Geometric parameters of 4D printed bilayer structure determine its deformation to a great extent. This paper proposed a geometric design method of 4D printed bilayer structures for accurate folding deformation. To precisely calculate the deformation, a folding deformation model of 4D printed bilayer structure is constructed considering thickness ratio and elastic modulus ratio. Then, for a target folding deformation, an adaptive surrogate-based optimization method is employed to obtain the geometric parameters of a given 4D printed bilayer structure. The numerical and physical experimental results show that the geometric parameters of 4D printed bilayer structure can be well designed by the proposed method.

4D打印双层结构的几何参数在很大程度上决定了其变形。本文提出了一种用于精确折叠变形的4D打印双层结构的几何设计方法。为了精确计算变形，考虑厚度比和弹性模量比，构建了4D打印双层结构的折叠变形模型。然后，对于目标折叠变形，采用基于自适应代理的优化方法来获得给定 4D 打印双层结构的几何参数。数值和物理实验结果表明，该方法可以很好地设计4D打印双层结构的几何参数。