scholarly journals An infinite plate with a curvilinear hole having three poles with complex parameters

2015 ◽  
Vol 11 (5) ◽  
pp. 5198-5210
Author(s):  
Fatimah Salem Bayones ◽  
B. M Alharbi
Keyword(s):  
Boundary Value Problem ◽  
Integrodifferential Equation ◽  
Complex Variable ◽  
Complex Potential ◽  
Infinite Plate ◽  
Cauchy Kernel ◽  
Curvilinear Hole ◽  
Elastic Media ◽  
Rational Mapping ◽  
Special Cases

This paper covered the study of the boundary value problem for isotropic homogeneous perforated infinite elastic media. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origin lie outside the hole is conformally mapped outside a unit circle by means of a specific rational mapping . The complex variable method has been applied and it transforms the problem to the integrodifferential equation with Cauchy kernel that can be solved to find two complex potential functions which called Gaursat functions. Many special cases are discussed and established of these functions .Also, many applications and examples are considered. Moreover the components of stress , in each application , are computed.

scholarly journals Fundamental problems for infinite plate with a curvilinear hole having finite poles

2001 ◽  
Vol 7 (6) ◽  
pp. 485-501 ◽  
Author(s):  
M. A. Abdou ◽  
A. A. El-Bary
Keyword(s):  
Complex Variable ◽  
Arbitrary Shape ◽  
Infinite Plate ◽  
Mapping Function ◽  
Curvilinear Hole ◽  
Two Dimensional ◽  
Rational Mapping ◽  
Special Cases ◽  
Elasticity Problems ◽  
Different Shapes

In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.

scholarly journals S-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes

2004 ◽  
Vol 2004 (24) ◽  
pp. 1255-1265
Author(s):  
I. S. Ismail
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Infinite Plate ◽  
Complex Variable Methods ◽  
Plane Analysis ◽  
Special Cases ◽  
Different Shapes ◽  
The Right ◽  
Curvilinear Holes

Complex variable methods are used to obtain exact and closed expressions for Goursat's functions for the stretched infinite plate weakened by two inner holes which are free from stresses. The plate considered is conformally mapped on the area of the right half-plane. Previous work is considered as special cases of this work. Cases of different shapes of holes are included. Also, many new cases are discussed using this mapping.

Stress Solutions for an Infinite Plate With Triangular Inlay

1956 ◽  
Vol 23 (3) ◽  
pp. 336-338
Author(s):  
R. M. Evan-Iwanowski
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Unit Circle ◽  
Complex Variable ◽  
Boundary Value ◽  
Infinite Plate ◽  
Mapping Function ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Uniform Tension

Abstract The method of solving two-dimensional problems in elasticity by means of the functions of complex variable, essentially developed by É. Goursat (1), and N. I. Muskhelishvili (2-4), has been applied to the following cases: (a) An infinite plate with a rigid triangular inlay under uniform tension at infinity; (b) A concentrated force; and (c) a moment acting on a triangular inlay in an infinite plate. All these problems are second boundary-value problems; i.e., the displacements are prescribed on the boundary. The first boundary-value problem for a triangular opening in an infinite plate was treated by Hu-Nan Chu (7). The mapping function used in this paper is z = ω ( ζ ) = K ( ζ + n ζ 2 ) , K is real, and 0 < n < 1/2 and real, and it maps an exterior of a triangle with rounded corners, Fig. 1, in the z-plane into an exterior of a unit circle in the ζ-plane [for detailed discussion of this mapping refer to (4)].

A Solution of the Mixed Boundary Value Problem for an Infinite Plate With a Hole Under Uniform Heat Flux

1991 ◽  
Vol 58 (4) ◽  
pp. 996-1000 ◽  
Author(s):  
Norio Hasebe ◽  
Hideaki Irikura ◽  
Takuji Nakamura
Keyword(s):  
Heat Flux ◽  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Infinite Plate ◽  
Mapping Function ◽  
Uniform Heat Flux ◽  
Mixed Boundary Value Problem ◽  
Rational Mapping ◽  
Uniform Heat

A general solution of the mixed boundary value problem with displacements and external forces given on the boundary is obtained for an infinite plate with a hole subjected to uniform heat flux. Complex stress functions, a rational mapping function, and the dislocation method are used for the analysis. The stress function is obtained in a closed form and the first derivative is given by such a form that does not contain the integral term. The mapping function is represented in the form of a sum of fractional expressions. A problem is solved for a crack initiating from a point of a circular hole on which the displacement is rigidly stiffened. Stress distributions and stress intensity factors are calculated.

scholarly journals The Electrostatic Energy of a Two-Dimensional System

1959 ◽  
Vol 42 ◽  
pp. 1-2
Author(s):  
LL. G. Chambers
Keyword(s):  
Complex Variable ◽  
Complex Potential ◽  
Unit Length ◽  
Electrostatic Energy ◽  
Dimensional System ◽  
Two Dimensional ◽  
Image System ◽  
Actual System ◽  
Image Domain ◽  
Two Dimensional System

The use of the complex variable z( = x + iy) and the complex potential W(= U + iV) for two-dimensional electrostatic systems is well known and the actual system in the (x, y) plane has an image system in the (U, V) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the (U, V) plane.

scholarly journals RESEARCH OF STATIONARY PLANE FIELDS BY MEANS OF COMPLEX POTENTIAL

2019 ◽  
pp. 39-46
Author(s):  
V. P. Nisonskii ◽  
Yu. V Kornuta ◽  
I. M-B. Katamai
Keyword(s):  
Field Theory ◽  
Complex Variable ◽  
Complex Potential ◽  
Vector Fields ◽  
Oil And Gas ◽  
Water Reservoir ◽  
Singular Points ◽  
Vector Analysis ◽  
Variable Theory ◽  
Complex Variable Theory

Some of the most frequently encountered and generic types of plane vector fields with singular points at the origin of the coordinate system have been studied using complex variable theory methods combined with complex potential methods and field theory methods. The basic concepts of field theory and vector analysis, which are used to study vector fields and the main numerical characteristics of these fields, have been considered. The study of the most frequently encountered vector fields with singular points of four types, namely the generator, the vortical point, the eddy source, the dipole, have been conducted. The application of the complex potential for finding the main characteristics of the vector fields of the considered types, namely their divergence and rotor, has been shown. Equipotential lines and streamlines of the considered vector fields have been obtained and graphically constructed using the method of complex potential. Studied using the vector analysis methods and the methods of the theory of complex variable functions (complex potential) characteristics of vector fields can be used for mathematical modeling of various problems, arising during the study of layers, namely soil and water reservoir filtration problems, as well as in studying the flow of fluid or gas in layers problems. The developed and considered mathematical models of flat vector fields and the found numerical characteristics of these fields can be used to solve other problems of the oil and gas complex, which require studies of the flow of liquids or gases in gas- or oil-bearing beds.

scholarly journals Positive solutions and eigenvalues of conjugate boundary value problems

1999 ◽  
Vol 42 (2) ◽  
pp. 349-374 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Patricia J. Y. Wong
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Lower Bounds ◽  
Boundary Value ◽  
Upper And Lower Bounds ◽  
Special Cases ◽  
Image Position

We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.

Tandem Conveyor Queues

1989 ◽  
Vol 3 (4) ◽  
pp. 517-536
Author(s):  
F. Baccelli ◽  
E.G. Coffman ◽  
E.N. Gilbert
Keyword(s):  
Boundary Value Problem ◽  
Joint Distribution ◽  
Queueing System ◽  
The Other ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Special Cases ◽  
A Cell ◽  
Service Times ◽  
Input Position

This paper analyzes a queueing system in which a constant-speed conveyor brings new items for service and carries away served items. The conveyor is a sequence of cells each able to hold at most one item. At each integer time, a new cell appears at the queue's input position. This cell holds an item requiring service with probability a, holds a passerby requiring no service with probability b, and is empty with probability (1– a – b). Service times are integers synchronized with the arrival of cells at the input, and they are geometrically distributed with parameter μ. Items requiring service are placed in an unbounded queue to await service. Served items are put in a second unbounded queue to await replacement on the conveyor in cells at the input position. Two models are considered. In one, a served item can only be placed into a cell that was empty on arrival; in the other, the served item can be placed into a cell that was either empty or contained an item requiring service (in the latter case unloading and loading at the input position can take place in the same time unit). The stationary joint distribution of the numbers of items in the two queues is studied for both models. It is verified that, in general, this distribution does not have a product form. Explicit results are worked out for special cases, e.g., when b = 0, and when all service times are one time unit (μ = 1). It is shown how the analysis of the general problem can be reduced to the solution of a Riemann boundary-value problem.

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