Stress-strain state in constructions corner areas

Abstract

The topical problem of investigation, development of numerical and analytical methods to research constructions, buildings and structures is stress-strain analysis of building structures with intricate shape of the boundary. Geometrically nonlinear shape of boundaries (notches, crosscuts) determines the occurrence of stress concentration zones, deformations with significant enormities and gradients. Theoretical analysis of stress-strain state (SSS) for angled cut-out zones of area boundaries under the action of ruptural forced deformations resolves itself to study the singular solutions of uniform problem of elasticity theory with degree type features. The novelty of the research in the present work is determined by the fact that SSS near the vertex of angled cut-out zones of area boundary is characterized by limit strains, similar to the stress-intensity factors KI, KII, KIII when applying force criteria in mechanics of damage. Two-dimensional Betti formula is used to determine the intensity factors as limit strains, for the area constrained by the contour-circle of small radius r = ε. The independence of the Betti integral from the integration path is taken into account, which allows us to consider the contour integral along the length of arc close to the circle r = ε. The limit strains obtained in angled cut-out zones of area boundary are analyzed depending upon the area cut apex angle and the eigenvalues of elastic problem for the case of boundary conditions homogeneous for stresses.