Comprehensive stress-driven multi-material problem for heat-sinking heterogeneous structures

In the realm of designing thermoelastic structures, particularly within aerospace and broader engineering fields, complex challenges arise from the diverse behaviors of heterogeneous materials and the intricate requirements of stress-based systems in coupled thermomechanical considerations. This study addresses these challenges by proposing a comprehensive methodology with two main contributions: (i) the development of an effective unified solution for stress-driven designs that tackle heat-sinking problems by accommodating a wide range of materials, from homogeneous to heterogeneous and (ii) the introduction of a robust stress-based optimization approach for multi-material problems within coupled thermomechanical systems. The methodology employs the well-established $P$-norm approach to consolidate heterogeneous stresses into a unified global metric. Additionally, it integrates effective material interpolation with the generalized Solid Isotropic Material with Penalization (SIMP) framework, resulting in comprehensive multi-material models that include the constitutive matrix, thermal conductivity, thermal stress coefficient, and thermoelastic stress distributions. To further enhance adaptability and flexibility, the methodology incorporates a polygonal discretization technique. Detailed sensitivity analyses, using the adjoint variable technique, are conducted to improve computational efficiency in gradient-based mathematical programming algorithms. The efficiency, robustness, and practicality of the proposed methodology are validated through numerical examples, demonstrating its effectiveness and reliability in real-world applications.