Open AccessThe stress state in an elastic body with a rigid inclusion of the shape of three segments broken line under the action of the harmonic oscillation of the longitudinal shift
Author(s) -
В. Г. Попов,
Oleksandr Lytvyn
Publication year - 2019
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/1.36
Subject(s) - singularity , mathematical analysis , antiplane shear , helmholtz free energy , mathematics , action (physics) , helmholtz equation , matrix (chemical analysis) , integral equation , displacement (psychology) , quadrature (astronomy) , physics , stress intensity factor , boundary value problem , fracture mechanics , materials science , psychology , quantum mechanics , optics , composite material , psychotherapist , thermodynamics
There is a thin absolutely rigid inclusion that in a cross-section represents three segments broken line in an infinite elastic medium (matrix) that is in the conditions of antiplane strain. The inclusion is under the action of harmonic shear force Pe^{iwt} along the axis Oz. Under the conditions of the antiplane strain the only one different from 0 z-component of displacement vector W (x; y) satisfies the Helmholtz equation. The inclusion is fully couple with the matrix. The tangential stresses are discontinuous on the inclusion with unknown jumps.The method of the solution is based on the representation of displacement W (x; y) by discontinuous solutions of the Helmholtz equation. After the satisfaction of the conditions on the inclusion the system of integral equations relatively unknown jumps is obtained. One of the main results is a numerical method for solving the obtained system, which takes into account the singularity of the solution and is based on the use of the special quadrature formulas for singular integrals.