On the theory of elssticity of a nonhomogeneous medium

Dhaliwal, Ranjit S.; Singh, Brij Mohan

doi:10.1007/bf00052484

Cited by 81 publications

(29 citation statements)

References 3 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Recently a few authors have investigated 2D-FGM especially its stress analysis. [27][28][29][30][31][32][33][34][35][36] The author also has investigated the natural frequencies of a thick hollow cylinder with finite length made of 2D-FGM. 37 The influence of constituent volume fractions on natural frequencies was studied by varying the volume fractions of the constituent metals and ceramics.…”

Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

View full text Add to dashboard Cite

A two-dimensional functionally heterogeneous thick hollow cylinder with a finite length is considered and its natural modes and frequencies are determined. Since mode shapes of a thick cylinder are three-dimensional, even with axisymmetric conditions, three-dimensional theory of elasticity implemented for problem formulation. The axisymmetric conditions are assumed for the cylinder. The material properties of the two-dimensional functionally graded material (2D-FGM) cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution on the different types of anti-symmetric mode shape configuration and vibrational behaviour of a simply supported cylinder are analyzed. Three-dimensional equations of motion are used and the eigen value problem is developed based on direct variational method. The study shows that the 2D-FGM cylinder exhibit interesting vibrational characteristics and mode shapes when the constituent volume fractions are varied.

show abstract

Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

View full text Add to dashboard Cite

show abstract

“…In this paper, we have solved the equations of equilibrium by the method discussed by Dhaliwal & Singh (1978).…”

Section: Introductionmentioning

confidence: 99%

Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

et al. 2009

View full text Add to dashboard Cite

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

show abstract

“…Most of the crack problems solved over the past two decades on nonhomogeneous materials [Dhaliwal and Singh 1978;Delale and Erdogan 1983;Erdogan 1985;Ozturk and Erdogan 1993] provide the basis for the fracture mechanics research on FGMs which are essentially nonhomogeneous materials. In [Erdogan 1995] a brief discussion is given on the application of elementary concepts of fracture mechanics in nonhomogeneous materials and a number of typical problem areas are identified which relate to the fracture of FGMs.…”

Section: Introductionmentioning

confidence: 99%

A surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions

El-Borgi

Abdelmoula

Dağ

et al. 2007

JOMMS

View full text Add to dashboard Cite

The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions is considered. The coating is graded along the thickness direction and modeled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The crack surfaces are subjected to arbitrary loadings which give rise to mixed fracture modes which can be uncoupled due to the fact that the crack axis is parallel to the material gradient. Therefore, the opening and sliding mode problems may be formulated separately. For each problem, the solution of the composite medium may be determined by obtaining the solution of the homogeneous substrate and that of the graded layer. The latter solution may be expressed as the sum of two solutions, namely an infinite graded medium with a crack and a graded strip without a crack. The resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically using Jacobi polynomials. The main objective of the paper is to study the effect of the layer thickness and nonhomogeneity parameter on the crack tip mixed-mode stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

show abstract

On the theory of elssticity of a nonhomogeneous medium

Cited by 81 publications

References 3 publications

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

A surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions

Contact Info

Product

Resources

About