SIM-AM 2025

Energy-based form-finding of column-like lattice elements

  • Bruggi, Matteo (Politecnico di Milano)
  • Guerini, Carlo (Politecnico di Milano)
  • Novati, Giorgio (Politecnico di Milano)

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Among the others, Wire-and-Arc Additive Manufacturing (WAAM) allows for the fabrication of lattices made of branches with fixed area, which may be used to fabricate lightweight structural components, see e.g. [1]. In this contribution, the design of reticulated shells for WAAM is addressed, adopting a combined approach of optimization and funicular analysis 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 of force to length in each branch of the network [2]. Independent sets of branches arise when enforcing symmetry properties of the column-like meso-element. An optimization problem is stated in terms of any independent subset of the force densities retrieving stretching-dominated lattices of minimal compliance. Local enforcements are formulated to control the location of a selected set of nodes and the range of variation of the length of the branches. A smooth eigenvalue buckling constraint is implemented to enforce a lower bound for the critical load, see [3]. The optimization problem is handled by methods of sequential convex programming, exploiting suitable approximations of the objective function and the constraints. Column-like elements that are characterized by different degrees of rotational symmetry are considered. Peculiar features of the achieved layouts are discussed, as well as of the implemented method. ACKNOWLEDGEMENTS Funded by the European Union - Next Generation EU, Mission 4, Component 1, CUP D53D23003900006, research project LATTICE (Lattice meso-elements for a new class of green steel structures) PRIN 2022P7FLNC. REFERENCES [1] Costello, S. C. A., Cunningham, C. R., Xu, F., Shokrani, A., Dhokia, V., and Newman, S. T. The state-of-the-art of wire arc directed energy deposition (WA-DED) as an additive manufacturing process for large metallic component manufacture. International Journal of Computer Integrated Manufacturing. (2023) 1-44. https://doi.org/10.1080/0951192x.2022.2162597 [2] Schek, H.-J. The force density method for form finding and computation of general networks. Computer Methods in Applied Mechanics and Engineering. (1974). 3(1), 115–134. https://doi.org/10.1016/0045-7825(74)90045-0. [3] Bruggi, M., and Guerini, C. Energy-based form-finding of reticulated shells accounting for eigenvalue buckling. Composite Structures. (2025). 354(118742). https://doi.org/10.1016/j.compstruct.2024.118742