Difference schemes of support operator method for equations of elasticity theory in cylindrical geometry

In the work on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed, the approximations of the vector analysis operations in cylindrical geometry are constructed with respect to difference schemes for problems of the theory of elasticity. In view of the energy balance of the medium, families of integrally consistent approximations of vector analysis operations are constructed that are sufficient for discrete modeling of these processes taking into account the curvature of the space caused by the cylindrical geometry of the system. The scalar product in the space of tensor grid functions, the components of the strain tensor, is chosen in accordance with the energy of the deformed body. On $(r,z)$–irregular grids by differential rotation in the azimuthal coordinate $\theta$, the difference schemes of the method of support operators for the equations of the theory of elasticity in displacements are constructed and investigated. The approximations considered preserve the properties of divergence, self-adjointness and sign-definiteness of differential operators, and also are applicable to the solution of non-stationary problems of hydrodynamics with allowance for elastic processes.