Optimization method for shape design of Auxetic Bending-Active Gridshells using discrete differential geometry

Abstract

The purpose of this paper is to propose an optimization method for shape design of Auxetic Bending-Active Gridshells (ABAGs). A 2-dimensional auxetic structure has negative Poisson’s ratio for in-plane deformation. Positive Gaussian curvature distributed on a curved surface of ABAG is obtained by out-of-plane deformation of the initial flat grid composed of reentrant structural units. We introduce discrete differential geometry into shape design of the surface of ABAG, which can be easily discretized into triangular meshes in accordance with the discrete member locations. The objective function of the proposed optimization problem is formulated using discrete Gaussian curvature, which is defined as the angle defect at node. In addition, discrete mean curvature vector is used for specifying the direction of convexity. We use particle swarm optimization for solving the problem. It is shown in the numerical examples, that surfaces with specified distribution of convex region on an ABAG can be obtained using the proposed method.