Modellazione strutturale di maglie metalliche = Structural Modelling of metallic knitted mesh

The use of technical fabrics is rapidly increasing in several fields: textiles, sports, construction, clothing, agriculture, medical devices, and aerospace applications. The materials used in the production of yarns may be of different natures. There is also an important widespread among the methods of interlacing and interconnection of the yarns. It follows that the mechanical behavior of fabrics is extremely complex to model and varied in response. The structural analysis can be faced on a different dimensional scale and it often presents non-linear behavior; consequently, even today universal simulation tools are missing. The modelling approaches are based on: purely geometric models although unable to grasp the mechanical characteristics; continuous models, difficult to calibrate; discrete and finite element models, the most promising ones, but applicable only to small portions of the fabric, to control the affective dimension of the solution system. Besides, these models require non-linear analysis that may include convergence traps. In this thesis, knitted structures made up of metal wires with flat geometry are considered. In the space communications field, these meshes are used as reflective surfaces in satellite antennas, making it possible to reduce costs, package dimension in launch configuration and resulting weight. The main scope is to develop an ad hoc finite element, capable of limiting the number of structural elements necessary to discretize the mesh so that larger structures could be handled. Various tools are proposed for the complete analysis of mesh structures, both under small and large displacements when considering the self-contact problems of the yarns. In particular, a new curved beam element with a thin section has been implemented. It is referred hereinafter as “Wire Element”. The single wire is topologically described by its radius of curvature. The law of variation chosen considers a cubic polynomial; this choice allows obtaining the stiffness matrix in closed form. Castigliano’s Theorem approach was used to derive the flexible coefficients of the wire element, considering the bending and axial loads, while shear deformations are neglected. The finite element thus generated has 2 end nodes for a total of 6 dof's in plane. Its main uses focus on the discretization of thin curved structures such are the single wires forming a knitted mesh. The deformed configuration after loading of the wire is obtained by the variation of the curvature radius as a consequence of the moment applied along the curvilinear abscissa. The knitted metal meshes used for space communications contain many sources of non-linearities: they present high flexibility and low loads, while the effective contacts among wires guarantee electromagnetic optimal performance. In the thesis, several approaches are explored for the nonlinear solution when large displacements and self-contacts occur. Based on the intersection of wires, an original method for contact finding has been proposed. Finally, many test cases are presented, involving both linear and non-linear simulations for single wires or portions of mesh under variously loaded.