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.

除了轻巧和出色的机械性能外，通过精心设计的周期性面板，夹层板还可以赋予可定制的面内热膨胀系数（CTE）。然而，尽管它们的周期性面板的微观结构拓扑结构具有独特的热膨胀性能，但也可能会对夹芯板的结构刚度带来重大影响。在这项研究中，我们应用拓扑优化方法来设计面板微结构，以使夹心板同时拥有所需的面内CTE，轻质和良性机械性能。通过引入基于贴片的单元作为初始配置，将用于热变形控制的现有热弯曲调整机制集成到拓扑优化过程中。包括等效机械性能预测和灵敏度计算在内的整个拓扑优化过程，是在内部程序中结合商业有限元分析软件执行的。为此，在渐近均质化方法的基础上，还开发了一种匹配的数值灵敏度分析方法，可以直接从软件输出中提取灵敏度。根据目标函数和约束条件的不同，提出，求解和研究了三种类型的具体优化问题，即结合最大刚度的面内零热膨胀，针对面零热膨胀的最佳比刚度，以及最小化平面内各向同性的热膨胀。一些特定的结果拓扑，微结构特征，并随后获得设计细节。特别是，通过将现有的热变形控制机制替换为其他的热变形控制机制，可以将当前有效机制与拓扑技术集成的策略扩展到设计更多的微结构，以同时实现可定制的CTE和高机械性能。