Topology optimization for transient thermomechanical coupling periodic structures based on material-field series expansion method

With the wide application of thermoelastic structures in the aerospace field, the problem of topology optimization of thermoelastic structures has become a very common and important research topic. Meanwhile, Periodic structures have been extensively adopted as critical load-bearing components in aerospace engineering owing to their exceptional specific stiffness, outstanding buckling resistance, and superior specific strength. To address the transient thermomechanical coupling topology optimization problem in periodic structure design, an optimization framework based on the material field series expansion method (MFSE) is proposed in this paper. The structural topology was represented using MFSE, which provides both an efficient parameterization of the design domain and a smooth description of structural boundaries, while significantly reducing the number of design variables compared to conventional methods. By employing variable linking, a uniform density field is enforced across all sub-regions, thereby satisfying the periodicity constraint of the structure. Furthermore, the newest identical second-order self-starting single-solve implicit method (IS-SSI) and optimal self-starting single-solve algorithm with first-order displacement and zero-order velocity overshooting (OSS10) are utilized for efficient computation of structural responses while optimally maintaining numerical accuracy. The sensitivity analysis of the proposed objective function is tackled through the discretize-then-differentiate approach. Numerical examples demonstrate the reliability and validity of the proposed method.