Sliding Frictional Contact of Functionally Graded Magneto-Electro-Elastic Materials Under a Conducting Flat Punch

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Ju Ma ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang
Keyword(s):  
Frictional Contact ◽  
Integral Transform ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Flat Punch ◽  
Coupled Equations ◽  
Fourier Integral Transform ◽  
Coulomb Type

This paper presents the two-dimensional sliding frictional contact between a rigid perfectly conducting flat punch and a functionally graded magneto-electro-elastic material (FGMEEM) layered half-plane. The electric potential and magnetic potential of the punch are assumed to be constant within the contact region. The magneto-electro-elastic (MEE) material properties of the FGMEEM layer vary as an exponential function along the thickness direction, and the Coulomb type friction is adopted within the contact region. By using the Fourier integral transform technique, the problem is reduced to coupled Cauchy singular integral equations of the first and second kinds for the unknown surface contact pressure, electric charge, and magnetic induction. An iterative method is developed to solve the coupled equations numerically and obtain the surface MEE fields. Then, the interior MEE fields are also obtained according to the surface MEE fields. Numerical results indicate that the gradient index and friction coefficient affect both the surface and interior MEE fields significantly.

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

1990 ◽  
Vol 57 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. K. Kaw ◽  
J. G. Goree
Keyword(s):  
Composite Laminates ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Elastic Media ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Fourier Integral Transform ◽  
Shaped Crack ◽  
Symmetric Crack

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

Mode I Crack Problem for a Functionally Graded Orthotropic COATING-Substrate Structure

2014 ◽  
Vol 936 ◽  
pp. 1999-2006
Author(s):  
Li Fang Guo ◽  
Xing Li ◽  
You Zheng Yang
Keyword(s):  
Integral Transform ◽  
Crack Problem ◽  
Integral Equation Method ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Mode I ◽  
Mode I Crack ◽  
Substrate Structure ◽  
Fourier Integral Transform ◽  
Principal Directions

In this paper, the Fourier integral transform-singular integral equation method is presented for the Mode I crack problem of the functionally graded orthotropic coating-substrate structure. The elastic property of the material is assumed vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. Numerical examples are presented to illustrate the effects of the crack length, the material nonhomogeneity and the thickness of coating on the stress intensity factors.

scholarly journals A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab

1991 ◽  
Vol 32 (3) ◽  
pp. 284-295 ◽  
Author(s):  
W. T. Ang
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Finite Part ◽  
Fourier Integral Transform ◽  
Anisotropic Elastic ◽  
Elastic Slab ◽  
Integral Transform Technique ◽  
Coplanar Cracks

AbstractThe problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.

The Effect of Poisson’s Ratio on the Contact Traction Distribution of a Functionally Graded Coating

2011 ◽  
Vol 197-198 ◽  
pp. 1591-1594
Author(s):  
Tie Jun Liu ◽  
Yue Sheng Wang
Keyword(s):  
Poisson’S Ratio ◽  
Integral Transform ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Obvious Effect ◽  
Functionally Graded Coating ◽  
Graded Coating ◽  
Traction Distribution

This paper deals with the finite frictional contact of a functionally graded coating with considering the effect of Poisson’s ratio. We assume that a functionally graded coated half-space is indented by a rigid spherical punch and that the shear modulus of FGMs varies as exponential function. The whole contact region is divided into the central adhesion zone and the slip annulus. Within the slip annulus, the shear stress is limited by friction. By using the Hankel integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. A numerical method is used to get the contact pressure and tangential tractions in the contact region for different Poisson’s ratio. The results show that the variation of Poisson’s ratio has obvious effect on both normal and tangential tractions. With the increase of ν, the peak value of the normal traction increases and that of the tangential traction decreases.

On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation

2003 ◽  
Vol 70 (5) ◽  
pp. 676-680 ◽  
Author(s):  
Y.-S. Wang ◽  
G.-Y. Huang ◽  
D. Dross
Keyword(s):  
Integral Transform ◽  
Mixed Boundary ◽  
Plane Deformation ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Griffith Crack ◽  
Elastic Solids ◽  
Fourier Integral Transform ◽  
Graded Interfacial Zone

An analytical model is developed for a functionally graded interfacial zone between two dissimilar elastic solids. Based on the fact that an arbitrary curve can be approached by a continuous broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and continuous on the interfaces between sublayers. With this new multilayered model, we analyze the problem of a Griffith crack in the interfacial zone. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a Cauchy singular integral equation. The stress intensity factors are calculated. The paper compares the new model to other models and discusses its advantages.

On the Interaction at Anti-Flat Deformation of Stress Concentrators of the Type of Cracks and Stringers with Regard to the Layer Manufactured from Miscellaneous Materials

2019 ◽  
Vol 828 ◽  
pp. 81-88
Author(s):  
Nune Grigoryan ◽  
Mher Mkrtchyan
Keyword(s):  
Integral Transform ◽  
Composite Layer ◽  
Singular Integral Equations ◽  
Original System ◽  
Fourier Integral ◽  
Quadrature Formulas ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Tangential Forces

In this paper, we consider the problem of determining the basic characteristics of the stress state of a composite in the form of a piecewise homogeneous elastic layer reinforced along its extreme edges by stringers of finite lengths and containing a collinear system of an arbitrary number of cracks at the junction line of heterogeneous materials. It is assumed that stringers along their longitudinal edges are loaded with tangential forces, and along their vertical edges - with horizontal concentrated forces. In addition, the cracks are laden with distributed tangential forces of different intensities. The case is also considered when the lower edge of the composite layer is free from the stringer and rigidly clamped. It is believed that under the action of these loads, the composite layer in the direction of one of the coordinate axes is in conditions of anti-flat deformation (longitudinal shift). Using the Fourier integral transform, the solution of the problem is reduced to solving a system of singular integral equations (SIE) of three equations. The solution of this system is obtained by a well-known numerical-analytical method for solving the SIE using Gauss quadrature formulas by the use of the Chebyshev nodes. As a result, the solution of the original system of SIE is reduced to the solution of the system of systems of linear algebraic equations (SLAE). Various special cases are considered, when the defining SIE and the SLAE of the task are greatly simplified, which will make it possible to carry out a detailed numerical analysis and identify patterns of change in the characteristics of the tasks.

Efficient Modeling of Fretting of Blade/Disk Contacts Including Load History Effects

2004 ◽  
Vol 126 (1) ◽  
pp. 56-64 ◽  
Author(s):  
H. Murthy ◽  
G. Harish ◽  
T. N. Farris
Keyword(s):  
Frictional Contact ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Numerical Approach ◽  
Design Tool ◽  
Load History ◽  
Near Surface ◽  
History Effects ◽  
Geometric Transitions ◽  
Fretting Damage

Fretting is a frictional contact phenomenon that leads to damage at the contact region between two nominally-clamped surfaces subjected to oscillatory motion of small amplitudes. The region of contact between the blade and the disk at the dovetail joint is one of the critical locations for fretting damage. The nominally flat geometry of contacting surfaces in the dovetail causes high contact stress levels near the edges of contact. A numerical approach based on the solution to singular integral equations that characterize the two-dimensional plane strain elastic contact of two similar isotropic surfaces presents itself as an efficient technique to obtain the sharp near-surface stress gradients associated with the geometric transitions. Due to its ability to analyze contacts of any two arbitrary smooth surfaces and its computational efficiency, it can be used as a powerful design tool to analyze the effects of various factors like shape of the contact surface and load histories on fretting. The calculations made using the stresses obtained from the above technique are consistent with the results of the experiments conducted in the laboratory.

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