Two-dimensional elastic inclusion problems

1961 ◽  
Vol 57 (3) ◽  
pp. 669-680 ◽  
Author(s):  
M. A. Jaswon ◽  
R. D. Bhargava
Keyword(s):  
Complex Variable ◽  
Equilibrium Shape ◽  
Elastic Inclusion ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Force Method ◽  
Equivalent Inclusion ◽  
Stress Magnification

ABSTRACTAn account is given of Eshelby's point-force method for solving elastic inclusion problems, and of his equations relating an in homogeneity to its equivalent inclusion. The introduction of complex variable formalism enables explicit solutions to be found in various two-dimensional cases. Strain energies are calculated. The equilibrium shape of an elliptic inclusion exhibits an interesting feature not previously expected. A fresh analysis of stress magnification effects is developed.

Two-Phase Potentials for the Treatment of an Elastic Inclusion in Plane Thermoelasticity

1995 ◽  
Vol 62 (1) ◽  
pp. 7-12 ◽  
Author(s):  
M. A. Kattis ◽  
S. A. Meguid
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Elastic Inclusion ◽  
Thermomechanical Properties ◽  
Two Dimensional ◽  
Elliptic Inclusion ◽  
Two Phase ◽  
Curvilinear Inclusion ◽  
Steady State Heat ◽  
Thermoelastic Problems

A solution to the uncoupled two-dimensional steady-state heat conduction and thermoelastic problems of an elastic curvilinear inclusion embedded in an elastic matrix, with different thermomechanical properties, is provided. The proposed analysis describes the heat conduction problem in terms of one holomorphic complex potential and the thermoelastic problem in terms of two holomorphic potentials; known hereafter as two-phase potentials. The general results of the developed analysis are applied to specific examples and explicit forms of the solution are obtained. It is shown that a uniform heat flow at infinity induces a linear stress distribution within the elliptic inclusion.

Two-dimensional elliptic inclusions

1963 ◽  
Vol 59 (4) ◽  
pp. 811-820 ◽  
Author(s):  
R. D. Bhargava ◽  
H. C. Radhakrishna
Keyword(s):  
Potential Energy ◽  
Elastic Field ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Minimum Potential Energy ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Equilibrium Size ◽  
The Matrix ◽  
Minimum Potential

AbstractThe simple concept of minimum potential energy of the classical theory of elasticity, first applied to solve inclusion problems (1) by one of the authors (R. D. B.), who considered spherical and circular inclusions, has now been extended to solve elliptic inclusion problems. The complex-variable method of determining the elastic field, first enunciated by A. C. Stevenson in the U.K. and N. I. Muskhelishvili in the U.S.S.R., has been used to determine the elastic field in the infinite material (the matrix) around the inclusion. Strain energies are calculated. The equilibrium size of an elliptic inclusion of elastic (Lamé's) constants λ1 and μ1, differing from those of matrix, for which the constants are λ and μ, has been determined.An independent check on the calculations has been made by testing the continuity of normal and shearing stresses. The results also agree with the known results for the much simpler case when inclusion and matrix are of the same material.

Two-dimensional elastic inclusion problems

1966 ◽  
Vol 62 (2) ◽  
pp. 303-311 ◽  
Author(s):  
R. D. List ◽  
J. P. O. Silberstein
Keyword(s):  
Exact Solution ◽  
Elastic Inclusion ◽  
Infinite Matrix ◽  
System Of Equations ◽  
Two Dimensional ◽  
Physical Change ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Finite Matrix ◽  
The Matrix

AbstractA system of equations is derived for determining the elastic fields in an inclusion and its surrounding finite matrix when the inclusion suffers a physical change and, if not constrained by the matrix, would undergo a deformation . A method for obtaining the exact solution of these equations, when the matrix and inclusion have the same elastic constants, is described and the particular problem of the square inclusion in an infinite matrix solved.

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 Solutions de similitude d'un jeu différentiel stochastique

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Similarity Solutions ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Controlled Processes ◽  
International Audience ◽  
First Time

International audience A two-dimensional controlled stochastic process defined by a set of stochastic differential equations is considered. Contrary to the most frequent formulation, the control variables appear only in the infinitesimal variances of the process, rather than in the infinitesimal means. The differential game ends the first time the two controlled processes are equal or their difference is equal to a given constant. Explicit solutions to particular problems are obtained by making use of the method of similarity solutions to solve the appropriate partial differential equation. On considère un processus stochastique commandé bidimensionnel défini par un ensemble d'équations différentielles stochastiques. Contrairement à la formulation la plus fréquente, les variables de commande apparaissent dans les variances infinitésimales du processus, plutôt que dans les moyennes infinitésimales. Le jeu différentiel prend fin lorsque les deux processus sont égaux ou que leur différence est égale à une constante donnée. Des solutions explicites à des problèmes particuliers sont obtenues en utilisant la méthode des similitudes pour résoudre l'équation aux dérivées partielles appropriée.

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

scholarly journals Accurate Solutions of Stress Intensity Factors of Standard Fracture Test Specimens

2010 ◽  
Vol 452-453 ◽  
pp. 405-408 ◽  
Author(s):  
Akihide Saimoto ◽  
Fumitaka Motomura ◽  
Hironobu Nisitani
Keyword(s):  
Stress Intensity ◽  
Body Force ◽  
General Purpose ◽  
Two Dimensional ◽  
Fracture Test ◽  
Intensity Factors ◽  
Force Method ◽  
Body Force Method ◽  
Standard Specimens ◽  
Significant Figures

Practically exact solutions of stress intensity factor for several two-dimensional standard specimens were calculated and shown in numeric tables. The solutions were confirmed to converge until 6 significant figures through a systematical computation of discretization analysis. The convergence analyses were carried out by using a general purpose program based on a body force method.

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