Geometrical uncertainties influence on the failure load estimation of lattice structures

Lattice structures can provide high strength with modest weight. For this reason, they are found in many natural systems at the microscopic level and have also been adopted in engineering at many scales. Assessment of the load-bearing capacity of such structures is crucial and cannot ignore considerations of imperfections, whether due to natural factors if the material exists naturally or to manufacturing defects if it is created artificially. Defects can affect many geometrical aspects of the lattice such as the shape of cells and the thickness and the waviness of trusses. In this paper, we will focus on the first aspect, investigating the effect of variation of the shape of the cells by applying a perturbation to the periodic configuration for common geometries. The failure load of these systems is evaluated by means of an upper bound limit analysis through linear programming, varying the relative density of the lattice and the intensity of imperfections. The failure load is addressed by statistical moments and probability density functions.