Comprehensive polygonal topology optimization for triplet thermo-mechanical-pressure multi-material systems

Current advancements in topology optimization research have extensively explored thermoelastic problems. Yet, notable limitations persist in effectively handling design-dependent fluidic pressure loads, particularly in the realm of coupled thermo-mechanical systems. To bridge this gap, this study proposes a novel and consistent methodology that comprehensively accommodates these challenges. The principal contributions of this research are threefold: (1) presenting an innovative and comprehensive solution for triplet thermo-mechanical-pressure problems, achieved through the establishment of a specific pressure field using Darcy’s law and a drainage term, (2) broadening the scope to incorporate flexible polygonal meshes within generalized Solid Isotropic Material with Penalization (SIMP)-based multi-material systems, and (3) introducing an alternative interpolated model related to independent material properties, specifically the general thermal stress coefficient, to simplify the complexity during sensitivity calculations of thermal-strain load in generalized SIMP-based multi-material problems. Additionally, within the scope of this study, several investigations into penalty parameters in solids, not unified in previous coupled thermo-mechanical multi-material problems, are also conducted. Three additional adjoint vectors are introduced using the adjoint variable technique for sensitivity analysis to enhance computational efficiency in the gradient-based mathematical programming algorithm. The effectiveness and reliability of this method are validated through numerical examples, demonstrating its efficiency, robustness, and practicality.