In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is em...

Several semianalytical approaches are now available for describing diffraction of a plane wave by the 2D (two dimensional) traction free isotropic elastic wedge. In this paper we follow Budaev and Bogy who reformulated the original diffraction problem as a singular integral one. This comprises two algebraic and two singular integral equations. Each integral equation involves two unknowns, a fun...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

This paper contains a theoretical formulation of multiple interface cracks in two bonded dissimilar half planes subjected to in-plane traction. The distributed dislocation technique is used to construct integral equations for a dissimilar mediums weakened by several interface cracks. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obta...

Keywords: Integro-differential equations Volterra equations Abel's integral equations Bernstein polynomials Singular volterra integral equations a b s t r a c t In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of a class of linear Volterra integro-differential equations with weakly singular kernel. If the exact solution is pol...

Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...

We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of mea...