Open AccessFormation of Discontinuities in Rectangular Plates as a Result of Residual Stress Relief
Author(s) -
Irina V. Menshova,
Alexander P. Kerzhaev,
Gaoming Yu,
Xian Kui Zeng
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/999/1/012004
Subject(s) - classification of discontinuities , discontinuity (linguistics) , rectangle , eigenfunction , residual stress , fourier series , residual , mathematics , mathematical analysis , geometry , boundary value problem , eigenvalues and eigenvectors , materials science , physics , composite material , algorithm , quantum mechanics
The paper deals with the problem of relieving residual stresses in an elastic domain of rectangular shape with free sides as a result of the formation of a discontinuity of particular shape. First, we construct the solution to the problem of residual stresses in an infinite strip with free sides and with a central transverse cut on which a discontinuity of displacements is known. Then, the solution for a rectangle is added to this solution, with the help of which the boundary conditions at the ends are satisfied. The formulas for the residual stresses and for the corresponding displacements are represented in the form of series in Papkovich-Fadle eigenfunctions. The expansion coefficients (Lagrange coefficients) have the form of simple Fourier integrals.