Numerical method for determining the load capacity of flat rotating reinforced discs

An extremal problem of determining the upper (kinematic) limit of the load-bearing capacity of a flat disk reinforced with continuous fibers and rotating in a quasi-steady state is formulated. At the inner edge, the disk blade is rigidly attached to the shaft (or hub), and reinforced vanes can be attached to its outer edge. The materials of the composition phases are assumed to be rigid-plastic, having different yield limits in tension and compression; the binder matrix material may be cylindrically orthotropic. Under conditions of a generalized plane stress state, the yield curves of the components of the composition in the principal stresses are piecewise linear. Reinforcement structures have radial and axial symmetry. The plastic deformation of the composition is calculated using the relations of the structural model of the mechanics of composites, which takes into account the plane stress state in all phase materials. The problem was discretized and a numerical algorithm for solving it was developed, based on the use of linear programming methods. Various variants of discretization of the problem under consideration have been studied. The convergence of the numerical solution and its good agreement with the previously obtained analytical solution are demonstrated. Numerical examples of calculating the maximum angular velocity of rotation of disks for different reinforcement structures of their fabric are analyzed. Cases of laying fibers along straight trajectories (geodesic lines), along logarithmic spirals, as well as along radial and circumferential directions are considered. In this case, the isotropic materials of the components of the composition obey the associated flow law corresponding to the yield criterion Hu. The influence of reinforcement parameters (directions and densities) on the bearing capacity of rotating disks has been studied. The comparison was carried out for composite disks of the same mass and with the same relative volume of reinforcement.