The Approach to the Construction of Difference Schemes with a Consistent Approximation of the Stress-Strain State and the Energy Balance of the Medium in Cylindrical Geometry

摘要

In the paper, on unstructured metric grids of the theory of the support operator method, on the topological and geometric structure of which minimal reasonable restrictions are imposed, applicable to the symmetricized displacement tensor t_u, discrete analogs of self-adjoint and sign-definite operations div(t_u) and div(tr(t_u)(5) which are invariants to solid rotations, were obtained for modeling of force fields of elastic processes, as well as approximation of integrals of the form ∫_Ω tr (t_u~2) dV and ∫_Ω tr~2 (t_u) dV, sufficient to simulate elastic-dependent energy balances of the medium taking into account the curvature of space of the cylindrical geometry of the system.