Boundary Integral Equation Analysis of an Inhomogeneous Medium Made of Functionally Graded Materials

2013 ◽  
Vol 685 ◽  
pp. 285-289
Author(s):  
H. Ashrafi ◽  
M.R. Bahadori ◽  
H. Keshmiri ◽  
M. Shariyat
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Boundary Integral Equation ◽  
Functionally Graded Materials ◽  
Inhomogeneous Media ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Element Formulation ◽  
Graded Materials ◽  
Integral Equation Formulation

The present work develops direct graded boundary integral equation formulation for behavior investigation of the inhomogeneous media made of functionally graded materials. The isoparametric boundary elements, the elastostatic governing equations and a weighted residual technique are implemented with the material characteristics that vary continuously along a given dimension. The resulting algorithm is capable of solving the quasistatic problems for elastic functionally graded media with a variety of the boundary conditions and loadings. The inhomogeneous media is made of a ceramic–metal mixture, in which the material properties vary continuously according to a power law graded distribution in a given direction. Avoiding the use of internal elements in the graded boundary element formulation is one of the main objectives of this paper, which results only in numerical discretization of the boundaries of the considered media. Some examples with continuously inhomogeneous isotropic materials were provided under different boundary conditions to evaluate the proposed numerical formulation for the FGMs.

A mathematical boundary integral equation for analysis of the heterogeneous media, using the functionally graded elements

2015 ◽  
Vol 04 (03) ◽  
pp. 1550017 ◽  
Author(s):  
H. Ashrafi ◽  
M. Shariyat
Keyword(s):  
Integral Equation ◽  
Behavior Analysis ◽  
Boundary Integral Equation ◽  
Heterogeneous Media ◽  
Heterogeneous Material ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Graded Materials

In the present research, a functionally graded (FG) boundary integral equation method capable of modeling quasistatic behavior of heterogeneous media fabricated from functionally graded materials (FGMs) whose distributions of the material properties obey either power or exponential laws is developed. Two heterogeneous material gradation models were employed to present the numerical formulations and solution algorithm. Somigliana's identity in 2D displacement fields of the isotropic heterogeneous domains is numerically implemented, employing FG elements. Based on the constitutive and governing equations and the weighted residual technique, the proposed boundary integral equation formulations are implemented for behavior analysis of the elastic heterogeneous isotropic solid structures. Results are verified and the proposed boundary element (BE) formulation is employed for behavior analysis of the plates and cylinders to demonstrate the proposed procedure more adequately.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

SINGULAR INTEGRAL EQUATION METHOD FOR A MOVING CRACK PROBLEM IN ANTIPLANE ELASTICITY OF FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (03) ◽  
pp. 475-492 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Functionally Graded Materials ◽  
Material Property ◽  
Singular Integral ◽  
Crack Problem ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Antiplane Elasticity

In this paper, elastic analysis for a Yoffe moving crack problem in antiplane elasticity of the functionally graded materials (FGMs) is presented. The crack is assumed to move with a constant velocity V. The traction applied on the crack face is arbitrary. The Fourier transform method is used to derive an elementary solution. Furthermore, using the obtained elementary solution a singular integral equation for the problem is obtained. After the singular integral equation is solved, the stress intensity factor (SIF) can be evaluated immediately. In the case of evaluating the SIFs at the leading crack tip and the trailing crack tip, the difference between the two cases is investigated. From the numerical solution of the SIFs, the influence caused by the velocity V and the FGM material property β1 are addressed. It is found that when the FGM material property β1 = 0, i.e. the homogeneous case, the SIFs at the crack tips do not depend on the moving velocity of the crack. Finally, numerical examples are given.

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