Sandwich structures have several potential applications in structural engineering because of the different material properties of the skin and core. In particular, sandwich structures with heteromorphic cores can satisfy the special requirements of engineering and structural design. In this study, to enhance the critical thermal buckling behavior of sandwich structures with heteromorphic cores, we developed a free-form optimization system based on a gradient method to optimize the core shapes under a volume constraint. The free-form optimization system combined with a finite element method code and an in-house program consists of thermal buckling analysis, initial thermal stress analysis, the derivation of the sensitivity function, velocity analysis, and shape update. According to the optimal results of the design examples, the developed free-form optimization system could significantly enhance the thermal buckling behavior of sandwich structures. In particular, by simply specifying the constraint conditions in the velocity analysis, we could maintain the initial shape of the specified parts in the heteromorphic core during the free-form optimization process to satisfy special requirements.

由于表皮和核心的不同材料特性，夹层结构在结构工程中具有多种潜在应用。特别是具有异形芯的夹层结构可以满足工程和结构设计的特殊要求。在这项研究中，为了增强具有异形芯的夹层结构的临界热屈曲行为，我们开发了一种基于梯度方法的自由形式优化系统，以在体积约束下优化芯形状。结合有限元方法代码和内部程序的自由形式优化系统包括热屈曲分析、初始热应力分析、灵敏度函数的推导、速度分析和形状更新。根据设计实例的优化结果，开发的自由形式优化系统可以显着增强夹层结构的热屈曲行为。特别是，通过简单地指定速度分析中的约束条件，我们可以在自由形式优化过程中保持异形核心中指定部分的初始形状以满足特殊要求。