Freeform surface morphing using honeycomb plates: Gaussian curvature control

Transforming a two-dimensional plane into a three-dimensional surface with a specific Gaussian curvature is a significant engineering challenge. Traditional methods are limited by the conservation of Gaussian curvature, which limits their ability to generate complex surfaces from plane deformation. In this study, we propose an innovative approach to freeform surface morphing using honeycomb panels that utilize the superior design flexibility and bending properties of honeycomb structures to break through traditional limitations. By manipulating the geometric parameters (such as wall thickness, wall length, and height) as well as the boundary conditions, precise control of curvature and Gaussian shape transformation is realized to transform the flat plate into target surfaces with different Gaussian curvatures. A key innovation of this study is the introduction of “curvature product” as a new quantitative descriptor to characterize the honeycomb deformation pattern, which provides a new perspective to understand the deformation behavior of honeycomb structures. Through homogenization analysis, numerical simulation, and experimental validation, we systematically investigate the influence of geometric parameters on the deformation properties. In addition, we reveal the coupling mechanism between bending and torsional stiffnesses in out-of-plane deformation, emphasizing the key role of boundary conditions. This study establishes an effective theoretical framework for the accurate realization of 2D to 3D surface transformation, demonstrates the great potential of honeycomb structures in constructing complex surfaces, and significantly advances the development of Gaussian curvature control techniques.