Multi-material topology optimization for buckling-resistant designs under thermo-mechanical coupling loads

• This study presents a novel topology optimization framework that concurrently takes into account coupled thermal and mechanical loads, along with buckling constraints. • The topological optimization of multiphase materials featuring different volume fractions and distinct properties was investigated. • The buckling performance can be effectively enhanced by incorporating buckling constraints, without unduly sacrificing the structural stiffness. • Topological optimization in the context of complex wall structures can effectively guarantee the convergence and reliability of the algorithm. Existing topology optimization research predominantly isolates thermal or mechanical effects, with insufficient attention to their coupled interactions. Furthermore, most studies neglect buckling constraints—critical for structural stability under varying loads. Multi-material systems offer distinct advantages, as their phase-specific properties (e.g., differential thermal expansion coefficients) can be strategically leveraged to enhance thermomechanical stress resistance. To address these gaps, this study introduces a constraint-reformulated framework optimizing global compliance for multi-material structures under simultaneous thermomechanical loads and buckling constraints. The methodology develops a comprehensive optimization approach that fully exploits multi-material potential to achieve optimal material distribution and stability in complex loading scenarios. Numerical case studies confirm the algorithm's efficacy in spatially allocating material phases to co-optimize stiffness and buckling performance within thermomechanical environments.