scholarly journals On the thermo-elastostatics of heterogeneous materials: I. General integral equation

2010 ◽  
Vol 213 (3-4) ◽  
pp. 359-374 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Integral Equation ◽  
Heterogeneous Materials ◽  
General Integral

Method of Fundamental Solutions in Micromechanics of Random Structure Linear Elastic Composites

2016 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Integral Equation ◽  
Meshfree Method ◽  
Fundamental Solutions ◽  
Effective Field ◽  
Method Of Fundamental Solutions ◽  
Random Structure ◽  
Linear Elastic ◽  
General Integral ◽  
Homogeneous Matrix ◽  
Linear Thermoelasticity

One considers a linear elastic composite material (CM, [1]), which consists of a homogeneous matrix containing the random set of heterogeneities. An operator form of the general integral equation (GIE, [2–6]) connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions in the infinite media. The new GIE is presented in a general form of perturbations introduced by the heterogeneities and defined at the inclusion interface by the unknown fields of both the displacement and traction. The method of obtaining of the GIE is based on a centering procedure of subtraction from both sides of a new initial integral equation their statistical averages obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs, and some particular cases, asymptotic representations, and simplifications of proposed GIEs are presented for the particular constitutive equations of linear thermoelasticity. In particular, we use a meshfree method [7] based on fundamental solutions basis functions for a transmission problem in linear elasticity. Numerical results were obtained for 2D CMs reinforced by noncanonical inclusions.

A Note on the Integral Equation Formulation of Dynamical Theory

1972 ◽  
Vol 27 (3) ◽  
pp. 434-436 ◽  
Author(s):  
Jon Gjønnes
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Perturbation Methods ◽  
Dynamical Theory ◽  
Forward Scattering ◽  
Equation Formulation ◽  
General Integral ◽  
Scattering Approximation ◽  
Integral Equation Formulation

AbstractThe coupled integral equations for dynamical scattering are developed from the general integral equation. The results are given in the forward scattering approximation. Extension to bade scattering is briefly mentioned. Expressions for distorted crystals are derived both in the column approximation and beyond. The formulation is suggested to be very useful as a basis for perturbation methods.

scholarly journals Note on a -Contour Integral Formula of Gasper-Rahman

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jian-Ping Fang
Keyword(s):  
Integral Equation ◽  
General Formula ◽  
Integral Formula ◽  
Contour Integral ◽  
Transformation Technique ◽  
General Integral ◽  
Cauchy Polynomial

We use the -Chu-Vandermonde formula and transformation technique to derive a more general -integral equation given by Gasper and Rahman, which involves the Cauchy polynomial. In addition, some applications of the general formula are presented in this paper.

Effective Properties of Heterogeneous Magnetoelectroelastic Materials with Multi-Coated Inclusions

2013 ◽  
Vol 550 ◽  
pp. 25-32 ◽  
Author(s):  
Abdel Bakkali ◽  
L. Azrar ◽  
A.A. Aljinadi
Keyword(s):  
Integral Equation ◽  
Effective Properties ◽  
Heterogeneous Materials ◽  
Local Concentration ◽  
Volume Fractions ◽  
Magnetoelectroelastic Materials ◽  
Self Consistent ◽  
Micromechanical Models ◽  
Global And Local

In this paper, the effective properties of magnetoelectroelastic heterogeneous materials with ellipsoidal multi-inclusions are modeled and numerically investigated. The modeling is based on the integral equation that takes into account the multi-coated effect as well as the magnetoelectroelastic interfacial operators and global and local concentration tensors. Various types and kinds of coatings can be considered. The effective properties are predicted based on various micromechanical models such as Mori-Tanaka, Self-Consistent and Incremental Self-Consistent. These properties are presented in terms of the volume fractions of the multi-coated inclusions, thicknesses of the coatings, type and kind of inclusions.

Sign in / Sign up

Export Citation Format

Share Document