Soluzione analitica di piastre circolari soggette a flessione simmetrica, antimetrica e torsione combinate

Aim of the work was the analytical solution of the stress state acting on circular plates subjected to the combination of symmetric bending, antimetric bending and torsion. The solution was needed to design a set of high speed quill shafts presenting a pinion at one side and a wide thin circular transverse flange at the other side, subjected to steady torque combined with symmetric and antimetric bending. The flange was considered as a thin plate problem with small displacements: a parametric solution was studied based on dimensionless ratios so that mostly the shape of the plate was dominant. The outer radius was analyzed in the two cases of simply supported and fixed. The three independent cases of symmetric bending, antimetric bending and torsion were solved: the stress components were finally combined in order to obtain the Von Mises stress distribution both in the case of uniform thickness plates and in the case of a non-uniform thickness plate with known profile.