Parametric Study of Non-periodic and Hybrid Auxetic Bending-Active Gridshells

This paper presents a design method of Auxetic Bending-Active Gridshells (ABAGs), which are curved surfaces generated from the initial flat grid with 2-dimensional auxetic patterns. One of the mechanical properties of ABAGs is that a dome-like shape of a curved surface can be easily obtained by bending a grid due to negative Poisson's ratio for in-plane deformation. Shapes of auxetic patterns are relevant to Poisson's ratio. Non-periodic and/or hybrid 2-dimensional auxetic patterns are developed for designing the initial flat grid of ABAGs. Shape parameters are the sizes of each plane unit for tuning its reentrant pattern, and two types of reentrant shapes are mixed on an initial flat grid. Using the non-uniform patterns, we can obtain an asymmetric and more complex free-form surface of ABAGs than those composed of a uniform reentrant pattern. Discrete Gaussian curvature at each node on a curved surface is computed for quantitatively evaluating the properties of shapes of the obtained surfaces. Possibility of ABAGs as a new design tool is demonstrated by showing that various shapes are generated through large deformation analysis with the forced displacements at the supports.