Optimal Design of Lattice Structure for Column-like Meso-Elements
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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, see e.g. [1]. In this contribution, the design of truss networks for WAAM is addressed, adopting a combined approach of optimization and funicular analysis for column-like meso-elements. The equilibrium of funicular networks can be conveniently 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. The optimization problem is stated both in terms of any independent subset of the force densities and in terms of the horizontal coordinates of the restrained nodes. The objective function to be maximized is the critical load of the column. This requires the solution of an eigenvalue-based problem, involving the computation of the elastic stiffness matrix and the geometric stiffness matrix of the meso-element. Local enforcements are formulated to prescribe lower and upper bounds for the coordinates of the unrestrained nodes, while controlling the slenderness of the branches. The optimization problem is handled by methods of sequential convex programming [3] to exploit suitable approximations. Peculiar features of the achieved topological layouts and the presented approach are pointed out. ACKNOWLEDGEMENTS The research project LATTICE - Lattice meso-elements for a new class of green steel structures (PRIN 2022P7FLNC), funded by the Italian Ministry of University and Research, is gratefully acknowledged. REFERENCES [1] M. Bruggi, V. Laghi and T. Trombetti. Stress-based form-finding of gridshells for Wire-and-Arc Additive Manufacturing considering overhang constraints. Engineering Structures, 279, 115654, 2023. [2] H. Schek. The force density method for form finding and computation of general networks. Computer Methods in Applied Mechanics and Engineering, 3(1):115-134, 1974. [3] K. Svanberg. The method of moving asymptotes-a new method for structural optimization International Journal for Numerical Methods in Engineering, 24(2):359-373, 1987.