Building a complete solution to the problem of determining the bearing capacity of a flat reinforced rotating disk

A complete solution to the problem of the second limiting state of flat reinforced discs rotating in the stationary regime is constructed. The structures are rigidly fixed to the inner contour (shaft mounted) and can have blades attached to the outer contour. The components of the composition are made of rigid-plastic materials and can have different tensile and compression yield stresses. The binder material of the disk can have cylindrical anisotropia. The characteristic feature of the reinforcement structures is the axial and radial symmetry. The mechanical behavior of the composition is described by the relations of the structural model that takes into account a two-dimensional stress state in all components. Smooth and piecewise-linear criteria for the yield stress of the disk material composition are investigated taking into account the heterogeneity of the structure of reinforcement structure and thickness variability. It is shown that in the general case of reinforcement, the problem of estimation of the bearing capacity of the composite discs is reduced to the numerical solution of one nonlinear functional equation for the threshold velocity of their rotation. For disks with radial, circular and radial-circular reinforcement structures, a complete solution to the problem is obtained in the analytical form. In this case, the orthotropic material of the binder obeys the associated flow rule determined by the modified Tresca-Hu yield criterion. For homogeneous discs of constant thickness, a comparison of the threshold angular velocities calculated for the first and second limiting state is carried out. It is shown that reinforcement of the disks considerably increases its bearing capacity compared to similar disk designs, which have the same mass but are made of traditional structural materials, in particular, high-strength steel. The highest bearing capacity of the discs is ensured by the radial-circular reinforcement. It is demonstrated that in the limiting state of the composite discs, a rigid circular region may appear in the vicinity of the internal contour.