Exact Two-Dimensional Contact Analysis of Piezomagnetic Materials Indented by a Rigid Sliding Punch

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Yue Ting Zhou ◽  
Kang Yong Lee
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Moving Contact ◽  
Cylindrical Punch

The aim of the present paper is to investigate the two-dimensional moving contact behavior of piezomagnetic materials under the action of a sliding rigid punch. Introduction of the Galilean transformation makes the constitutive equations containing the inertial terms tractable. Eigenvalues analyses of the piezomagnetic governing equations are detailed, which are more complex than those of the commercially available piezoelectric materials. Four eigenvalue distribution cases occur in the practical computation. For each case, real fundamental solutions are derived. The original mixed boundary value problem with either a flat or a cylindrical punch foundation is reduced to a singular integral equation. Exact solution to the singular integral equation is obtained. Especially, explicit form of the stresses and magnetic inductions are given. Figures are plotted both to show the correctness of the derivation of the exact solution and to reveal the effects of various parameters on the stress and magnetic induction.

On the contact problem of a moving rigid cylindrical punch sliding over an orthotropic layer bonded to an isotropic half plane

2020 ◽  
Vol 25 (10) ◽  
pp. 1924-1942
Author(s):  
I Çömez ◽  
MA Güler
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Orthotropic Layer ◽  
Moving Contact ◽  
Contact Width ◽  
Cylindrical Punch

In this study, the frictional moving contact problem for an orthotropic layer bonded to an isotropic half plane under the action of a sliding rigid cylindrical punch is considered. Boundary conditions of the problem include the normal and tangential forces applied to the layer with a cylindrical punch moving on the surface of the layer in the lateral direction at a constant velocity V. It is assumed that the contact area is subjected to the sliding condition where Coulomb’⣙s law is used to relate the tangential traction to the normal traction. Using the Fourier integral transform technique and Galilean transformation, the plane contact problem is reduced to a singular integral equation in which the unknowns are the contact stress and the contact width. The singular integral equation is solved numerically using Gauss–Jacobi integration formulae. Numerical results for the contact widths and the contact stresses are given as a solution.

scholarly journals Torsional Impact Response of a Penny-Shaped Interface Crack in Bonded Materials With a Graded Material Interlayer

2002 ◽  
Vol 69 (3) ◽  
pp. 303-308 ◽  
Author(s):  
C. Li ◽  
Z. Duan ◽  
Z. Zou
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Interface Crack ◽  
Singular Integral ◽  
Dynamic Stress ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Cauchy Kernel ◽  
Dynamic Stress Intensity Factors

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces are assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically and using a numerical Laplace inversion technique, the dynamic stress intensity factors are obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

Elasticity Solution of Deep Beam Under Settlement of Supports

1976 ◽  
Vol 43 (4) ◽  
pp. 613-618 ◽  
Author(s):  
S. N. Prasad ◽  
P. K. Chiu
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
The Other ◽  
Tangential Displacement ◽  
Deep Beam ◽  
Two Dimensional ◽  
Singular Behavior ◽  
Elasticity Solution ◽  
Collocation Technique

The present study investigates the two-dimensional stresses and displacements in a finite rectangle whose one set of parallel edges is given a relative tangential displacement by means of rigidly attached planes. The other set of parallel edges is free from tractions. The problem is formulated in terms of a singular integral equation of the first kind, which yields the correct singular behavior of stresses at the corners. The integral equation is solved numerically by employing Gauss-Jacobi quadrature in conjunction with certain collocation technique. Numerical results of quantities of practical interests are shown graphically and also compared with the classical bending analysis.

scholarly journals Application of Jacobi Polynomials to the Approximate Solution of a Singular Integral Equation with Cauchy Kernel on the Real Half-line

2006 ◽  
Vol 6 (3) ◽  
pp. 326-335
Author(s):  
D. Pylak
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Approximate Solutions ◽  
Half Line ◽  
Cauchy Kernel ◽  
The Real

AbstractIn this paper, exact solution of the characteristic equation with Cauchy kernel on the real half-line is presented. Next, Jacobi polynomials are used to derive approximate solutions of this equation. Moreover, estimations of errors of the approximated solutions are presented and proved.

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