Application of an Integral Transform with Generalized Legendre Kernel to the Solution of Integral Equations with Symmetric Kernels

1970 ◽  
pp. 53-56
Author(s):  
B. G. Nikolaev
Keyword(s):  
Integral Equations ◽  
Integral Transform

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

Stress Analysis for a Double Lap Joint

1975 ◽  
Vol 42 (2) ◽  
pp. 353-357 ◽  
Author(s):  
L. M. Keer ◽  
K. Chantaramungkorn
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Lap Joint ◽  
Intensity Factors

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.

scholarly journals Alenezi Transform–A New Transform to Solve Mathematical Problems

2021 ◽  
pp. 1-8
Author(s):  
Ahmad M. Alenezi
Keyword(s):  
Laplace Transform ◽  
Integral Equations ◽  
Integral Transform ◽  
The Other ◽  
The Laplace Transform ◽  
Mathematical Problems ◽  
Sumudu Transforms

In this paper, we present a new integral transform called Alenezi-transform in the category of Laplace transform. We investigate the characteristic of Alenezi-transform. We discuss this transform with the other transforms like J, Laplace, Elzaki and Sumudu transforms. We can demonstrate that Alenezi transforms are near to the condition of the Laplace transform. We can explain the new Properties of transforms using Alenezi transform. Alenezi transform can be applied to solve differential, Partial and integral equations.

scholarly journals On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients

2020 ◽  
Vol 35 (1) ◽  
pp. 01-06
Author(s):  
Mohamed E. Attaweel ◽  
Haneen Almassry
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Integral Transform ◽  
Variable Coefficients ◽  
Sumudu Transforms ◽  
Differential And Integral Equations

The Mohand transform is a new integral transform introduced by Mohand M. Abdelrahim Mahgoub to facilitate the solution of differential and integral equations. In this article, a new integral transform, namely Mohand transform was applied to solve ordinary differential equations with variable coefficients by using the modified version of Laplace and Sumudu transforms.

Anti-Plane Moving Crack in Functionally-Graded Material

2010 ◽  
Vol 29-32 ◽  
pp. 549-553
Author(s):  
Qi Liu
Keyword(s):  
Integral Equations ◽  
Functionally Graded Material ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Fourier Cosine ◽  
Graded Material

In this paper the anti-plane moving crack in a functionally-graded material is studied by the analytical method. First the governing equations for a functionally-graded material are obtained using a Fourier cosine integral transform. Then the dual integral equations for moving crack are established according to the mixed boundary value conditions. It is shown that the dual integral equations can be reduced to the Fredholm integral equation of the second kind. Numerical results shown in the present paper indicate that the non-homogeneity of material has an important influence on the dynamic stress intensity factor.

Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2104) ◽  
pp. 1249-1269 ◽  
Author(s):  
B.M Singh ◽  
J Rokne ◽  
R.S Dhaliwal ◽  
J Vrbik
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Piezoelectric Materials ◽  
Mass Density ◽  
Electric Displacement ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

scholarly journals A procedure for deriving inversion formulae for integral transform pairs of a general kind

1968 ◽  
Vol 9 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Function ◽  
Integral Equations ◽  
Integral Transform ◽  
Classical Orthogonal Polynomials ◽  
General Kind ◽  
Image Position

In recent years there have appeared solutions of several integral equations of the typein which the kernel K(x) contains (as a factor) one of the classical orthogonal polynomials or a hypergeometric function.

scholarly journals On an integral transform

1986 ◽  
Vol 9 (2) ◽  
pp. 283-292 ◽  
Author(s):  
D. Naylor
Keyword(s):  
Bessel Function ◽  
Integral Equations ◽  
Inversion Formula ◽  
Integral Transform ◽  
Zero Order ◽  
Convolution Type ◽  
Type Integral ◽  
Related Integral

This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.

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