Coupled thermo-mechanical design optimization of multi-materials under material-specific stress constraints

Stress-constrained topology optimization (TO) of thermo-mechanical coupling issues has been extensively applied in sectors such as aerospace. Nonetheless, the majority of earlier topology optimization techniques for steady-state heat transfer structures employ a single material with a single stress constraint or aim to minimize global stress, rendering them unsuitable for material-specific stress constraints in coupled thermo-mechanical multi-material topology optimization. This paper presents an effective steady-state thermoelastic coupling topology optimization approach for multi-materials that incorporates material-specific stress constraints by establishing a stress interpolation scheme for each material (thermal and mechanical) using the q p relaxation technique. This study computes the individual maximum von Mises stress for each material by employing a p-norm function within a cohesive multi-material topology optimization framework. To address the singularity induced by intermediate density, a Heaviside projection function is formulated for all design variables. To address the design difficulty of total cost fractions, a novel cost function formulation is created that eliminates the necessity for normalization of price and material density, akin to the ordered SIMP method. A thorough approach integrating thermoelastic coupling with material-specific stress analysis has been completely resolved, extending from 2D to 3D. Conventional 2D and 3D numerical illustrations are conducted to showcase the efficacy, stability, and adaptability of the suggested approach.