Optimal Design of Lattice Structure for Column-like Meso-Elements

Wire-and-Arc Additive Manufacturing (WAAM) allows for the fabrication of lattice structures made of branches having fixed area, with a certain freedom in terms of the overall form. In this contribution, the design of spatial networks for WAAM is addressed, adopting a combined approach of optimization and funicular analysis that is especially conceived for column-like meso-elements. The equilibrium of funicular networks is handled through the force density method, i.e. writing the problem in terms of the ratio force to length in each branch of the network. Independent sets of branches arise when enforcing sector symmetry of the column-like meso-element. An optimization problem is stated in terms of any independent subset of the force densities aiming at retrieving solutions of minimal weight. Local enforcements are formulated to control the location of a selected set of nodes, the range of variation of the length of the branches, and the radius of the column-like structural component. The optimization problem is handled by methods of sequential convex programming, exploiting suitable approximations of the objective function and the constraints. Peculiar features of the achieved layouts are pointed out, as well as of the presented approach.