Optimal Design of Lattice Domes by Means of a Constrained Force Density Method

In this contribution the design of reticulated domes is dealt with, exploring the optimal solutions that can be retrieved by a form-finding approach. To this goal a numerical tool is implemented to address the design of reticulated shells through funicular analysis. The force density method is implemented to cope with the equilibrium of reticulated shells whose branches are required to behave as bars. Optimal networks are sought by coupling the force density method with techniques of sequential convex programming that were originally conceived to handle formulations of size optimization for elastic structures. The Maxwell number, which is the sum of the force-timeslength products for all the branches in the spatial network, is used as objective function to be minimized, whereas constraints on the length of the branches are enforced. Funicular networks that are fully feasible with respect to the set of local enforcements are retrieved in a limited number of iterations, with no need to initialize the procedure with a feasible starting guess. Optimal solutions are explored, considering different types of grids, i.e. different types of lattices, while considering self-weight.