superplasticizer. The results show that MK significantly enhances the mechanical performance of laterite rock concrete, with an optimum at 10% replacement: the 28-day compressive strength increased from 35.6 MPa (control) to 53.9 MPa in the superplasticized mix, accompanied by corresponding gains in tensile and flexural strengths. SEM–EDS analyses revealed microstructural densification, reduced portlandite, and a refined interfacial transition zone, explaining the improved strength and cracking resistance. From an environmental perspective, a 10% MK replacement corresponds to an approximate 10% reduction in clinker-related CO₂ emissions, while the use of locally available laterite rock reduces the dependence on quarried granite and transportation impacts. The findings demonstrate that MK-modified laterite rock concrete is a viable and eco-efficient option for structural applications in tropical regions. The study concludes that MK-enhanced laterite rock aggregate concrete can deliver higher structural performance and improved sustainability without altering conventional mix design and curing practices.

Existing studies often rely on deterministic numerical analyses for structural models. However, test results consistently highlight uncertainties, particularly in variables such as magnitude of the applied load, geometrical dimensions, material randomness, and limited experiential data. As a response, researchers have increasingly turned their attention to probabilistic design models, recognizing their crucial role in accurately predicting structural performance. This study aims to integrate reliability-based analysis into the numerical modeling of sinusoidal-web steel beams. Two sinusoidal-web beams are considered. The web and the flange thicknesses, in addition to the magnitude of the applied load, are treated as random variables with mean values and standard deviations. Notably, the study demonstrates the efficiency of the reliability index as a governing limit in the analysis process. A detailed comparison between deterministic and probabilistic designs of sinusoidal-web beams is conducted, focusing on the impact of introducing the nature of randomness. Therefore, this study’s results deepen our understanding of how uncertainties significantly influence deformations and stresses.

In this manuscript, a novel approach to topology optimization is proposed which integrates considerations of uncertain load positions, thereby enhancing the reliability-based design within the context of structural engineering. Extending the conventional framework to encompass imperfect geometrically nonlinear analyses, this research discovers the intricate interplay between nonlinearity and uncertainty, shedding light on their combined effects on probabilistic analysis. A key innovation lies in treating load position as a stochastic variable, augmenting the existing parameters, such as volume fraction, material properties, and geometric imperfections, to capture the full spectrum of variability inherent in real-world conditions. To address these uncertainties, normal distributions are adopted for all relevant parameters, leveraging their computational efficacy, simplicity, and ease of implementation, which are particularly crucial in the context of complex optimization algorithms and extensive analyses. The proposed methodology undergoes rigorous validation against benchmark problems, ensuring its efficacy and reliability. Through a series of structural examples, including U-shaped plates, 3D L-shaped beams, and steel I-beams, the implications of considering imperfect geometrically nonlinear analyses within the framework of reliability-based topology optimization are explored, with a specific focus on the probabilistic aspect of load position uncertainty. The findings highlight the significant influence of probabilistic design methodologies on topology optimization, with the defined constraints serving as crucial conditions that govern the optimal topologies and their corresponding stress distributions.

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 × 10 ⁵ 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.