Keywords: form-finding, structural optimization, force density method, evolutionary algorithms, Galapagos, Grasshopper, lattice domes, lightweight structures, Maxwell number.

This contribution presents a form-finding approach for the optimal design of reticulated domes implemented within a commercial parametric environment. The proposed methodology leverages Galapagos, the evolutionary solver embedded in the Rhino-Grasshopper platform, to explore optimal funicular configurations of lattice shells under self-weight. The equilibrium of the spatial network is enforced through a compact Python script that implements the Force Density Method (FDM), interfaced with the parametric model: by expressing the ratio of axial force to length for each branch as the design variable, the FDM reduces the equilibrium equations of the unrestrained nodes to a linear system, from which the shape of the network is directly recovered. The evolutionary solver optimizes the force densities of the branches, subject to geometric constraints on member lengths and node positions, effectively driving the shape of the dome toward the optimal funicular configuration. The Maxwell number, defined as the sum of the force-times-length products over all branches of the network, is adopted as the objective function to be minimized. The approach is tested on a Schwedler dome topology, and the results demonstrate that the evolutionary algorithm converges to solutions in close agreement with those obtained via gradient based optimization techniques. The key advantage of the proposed workflow lies in its accessibility: by exploiting widely adopted commercial tools and requiring only minimal scripting, the method lowers the barrier for practitioners and researchers to perform structurally informed shape optimization of lattice shells without the need for custom numerical solvers.

download the full-text of this paper (PDF, 3099 Kb)

go to the previous paper
go to the next paper
return to the table of contents
return to the volume description