Form-finding of grid-shells using the ground structure and potential energy methods: a comparative study and assessment

The structural performance of a grid-shell depends directly on the geometry of the design. Form-finding methods, which are typically based on the search for bending-free configurations, aid in achieving structurally efficient geometries. This manuscript proposes two form-finding methods for grid-shells: one method is the potential energy method, which finds the form in equilibrium by minimizing the total potential energy in the system; the second method is based on an augmented version of the ground structure method, in which the load application points become variables of the topology optimization problem. The proposed methods, together with the well-known force density method, are evaluated and compared using numerical examples. The advantages and drawbacks of the methods are reviewed, compared and highlighted.