*Result*: Computational framework for a family of methods based on stress-constrained topology optimization.

*This study presents a general computational framework for topology optimization under constraints related to various engineering design problems, including: reliability analysis, low-cycle fatigue assessment, and stress limited analysis. Such a framework aims to facilitate comprehensive engineering design considerations by incorporating traditional constraints such as displacement and stress alongside probabilistic assessments of fatigue failure and the complex behaviors exhibited by structures made of elastoplastic material. The framework's amalgamation of diverse analytical components offers engineers a versatile toolkit to address intricate design challenges. Notably, the inclusion of reliability analysis introduces a probabilistic perspective, transforming conventional design constraints into random parameters, thereby enhancing the robustness of the design process. Key to the framework's efficacy is its implementation using MATLAB mathematical computing software, leveraging the platform's efficient code execution and object-oriented programming paradigm. This choice ensures an intuitive and potent environment for designers and researchers, facilitating seamless adaptation across various engineering applications. Additionally, the proposed previously by the Authors algorithm for the topology optimization is extended by adaptive strategy allowing for efficient adjustment of an amount of material removed at individual optimization step. The presented framework is offering a comprehensive and integrated approach to address multifaceted design challenges while enhancing design robustness and efficiency. • Software architecture for the proposed approaches is described and implemented in the MATLAB environment. • A reliability-based topology optimization with plasticity-based stress and displacements constraints presented. • Effective algorithms are introduced to solve the topology optimization problem with reliability constraints. • Numerical examples demonstrate the correlation between volume fraction and probability of failure. • The presented framework offers a versatile and robust approach in case of diverse constraints and uncertainties. [ABSTRACT FROM AUTHOR]*