Airy-Based Form-Finding of Purely Compressed Masonry Shells Under Vertical and Horizontal Loads

The assessment and design of masonry vaulted structures in seismic regions presents challenges to the designer. Typical form-finding methods for compression-only shells may not directly consider horizontal loading, leading to uncertainty regarding structural performance during earthquake events. In the case of new design, this can result in inefficient structures and material overuse, while historic structures may be condemned or damaged through inappropriate interventions. Direct consideration of the static horizontal force capacity - the threshold at which hinge formation triggers dynamic, rocking-like mechanisms in the vault - would allay these concerns, and is primarily a product of the structural geometry. Recent work by the authors has presented a methodology for form-finding compression-only shells under combined vertical and horizontal loading, which is based on the theories of Limit Analysis and Membrane Equilibrium Analysis. However, this method relies on the constrained optimisation of a concave stress potential, which can result in computational challenges. Solutions may be further complicated in the case of vaults containing either cracking damage or intentional geometric discontinuities, such as cross vaults. This paper outlines the key challenges in refinement and implementation of the new form-finding methodology and presents two potential computational solutions, utilising non-convex optimisation and machine learning methods.