A meshless method for the nonlinear von Karman plate with folds

In recent years, researchers in aeronautics and space sectors were strongly interested in innovative ways to develop structures that reduce weights and spaces without a detriment in performances. Folded structures were intensively studied and their applications are still under development because of the complexity of the possible geometries and the improvements in materials science. Although, there is no physical-mathematical model that is able to deal with all the existing folded structures. In particular, Origami and Kirigami structures experience many issues with the classical theories in literature. In fact, most of the simulations of them consider the plates as infinitely stiff and the deformations are essentially rigid motions [1] or bar-hinge models [2]. Instead, for deformable plates, it is necessary to solve the governing equations for plates, either for small or large normal deflections w. The novel meshless method, proposed and validated in this thesis work, is not limited to small displacements, small rotations and small curvatures. By taking advantage of a hyperelastic constitutive model was possible to deal with plates with folds and cracks and analyse their behaviour in a tensile loading case. In addition, was proposed in an analytical way the response of a von Kármán plate with folds to a buckling load.