An Integral Equation Approach to the Semi-Infinite Strip Problem

1973 ◽  
Vol 40 (4) ◽  
pp. 948-954 ◽  
Author(s):  
G. D. Gupta
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Laminate Composite ◽  
Integral Transform ◽  
Stress Singularity ◽  
Infinite Strip ◽  
Integral Equation Approach ◽  
Fixed End ◽  
Integral Transform Technique

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

On the contact problem of a moving rigid cylindrical punch sliding over an orthotropic layer bonded to an isotropic half plane

2020 ◽  
Vol 25 (10) ◽  
pp. 1924-1942
Author(s):  
I Çömez ◽  
MA Güler
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Orthotropic Layer ◽  
Moving Contact ◽  
Contact Width ◽  
Cylindrical Punch

In this study, the frictional moving contact problem for an orthotropic layer bonded to an isotropic half plane under the action of a sliding rigid cylindrical punch is considered. Boundary conditions of the problem include the normal and tangential forces applied to the layer with a cylindrical punch moving on the surface of the layer in the lateral direction at a constant velocity V. It is assumed that the contact area is subjected to the sliding condition where Coulomb’⣙s law is used to relate the tangential traction to the normal traction. Using the Fourier integral transform technique and Galilean transformation, the plane contact problem is reduced to a singular integral equation in which the unknowns are the contact stress and the contact width. The singular integral equation is solved numerically using Gauss–Jacobi integration formulae. Numerical results for the contact widths and the contact stresses are given as a solution.

The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip

1982 ◽  
Vol 49 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Fourier Transforms ◽  
Infinite Strip ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Soft Ferromagnetic

Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.

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