We introduce a framework for the generation of polygonal grid-shell architectural structures, whose topology is\ud designed in order to excel in static performances. We start from the analysis of stress on the input surface and\ud we use the resulting tensor field to induce an anisotropic non-Euclidean metric over it. This metric is derived\ud by studying the relation between the stress tensor over a continuous shell and the optimal shape of polygons in\ud a corresponding grid-shell. Polygonal meshes with uniform density and isotropic cells under this metric exhibit\ud variable density and anisotropy in Euclidean space, thus achieving a better distribution of the strain energy over\ud their elements. Meshes are further optimized taking into account symmetry and regularity of cells to improve\ud aesthetics. We experiment with quad meshes and hex-dominant meshes, demonstrating that our grid-shells achieve\ud better static performances than state-of-the-art grid-shells

The corner mechanism in masonry structures is one of the out-of-plane modes that may frequently occur under dynamic actions such as earthquakes. The three dimensional motion, in principle complex to treat, can be simplified into a two-dimensional problem, where a prismatic equivalent block is associated to the corner mechanism. This paper provides a method to treat the corner mechanism in two dimensional rocking analysis, taking into account the roof actions -especially the roof thrust that acts as destabilizing force in the preliminary phases of motion -and the boundary conditions such as the transverse walls. A case study is taken as benchmark to perform rocking non-linear analyses and discuss the role of geometry, energy dissipation and boundary conditions. It is shown the relevant influence of the geometry and of the coefficient of restitution on the stability conditions, whenever the oscillation produce horizontal displacement values of some cm. The results of the case study, subjected to the Central Italy earthquake, are compared to the actual response of the corner mechanism, which collapsed during this seismic swarm, showing that the rocking analysis on the equivalent block correctly predicts the collapse occurred.

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