On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

Elastic Layer Pressed Against a Half Space

1974 ◽  
Vol 41 (3) ◽  
pp. 703-707 ◽  
Author(s):  
K. C. Tsai ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Layer ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Auxiliary Functions ◽  
Receding Contact ◽  
Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

Steady Motion of a Rigid Strip Bonded to an Elastic Half Space

1971 ◽  
Vol 38 (2) ◽  
pp. 328-334 ◽  
Author(s):  
M. A. Oien
Keyword(s):  
Approximate Solution ◽  
Galerkin Method ◽  
Integral Equations ◽  
Half Space ◽  
Steady Motion ◽  
Elastic Half Space ◽  
Fredholm Integral Equations ◽  
Harmonic Waves ◽  
Forced Motion ◽  
Inertia Properties

The diffraction of harmonic waves by a movable rigid strip bonded to the surface of an elastic half space is divided into two more fundamental problems, the diffraction of waves by a fixed strip and the forced motion of an inertialess strip. These problems are formulated in terms of a pair of coupled Fredholm integral equations of the first kind. An approximate solution for the resultant loads acting on the strip is obtained using the Bubnov-Galerkin method. These loads provide a simple means of studying the excited motion of a movable strip having a variety of inertia properties.

Dynamic Analysis of a Piezoelectric Material with an Impermeable Penny-Shaped Crack under Pure Torsional Wave

2007 ◽  
Vol 345-346 ◽  
pp. 433-436
Author(s):  
Zeng Tao Chen
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Transient Wave ◽  
Total Displacement ◽  
Penny Shaped Crack ◽  
Shaped Crack

A torsional transient wave was assumed acting at infinity on the piezoelectric body with an embedded penny-shaped crack. Appropriate governing equations and boundary conditions have been built within the three-dimensional electroelasticity. The total displacement field was simply considered as the combination of two parts, one related to incident waves inducing an oscillating motion, and another with the scattered waves. An electric impermeable crack was assumed to simplify the mathematical analysis. The problem was formulated in terms of integral transforms techniques. Hankel transform were applied to obtain the dual integral equations, which were then expressed to Fredholm integral equations of the second kind.

Torsion of a Cylindrical Rod Welded to an Elastic Half Space

1967 ◽  
Vol 34 (3) ◽  
pp. 687-692 ◽  
Author(s):  
N. J. Freeman ◽  
L. M. Keer
Keyword(s):  
Integral Equation ◽  
Stress Distribution ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Cylinder ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Dual Integral Equations ◽  
Single Integral

A solution is given for the problem of the torsion of an elastic cylinder welded to an elastic half space. The problem was formulated so as to involve coupling between dual-integral equations and Dini series. These equations were reduced to a single integral equation. Numerical results are given and functions found that approximate the stress distribution.

Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium

1984 ◽  
Vol 51 (4) ◽  
pp. 811-815 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.

scholarly journals A mixed boundary value problem of a cracked elastic medium under torsion

2021 ◽  
pp. 10-10
Author(s):  
Belkacem Kebli ◽  
Fateh Madani
Keyword(s):  
Boundary Value Problem ◽  
Elastic Medium ◽  
Integral Equations ◽  
Integral Transformation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Crack Problem ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack

The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.

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