Difference schemes of support operator method for equations of elasticity with azimuthal rotation
In the work, for full displacement vectors and velocities, taking into account the azimuthal rotations, on irregular grids with minimal reasonable restrictions for their topological and geometric structure, the approximations of vector analysis operations in cylindrical geometry were constructed with respect to the difference schemes for elasticity theory problems. Taking into account the energy balance of the medium in the presence of azimuthal rotations, families of integrally consistent approximations of vector analysis operations were made, sufficient for discrete modeling of these processes, with respect to the curvature of space caused by the cylindrical geometry of the system. On (r,z)–regular grids with differential rotation along the azimuthal coordinate θ, the difference schemes of the support operator method for the equations of the elasticity theory in displacements were constructed and investigated. The considered approximations retain the properties of divergence, self-adjointness and sign-definiteness of differential operators, and are also applicable for solving nonstationary problems of hydrodynamics with allowance for elastic processes.
difference schemes, support operator method, theory of elasticity, cylindrical geometry, azimuthal rotation
Mathematical modelling in actual problems of science and technics