Constrained shape optimization of grid shells based on deep learning

Designing grid shells requires finding a happy medium between aesthetics and engineering quality: architects and structural engineers join efforts to define geometries and grid topologies that achieve structural efficiency. In sculptural architecture, the artistic intent prevails, and produces freeform shapes with possibly large openings to create spectacular effects. This calls for shape optimization methods to mitigate inefficiency caused by bending forces. However, if modifications are not bounded, optimization may either alter the surface aesthetics or violate design constraints. This paper implements a shape optimization method that improves the performance of triangular grid shells while ensuring small shape changes. A graph neural network learns to update the nodal coordinates of the grid shell and reduce both strain-energy, as a measure of structural efficiency, and the total weight of the structure, as a measure of sustainability. Our case studies include regular shapes among the baseline structures of the FreeGrid benchmark, as well as non-conventional geometries.