Microstructural topology optimization for patch-based sandwich panel with desired in-plane thermal expansion and structural stiffness

Apart from the lightweight and excellent mechanical properties, sandwich panels can be endowed with tailorable in-plane coefficient of thermal expansion (CTE) through an elaborate design of periodic face-sheets. However, albeit that the microstructural topology of their periodic face-sheets promises unique thermal expansion behaviors, it may also bring significant influences to the structural stiffness of sandwich panels. In this study, we apply the topology optimization method to design face-sheet microstructures to enable the sandwich panels to possess desired in-plane CTEs, lightweight and benign mechanical properties, simultaneously. By introducing the patch-based cell as initial configuration, the existing thermally bending adjustment mechanism for thermal deformation control is integrated to the process of topology optimization. The entire topology optimization process including the equivalent mechanical properties prediction and the sensitivity computation is performed within an in-house program coupled with commercial finite element analysis software. To this end, a matching numerical sensitivity analysis method to extract sensitivities straightforwardly from software’s output is also developed on the basis of asymptotic homogenization method. Three types of specific optimization problems in terms of different objective functions and constraint conditions are proposed, solved, and studied, namely, in-plane zero thermal expansion combining with maximum stiffness, the other for in-plane zero thermal expansion optimal specific stiffness, and minimizing in-plane isotropic thermal expansion. Some specific resulting topologies, microstructural features, and design details are subsequently obtained. In particular, the current strategy of integrating effective mechanism and topological technology can be extended to design more microstructures for simultaneously tailorable CTE and high mechanical performance by replacing present thermal deformation control mechanism with others.