An initially two-dimensional grid of elastic rods may be actuated into a three-dimensional shell-like structure, through buckling, when the end-points of the rods are constrained to a shrunk boundary. The shape of the 3D gridshell is a joint result of elasticity and geometric constraint. We develop a discrete differential geometry-based model of elastic gridshell to investigate their form-finding process. Even though the forward process from 2D footprint to 3D gridshell can be captured by physics-based simulation, the inverse problem of obtaining the original footprint given the 3D deformed shape still lacks a generalized method. In this paper, we propose a genetic algorithm (GA)-based inverse design method to explore the planar footprint of an elastic gridshell as well as the corresponding geometric constraints. Geometric features extracted from the original planar form are encoded into various chromosomes to constitute a population in every generation. With the fitness function constructed based on the deviation of the candidate solution from the 3D target shape, the population evolves gradually until the individual of the smallest fitness value representing the optimal footprint and final boundary constraints is found under seven predefined geometric constraints. Given a series of representative target shapes, e.g., hemispherical cap, paraboloid structure, Gaussian curve shape, and semi-ellipsoid, their original footprints are quantified using a network of 10 elastic rods. Excellent agreement is obtained between the prescribed 3D shape and the simulated buckled structures as small fitness value is obtained and little difference between them is observed, which validates the effectiveness of the proposed GA-based inverse design method.

当弹性杆的端点被约束到收缩边界时，弹性杆的最初的二维网格可以通过屈曲而被驱动为三维壳状结构。3D网格的形状是弹性和几何约束的共同结果。我们开发了基于离散微分几何的弹性网格模型，以研究其找形过程。即使可以通过基于物理的模拟捕获从2D覆盖区到3D网格的正向过程，但是在3D变形的情况下获取原始覆盖区的反问题仍然缺乏通用的方法。在本文中，我们提出了一种基于遗传算法的逆设计方法，以探索弹性网格壳的平面足迹以及相应的几何约束。从原始平面形式中提取的几何特征被编码为各种染色体，以构成每一代的种群。使用基于候选解与3D目标形状的偏差构造的适应度函数，总体逐渐演化，直到在七个预定义的几何约束下找到代表最佳足迹和最终边界约束的最小适应度值的个体。给定一系列具有代表性的目标形状，例如半球形帽，抛物面结构，高斯曲线形状和半椭圆形，使用10条弹性杆的网络对它们的原始足迹进行量化。在规定的3D形状和模拟的弯曲结构之间获得了极好的一致性，这是因为获得的适应度值很小，并且观察到它们之间的差异很小，