Physics-informed, Generative Adversarial Design of Funicular Shells
Abstract
Abstract Shell-shaped structures are fundamental in the fields of architecture and engineering, owing to their aesthetic appeal and structural efficiency. However, a fundamental challenge has remained unresolved ever since Robert Hooke 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.
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