scholarly journals On the Stress State of the Semi-Strip with a Longitudinal Crack

2018 ◽  
Vol 10 (2) ◽  
pp. 104
Author(s):  
Natalya Vaysfeld ◽  
Zinaida Zhuravlova
Keyword(s):  
Stress State ◽  
Integral Equations ◽  
Singular Integral ◽  
Mechanical Load ◽  
Longitudinal Crack ◽  
Singular Integral Equations ◽  
Dimensional Problem ◽  
Green Matrix ◽  
One Dimensional ◽  
The One

The stress state of the elastic semi-strip is investigated in the paper. The lateral sides of the semi-strip are fixed and the semi-strip’s short edge is under the mechanical load. The longitudinal crack is located inside the semi-strip. The problem is reduced to the one-dimensional problem with the help of Fourier sin-, cos- transformation, which was applied directly to the Lame’s equilibrium equations and the boundary conditions. The one-dimensional problem is formulated is a vector form. Its solution is constructed with the help of the matrix differential calculation and the Green matrix-function, which was constructed in the bilinear form. The solution of the problem is reduced to the solving of three singular integral equations. The first equation in this system contains two fixed singularities in its kernel. To consider them the corresponding transcendental equation is constructed, and its roots are found. The special generalized method is applied to solve the system of singular integral equations. The stress intensity factors are calculated.

scholarly journals Plane stress state of a strip weakened by a crack

2019 ◽  
pp. 182-185
Author(s):  
V. V. Reut ◽  
Yu. V. Molokanov
Keyword(s):  
Stress State ◽  
Plane Stress ◽  
Integral Transform ◽  
Longitudinal Crack ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Infinite Plane ◽  
Transform Method ◽  
One Dimensional ◽  
The One

The plane stress elastic infinite strip problem of a finite longitudinal crack is investigated. The method that can be applied to calculate the stress state and the displacements for an infinite and semi-infinite strip with the longitudinal crack and arbitrary configuration of the boundary conditions is proposed. The main advantage of this method lies in the absence of necessity for use of the apparatus of the matrix differential calculus. Initial problem is reduced to the one-dimensional boundary value problem with the help of the generalized scheme of the integral transform method. By using the inverse integral Fourier transform, the one-dimensional problem is reduced to solving of the system of singular integral equations on a finite interval. The solution of this system was constructed with the help of the method of orthogonal polynomials by means of the second kind Chebyshev polynomials series expansion of the unknown functions. A graph of dependence of the stress intensity factor (SIF) on the geometric parameters of the problem is plotted. It is shown that the SIF for the case of the said strip tends to the SIF for the case of an infinite plane as the width of the strip approaches infinity.

General Solution of the One-Channel-Scattering Singular Integral Equations

1967 ◽  
Vol 154 (5) ◽  
pp. 1345-1357 ◽  
Author(s):  
S. Ciulli ◽  
Gr. Ghika ◽  
M. Stihi ◽  
M. Vişinescu
Keyword(s):  
General Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
The One

scholarly journals Investigation of the semi-strip’s stress state in the case of steady-state oscillations

2019 ◽  
pp. 54-57
Author(s):  
N. D. Vaysfeld ◽  
Z. Yu. Zhuravlova ◽  
O. P. Moyseenok ◽  
V. V. Reut
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
General Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Partial Solution ◽  
Initial Problem ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

The elastic semi-strip under the dynamic load concentrated at the centre of the semi-strip’s short edge is considered. The lateral sides of the semi-strip are fixed. The case of steady-state oscillations is considered. The initial problem is reduced to the one-dimensional problem with the help of the semi-infinite sin-, cos-Fourier’s transform. The one-dimensional problem is formulated in the vector form. Its solution is constructed as a superposition of the general solution for the homogeneous equation and the partial solution for the inhomogeneous equation. The general solution for the homogeneous vector equation is found with the help of the matrix differential calculations. The partial solution is expressed through Green’s matrixfunction, which is constructed as the bilinear expansion. The inverse Fourier’s transform is applied to the derived expressions for the displacements. The solving of the initial problem is reduced to the solving of the singular integral equation. Its solution is searched as the series of the orthogonal Chebyshev polynomials of the second kind. The orthogonalization method is used for the solving of the singular integral equation. The stress-deformable state of the semi-strip is investigated regarding both the frequency of the applied load, and the load segment’s length.

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