scholarly journals A two-dimensional singular integral equation of diffraction theory

1964 ◽  
Vol 70 (4) ◽  
pp. 596-600 ◽  
Author(s):  
James Radlow
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Diffraction Theory ◽  
Two Dimensional

Elasticity Solution of Deep Beam Under Settlement of Supports

1976 ◽  
Vol 43 (4) ◽  
pp. 613-618 ◽  
Author(s):  
S. N. Prasad ◽  
P. K. Chiu
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
The Other ◽  
Tangential Displacement ◽  
Deep Beam ◽  
Two Dimensional ◽  
Singular Behavior ◽  
Elasticity Solution ◽  
Collocation Technique

The present study investigates the two-dimensional stresses and displacements in a finite rectangle whose one set of parallel edges is given a relative tangential displacement by means of rigidly attached planes. The other set of parallel edges is free from tractions. The problem is formulated in terms of a singular integral equation of the first kind, which yields the correct singular behavior of stresses at the corners. The integral equation is solved numerically by employing Gauss-Jacobi quadrature in conjunction with certain collocation technique. Numerical results of quantities of practical interests are shown graphically and also compared with the classical bending analysis.

Analysis of Branched Cracks

1978 ◽  
Vol 45 (4) ◽  
pp. 797-802 ◽  
Author(s):  
K. K. Lo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Complex Form ◽  
Function Technique ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Potential Formulation ◽  
Crack Problems

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.

Exact Two-Dimensional Contact Analysis of Piezomagnetic Materials Indented by a Rigid Sliding Punch

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Yue Ting Zhou ◽  
Kang Yong Lee
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Moving Contact ◽  
Cylindrical Punch

The aim of the present paper is to investigate the two-dimensional moving contact behavior of piezomagnetic materials under the action of a sliding rigid punch. Introduction of the Galilean transformation makes the constitutive equations containing the inertial terms tractable. Eigenvalues analyses of the piezomagnetic governing equations are detailed, which are more complex than those of the commercially available piezoelectric materials. Four eigenvalue distribution cases occur in the practical computation. For each case, real fundamental solutions are derived. The original mixed boundary value problem with either a flat or a cylindrical punch foundation is reduced to a singular integral equation. Exact solution to the singular integral equation is obtained. Especially, explicit form of the stresses and magnetic inductions are given. Figures are plotted both to show the correctness of the derivation of the exact solution and to reveal the effects of various parameters on the stress and magnetic induction.

On some problems of similarity flow of fluid with a free surface

1969 ◽  
Vol 36 (4) ◽  
pp. 805-829 ◽  
Author(s):  
Z. N. Dobrovol'skaya
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Singular Integral Equation ◽  
Incompressible Fluid ◽  
Singular Integral ◽  
Classical Problem ◽  
Flow Region ◽  
Hydrodynamic Characteristics ◽  
Two Dimensional ◽  
Free Surfaces

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.

scholarly journals On the solvability of some operators with several moved and fixed

2020 ◽  
pp. 10-25
Author(s):  
Д.М. Одинабеков
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problems ◽  
Bounded Domain ◽  
Singular Integral ◽  
Elliptic Systems ◽  
Two Dimensional ◽  
Systems Of Equations ◽  
Singular Coefficients ◽  
Work First

В работе рассматриваются двумерные сингулярные интегральные операторы по ограниченной области с коэффициентами при интегралах, содержащими в нескольких точках существенный разрыв и операторы с ядрами, имеющими в нескольких точках фиксированные особенности типа однородных функций порядка -2. Такие операторы широко применяются при изучении различных краевых задач для эллиптических систем уравнений первого и второго порядка с сингулярными коэффициентами на плоскости (см. напр. [1]-[4]). Одно из таких приложений приведено в конце настоящей работы. Сначала излагаются результаты исследования разрешимости (нетеровости) двумерного сингулярного интегрального уравнения с коэффициентом при интеграле, содержащим в одной точке существенный разрыв. In this paper we consider two-dimensional singular operators over a bounded domain with coefficients of the integrals, containing an essential discontinuity at several points and operators with kernels having fixed singularities at several points of the type of homogeneous functions order -2. Such operators are widely used in various boundary value problems for elliptic systems of equations of the first and second order with singular coefficients on the plane (see eg. [1]-[4]). One such application is given at the end of this work. First of all set out the results of studying the solvability (Noethericity) of a two-dimensional singular integral equation with a coefficient of the integral containing an essential discontinuity at one point.

Sign in / Sign up

Export Citation Format

Share Document