Design of purely compressive shells under vertical and horizontal loads through Machine Learning-driven form-finding

Form-finding methodologies can offer creative avenues for the design of shell structures under constraints, such as the need to ensure that only compressive stresses arise within masonry vaults. However, these methods most typically consider only vertical design loads, which may lead to significant challenges in demonstrating the structural safety of shells in scenarios where appreciable horizontal loading may arise. Examples include extreme climate-driven loading in the form of increased wind forces, or earthquake loading in seismic regions. Where horizontal loads are directly considered, additional challenges arise in the computationally demanding constrained optimisation step needed to obtain an ideal structural form. Specifically, for recently developed form-finding methods based on Membrane Equilibrium Analysis, this step is needed to find the optimal parameters of a concave Airy Stress Function that ensures shell equilibrium. This paper presents an alternative to this optimisation step: Machine Learning regression analysis to identify optimal Airy Stress Function parameters. Three regression techniques are considered – XGBoost, Random Forests, and k-Nearest Neighbours – and their integration into the form-finding framework is described. For a case study vault, these techniques are tested and evaluated on the basis of the material efficiency of their final form-found designs and their fidelity to the original reference design. It is seen that these methods offer greater computational efficiency than the constrained optimisation approach, while k-Nearest Neighbours regression performs best for this particular case study.