Shell structures are pivotal in the fields of architecture and engineering, due to their aesthetic appeal and structural efficiency. Recently, 3D concrete printing has reignited the interest in these structures. But, as printed concrete cannot be reinforced with steel, structures built in this way must be designed to withstand primarily pure compression: they must be funicular shells. Nevertheless, a fundamental challenge remains unsolved since Robert Hooke's discovered the catenary arch in 1675: it is not known whether the concept of a funicular polygon can be generalised to three-dimensional structures. Generative Adversarial Networks (GANs), have shown remarkable success in generating realistic data samples matching the distribution of the training data and have been shown to produce highly convincing synthetic images. This work proposes a physics-informed generative adversarial framework for the design of funicular shell structures. The approach employs a modified Deep Convolutional Generative Adversarial architecture physically guided by an auxiliary discriminator to generate realistic and structurally efficient shell geometries. Specifically, the model is constrained by the membrane factor to penalize geometries dominated by bending. An additional discriminator is also employed allowing the model to deal with more complex structures. Results show that the developed model is stable and capable of generating physically optimal, previously unseen, funicular shells with smooth forms and high membrane factor distributions.

翻译：壳体结构因其美学吸引力和结构效率，在建筑与工程领域具有关键作用。近年来，3D混凝土打印技术重新激发了人们对这类结构的兴趣。但由于打印混凝土无法配置钢筋，以此方式建造的结构必须设计成主要承受纯压缩荷载——即必须为反重力壳。然而，自1675年罗伯特·胡克发现悬链线拱以来，一个根本性挑战始终未解：反力多边形概念能否推广至三维结构？生成对抗网络已在生成符合训练数据分布的逼真数据样本方面展现出卓越成效，并成功产生了高度可信的合成图像。本研究提出一种物理信息驱动的生成对抗框架，用于反重力壳结构设计。该方法采用改进的深度卷积生成对抗网络架构，通过辅助判别器进行物理引导，生成兼具真实感与结构效率的壳体几何形态。具体而言，模型受到薄膜因子约束，以惩罚以弯曲为主的几何形状。此外，引入额外判别器使模型能够处理更复杂的结构。结果表明，所开发模型具有稳定性，能够生成物理最优、前所未见的反重力壳体，其形态平滑且具有高薄膜因子分布。