Deep-learning based inverse design of hierarchical curved beams with prescribed nonlinear responses for multistable honeycomb structures

Morphing structures are attractive for applications in aerospace, robotics, and biomedical devices because they can switch among multiple geometric configurations. Among them, multistable honeycomb (MSHC) structures are particularly promising for achieving large and reversible shape reconfiguration. However, the nonlinear response of their bistable curved beams remains difficult to tailor, especially under fixed global geometric constraints, which limits the programmable deformation capability of MSHC structures. To address this issue, this study proposes a microstructure-filled hierarchical curved beam that introduces additional internal design freedom through microstructure parameterization, thereby expanding the achievable nonlinear response space. Based on this concept, a two-level deep-learning inverse-design framework is developed. At the microstructure level, a deep convolutional generative adversarial network (DCGAN) and a convolutional neural network (CNN) are combined in a closed-loop strategy to generate microstructures with target homogenized elastic properties. At the structural level, each hierarchical curved beam is represented by a segment-wise sequence of elastic properties, and a multilayer perceptron (MLP) together with a conditional variational autoencoder (CVAE) is used to inversely design curved beams with prescribed nonlinear response curves. The designed property sequences are then mapped back to explicit microstructures and assembled into hierarchical bistable curved beams. The proposed framework enables the inverse design of hierarchical curved beams with tailored nonlinear responses and provides an effective route for programmable multistable honeycomb structures and morphing applications such as airfoils.