Comprehensive thermoelastic stress-driven approach for thermo-mechanical-pressure multiphysics systems

Abstract

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.