Application of Differential Geometry to Calculations of Stress–Strain State of Nuclear Reactors Covers of WWER Type

Abstract

The problem of determining the stress–strain state (SSS) of the covers of nuclear reactors of the WWER type is considered, which is reduced to calculating an inexact two-layer shell trapped along the contour in the form of a truncated circular rotation ellipsoid under the combined action of internal pressure and temperature. To construct the equations of thermoelasticity of such shells, it is necessary to have expressions describing the internal and external geometry of the surface of the junction of the two-layer shell. In this paper, the basic relations of differential geometry are constructed for an inexact ellipsoidal bimetallic shell of revolution simulating the cover of a WWER-type nuclear reactor. As a result of the analysis, based on the study of quadratic forms of the ellipsoid surface, expressions are obtained for the Lame coefficients and the main radii of curvature of the ellipsoidal bilayer shell of revolution, while the first quadratic form allows the determination of the Lame coefficients, and the main radii of curvature were obtained from their second quadratic form. Their validity is confirmed on the basis of the fulfillment of the Codazzi–Gauss relations.