On Invariant Perforation in an Infinite Strip

1959 ◽  
Vol 26 (3) ◽  
pp. 422-431
Author(s):  
Chih-Bing Ling
Keyword(s):  
Finite Group ◽  
Stress Function ◽  
Harmonic Functions ◽  
Infinite Group ◽  
The Other ◽  
Infinite Strip ◽  
Method Of Images ◽  
Numerical Examples ◽  
Sigma Function ◽  
Working Out

Abstract The invariant perforation in an infinite strip can be classified into two groups. One is the finite group and the other is the infinite group. There are five cases in the finite group and nine cases in the infinite group. All the cases can be solved by the method of images. This method has, in fact, been used by the author to solve the stresses in an infinite strip containing either an unsymmetrically located single hole or a series of uniformly distributed equal holes. The solution is illustrated by working out in detail one of the cases in the infinite group, in which the strip contains two series of equal holes symmetrically staggered along the strip. The stress function is constructed by using a class of periodic harmonic functions derived from Weierstrass’ sigma function. Numerical examples also are given to show the effect of such a perforation on the stresses in the strip.

Stresses in a Perforated Strip

1957 ◽  
Vol 24 (3) ◽  
pp. 365-375
Author(s):  
Chih-Bing Ling
Keyword(s):  
Stress Function ◽  
Harmonic Functions ◽  
Analytic Solution ◽  
Complete Solution ◽  
Classical Problem ◽  
Stress System ◽  
Infinite Strip ◽  
Numerical Examples ◽  
Biharmonic Functions ◽  
Transverse Bending

Abstract This paper presents an analytic solution of the classical problem dealing with the stresses in an infinite strip having an unsymmetrically located perforating hole. The solution is applicable to any stress system acting in the strip, which is symmetrical with respect to the line of symmetry of the strip. The required stress function is constructed by using four series of biharmonic functions and a bihamonic integral. The four series of biharmonic functions are formed from a class of periodic harmonic functions specially constructed for the purpose. The solution can be regarded as a complete solution of the problem in the sense that, unlike the previous solutions by Howland, Stevenson, and Knight for a symmetrically perforated strip, it is valid in the entire strip. Numerical examples are given for the fundamental cases of longitudinal tension and transverse bending.

Stresses in a Perforated Wedge

1973 ◽  
Vol 40 (3) ◽  
pp. 759-766 ◽  
Author(s):  
Chih-Bing Ling ◽  
Chang-Ming Hsu
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Stress Function ◽  
The Other ◽  
Numerical Examples ◽  
Biharmonic Functions ◽  
Method Of Solution ◽  
The Given ◽  
Infinite Wedge

This paper presents a method of solution for an infinite wedge containing a symmetrically located circular hole. The solution is formulated separately according to the given in-plane edge tractions being even or odd with respect to the axis of the wedge. In either case, the stress function is constructed as the sum of four parts of biharmonic functions, two in the form of integrals and the other two in the form of series, in addition to a basic stress function for an otherwise unperforated wedge. The four parts as a whole give no traction along the edges and no stress at infinity of the wedge. Together with the basic stress function, the boundary conditions of no traction at the rim of hole are adjusted. Complex expressions are used in adjusting the boundary conditions. Finally, numerical examples are given for illustration.

scholarly journals Hiketeia

1973 ◽  
Vol 93 ◽  
pp. 74-103 ◽  
Author(s):  
John Gould
Keyword(s):  
Dominant Role ◽  
Ancient Greece ◽  
Social Institutions ◽  
The Other ◽  
Sixth Century ◽  
Dead Body ◽  
Greek Literature ◽  
The World ◽  
The One ◽  
Working Out

To Professor E. R. Dodds, through his edition of Euripides'Bacchaeand again inThe Greeks and the Irrational, we owe an awareness of new possibilities in our understanding of Greek literature and of the world that produced it. No small part of that awareness was due to Professor Dodds' masterly and tactful use of comparative ethnographic material to throw light on the relation between literature and social institutions in ancient Greece. It is in the hope that something of my own debt to him may be conveyed that this paper is offered here, equally in gratitude, admiration and affection.The working out of the anger of Achilles in theIliadbegins with a great scene of divine supplication in which Thetis prevails upon Zeus to change the course of things before Troy in order to restore honour to Achilles; it ends with another, human act in which Priam supplicates Achilles to abandon his vengeful treatment of the dead body of Hector and restore it for a ransom. The first half of theOdysseyhinges about another supplication scene of crucial significance, Odysseus' supplication of Arete and Alkinoos on Scherie. Aeschylus and Euripides both wrote plays called simplySuppliants, and two cases of a breach of the rights of suppliants, the cases of the coup of Kylon and that of Pausanias, the one dating from the mid-sixth century, the other from around 470 B.C. or soon after, played a dominant role in the diplomatic propaganda of the Spartans and Athenians on the eve of the Peloponnesian War.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

The Mechanical Performance Evaluation of a Mechanism with Curved Edge Driving Component

2013 ◽  
Vol 834-836 ◽  
pp. 1290-1294
Author(s):  
Xin Qin Liu
Keyword(s):  
Performance Evaluation ◽  
Fast Moving ◽  
Mechanical Performance ◽  
Gain Coefficient ◽  
The Other ◽  
Force Transmission ◽  
Transmission Performance ◽  
Connecting Rod ◽  
Numerical Examples ◽  
Straight Line

Mechanicalmethods were employed to study the motion and force transmission performance ofa kind of connecting rod slider mechanism with a curved edge driving component.The deduction methods and the computation formulae of the slider displacement,velocity, acceleration and the executive force gain coefficient were given.Considering two cases of the driving components with straight line edge andexponential function edge, the numerical examples was computed respectively,the results show that the former one is suitable for the force transmission andcan be used in the grip design and the other one is suitable for the motiontransmission which can be used in the fast moving mechanism

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

Sign in / Sign up

Export Citation Format

Share Document