Form-finding of reticulated shells for a given plan layout with geometric constraints

A numerical tool is implemented to address the design of reticulated shells through funicular analysis. As discussed in the literature, the force density method can be conveniently implemented to cope with the equilibrium of funicular networks, using independent sets of branches in the case of grids having fixed plan projection. In this contribution, optimal networks are sought not only in terms of an independent set of force densities, but also in the vertical coordinates of the restrained nodes. Constraints are enforced on the coordinates of the nodes, to prescribe a feasible design domain, and on the geometry of the members, to control their length and inclination with respect to a given reference direction. Due to its peculiar form, the arising multiconstrained problem can be efficiently solved through techniques of sequential convex programming that were originally conceived to handle formulations of size optimization for elastic structures. Networks that are fully feasible with respect to the enforced local constraints are retrieved in a limited number of iterations, with no need to initialize the procedure with a feasible starting guess. The same algorithm applies to general networks with any type of geometry and restraints.