In the design of multiphysics systems, particularly in aerospace, automotive, and civil engineering , optimizing stress distribution is crucial for ensuring the longevity and safety of structures. This study proposes a comprehensive methodology to address stress-related challenges in multiphysics systems, essential for maintaining structural integrity under complex thermo-mechanical-pressure loading conditions. The proposed methodology provides three principal contributions: (i) a novel solution for stress-related problems involving design-dependent pressure loads, achieved by establishing a design-dependent pressure field using Darcy’s law and a drainage term to implicitly identify pressure-bounding surfaces, providing an efficient method for evaluating load sensitivities; (ii) a comprehensive thermoelastic stress methodology for thermo-mechanical-pressure systems; and (iii) an extension to multiple material candidates to enhance robustness and design flexibility. To achieve these objectives, the well-established P -norm approach is employed to consolidate stresses into a unified global metric, while clustered regional and adaptive scaling techniques are used to manage localized stress concentrations effectively. The Moved and Regularized Heaviside function (MRHF)-based stress interpolation is integrated within the generalized Solid Isotropic Material with Penalization (SIMP) framework to handle multi-material problems efficiently. Furthermore, three adjoint vectors are introduced for thermoelastic stress sensitivity analysis using the adjoint variable technique, improving computational efficiency alongside a polygonal discretization scheme that enhances adaptability with diverse element types. The methodology’s efficiency, robustness, and practicality are demonstrated through various numerical examples, showing significant improvements in stress distribution and overall multiphysics system performance . Validation and verification processes further confirm the approach’s effectiveness, while numerical results highlight the influence of heat flux magnitude and material selection on optimized outcomes, demonstrating the methodology’s versatility for both stress minimization and stress-constrained problems. These contributions advance the field of multiphysics topology optimization by offering practical, robust, and efficient solutions to complex engineering challenges, providing a solid foundation for future developments in complex systems. • Novel stress topology optimization under design-dependent load using Darcy’s law. • New stress-related approach in triplet thermal-mechanical-pressure systems. • Extending the proposed method to multiple material evaluations.

This paper presents an efficient and comprehensive numerical approach to address topology optimization challenges within the multi-material framework. The focus encompasses several key aspects: solving various stress-related problems from compressible to incompressible materials , broadening the scope to encompass multi-material systems, adopting a flexible methodology suitable for various elements (triangular, quadrilateral, and polygonal), and expanding to incorporate frequency constraints within the stress-driven system. The core idea to accommodate a broad range of materials, from compressible to nearly incompressible, is to implement a specialized polytopal composite finite element (PCE) technique to mitigate volumetric locking issues often prevalent in nearly incompressible materials. Then, to effectively solve the stress-related multi-material system, a well-known P -norm function integrated with the Moved and Regularized Heaviside function (MRHF) is employed, capitalizing on the correlation between topological phases and material allocation to handle multi-material problems effectively. Additionally, to deal with frequency-related multi-material problems, an extended technique addressing localized mode issues based on the relationship between representative solid and void is also employed. Several numerical examples are tested to validate the method’s efficiency and reliability within a multi-material framework, considering a diverse range of materials from compressible to nearly incompressible. • Solving various stress-related problems, from compressibility to incompressibility. • Expanding the scope to include polygonal meshes and multi-material problems. • Broadening to include frequency constraints within the scope of ongoing research.