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.

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 Abelian theorems for Whittaker transforms

1987 ◽  
Vol 10 (3) ◽  
pp. 417-431 ◽  
Author(s):  
Richard D. Carmichael ◽  
R. S. Pathak
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Absolute Value ◽  
Final Value ◽  
The Right ◽  
Abelian Theorems

Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches0or∞in absolute value inside a wedge region in the right half plane.

Asymptotic behaviour of the H-transform in the complex domain

1987 ◽  
Vol 102 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Richard D. Carmichael ◽  
Ram S. Pathak
Keyword(s):  
Asymptotic Behaviour ◽  
Half Plane ◽  
Complex Variable ◽  
Structure Theorem ◽  
Generalized Functions ◽  
Complex Domain ◽  
The Right ◽  
Abelian Theorems

AbstractAbelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.

scholarly journals On Generalized Bazilevic Functions Related with Conic Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Khalida Inayat Noor ◽  
Kamran Yousaf
Keyword(s):  
Half Plane ◽  
Convex Domains ◽  
Special Cases ◽  
Generalized Classes ◽  
The Right ◽  
Bazilevic Functions

We define and study some generalized classes of Bazilevic functions associated with convex domains. These convex domains are formed by conic regions which are included in the right half plane. Such results as inclusion relationships and integral-preserving properties are proved. Some interesting special cases of the main results are also pointed out.

The analysis of singularly loaded and rigidly clamped thin elastic slabs with curvilinear boundaries. I

1959 ◽  
Vol 55 (1) ◽  
pp. 121-136 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solutions ◽  
Complex Variable ◽  
Elastic Plates ◽  
Complex Variable Methods ◽  
Isotropic Plates ◽  
Special Cases ◽  
Concentrated Forces ◽  
Quartic Curves ◽  
Thin Elastic Plates

ABSTRACTIn this paper complex variable methods are used to derive exact solutions in closed forms for the small deflexions of certain thin elastic plates due to transverse concentrated forces or couples applied at arbitrary or specified points. The isotropic plates considered are bounded by curvilinear edges of certain types along which the plates are rigidly clamped. Plates bounded by quartic curves having the forms of the inverses of an ellipse with respect to its centre or its focus are included as special cases.

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 Final Value Abelian Theorems for the Stieltjes Transform of Generalized Functions

2011 ◽  
Vol 127 (2) ◽  
pp. 179-183
Author(s):  
RICHARD D. CARMICHAEL
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Equivalent Form ◽  
Generalized Functions ◽  
Stieltjes Transform ◽  
Initial Value ◽  
Final Value ◽  
The Right ◽  
Abelian Theorems

Abstract Limit results are obtained for the Stieltjes transform of generalized functions as the domain complex variable s approaches ∞ (final value results) in the right half plane. These results are of equivalent form as results for the transform as s approaches 0 (initial value results) in the right half plane.

Analysis of Stress Concentration for Curvilinear Holes by Complex Variable Function Method

2011 ◽  
Vol 314-316 ◽  
pp. 1052-1055 ◽  
Author(s):  
Hong Li ◽  
Guang Lei Li ◽  
Da Lu Qiu
Keyword(s):  
Stress Concentration ◽  
Complex Variable ◽  
Infinite Plate ◽  
Bending Moment ◽  
Engineering Structures ◽  
Complex Variable Function ◽  
Concentration Phenomena ◽  
Variable Function ◽  
Curvilinear Holes ◽  
Element Method

A solving method with complex variable function which is fit for numerical calculation for stress concentration phenomena on an infinite plate where there are curvilinear holes is described in this paper. According to the method, the computer programs are made to study the stress concentration problems with curvilinear holes (hexagonal form and oblate form) that are often used in ship and other engineering structures. The maximum of the stresses at the edge of the holes and the distribution of the stresses under axial loading and pure bending moment are calculated respectively. Furthermore, the variations of factors of stress concentration with the different proportions of length and width for oblate holes are considered. The influence on factors of stress concentration due to the change of plate width is indicated. The solutions are consistent with the numerical results of boundary element method, finite element method and related articles.

Fatigue sensitivity analysis using complex variable methods

2012 ◽  
Vol 40 ◽  
pp. 61-73 ◽  
Author(s):  
A. Voorhees ◽  
H. Millwater ◽  
R. Bagley ◽  
P. Golden
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
Complex Variable Methods ◽  
Fatigue Sensitivity
Sign in / Sign up

Export Citation Format

Share Document