: One encounters difficulties in the solution of integral equations, namely, the occurrence of singularities in the kernel, and the occurence of unknown-type singularities in the solution of the integral equation. Standard methods of approximation based on exactness for polynomials up to a certain degree are very poor, and frequently fail for functions having such singularities. The purpose of this contract was to develop methods for solving integral equations which work well in spite of the presence of singularities. This goal has been accomplished, in that the new approximation methods which were developed do work well in the presence of singularities. (Author)

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Numerical Solution of Singular Integral Equations.

Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods

Magneto-electro-elastic (MEE) materials have been receiving a special attention from the research community owing to their specialized performance and coupled behavior under thermal, electric, magnetic and mechanical loads. The possibility of prospective energy conversion means, have additionally been added to the cause of researching about these materials. Therefore, the review presented here may be considered as a topical discussion on MEE materials and structures. Through this paper, all critical concepts revolving around MEE materials are discussed in separate sections ranging from the very definition of MEE materials, their material phenomenon, types and properties, to certain fundamental theories and micromechanical models, structural analyses of MEE structures and their nano-sized counterparts, effects of various external and internal parameters and prospective applications of these materials. The present study is in no ways exhaustive to the methods and results observed, but it may be considered as a guide to researchers and scholars about the behavior of MEE materials, wherein critical observations and analyses’ techniques are discussed.

Computational Analysis of Smart Magneto-Electro-Elastic Materials and Structures: Review and Classification

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Numerical Solution Of Integral Equations

Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons

Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating

This paper investigates the linear steady state problem of several moving cracks in a functionally graded magneto-electro-elastic strip subjected to anti-plane mechanical and in-plane electric and magnetic loading. For simplicity, it is assumed that the properties of the strip vary continuously according to exponential functions along the thickness of the functionally graded piezoelectric piezomagnetic (FGPP) layer. By combining the dislocation method and integral transform technique, an exact solution in closed form to this problem is obtained. Electro-magneto-mechanical loads are applied on the crack surfaces, which are assumed to be magneto-electrically impermeable. Numerical examples are presented to show the interesting mechanical and electromagnetic coupling phenomena induced by multi-crack interactions. Finally, the effects of crack velocity, material constants, and geometric parameters upon the field intensity factors are studied. The results are useful for the design of the magneto-electro-elasti...

Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks:

The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations

This paper deals with the fracture analysis of multiple cracks in a functionally graded piezoelectric (FGP) layer under applied anti-plane time-harmonic mechanical and in-plane electrical loading within the framework of linear electro-elasticity. The analysis is based on the stress and electric fields caused by Volterra-type screw dislocation in the medium. The crack surfaces are assumed to be impermeable condition. The material properties of the medium are considered to obey exponential variations. In order to model the cracked layer, the distributed dislocation technique is employed to perform Cauchy-type singular integral equations for layer, in which the unknown variables are dislocation densities. The dislocation densities are then employed to derive field intensity factors at the crack tips. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the cracks configuration, frequency and material properties. Finally, several numerical examples are solved to obtain the dynamic stress intensity factors (DSIFs) and electric displacement intensity factors.

R. Bagheri

Papers

Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating

Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks:

The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations

Several embedded cracks in a functionally graded piezoelectric strip under dynamic loading

The multiple parallel cracks in an orthotropic non-homogeneous infinite plane subjected to transient in-plane loading