An Internal Penny-Shaped Crack Problem in an Infinite Thermoelastic Solid

Author:
RAJESH KUMAR SAKALE and P. K. MATHUR*
Affiliation:

Department of  Mathematics, Laxmin Narain College of Technology Bhopal MP India

*Department of  Mathematics, Saifia P.G. College of Science & Education Bhopal MP India

Email:-pk1321@gmail.com

Keyword:
 Stress distribution, Thermoelastic, Romberb techniques of numerical integral, density, Hankel transform, Inverse Hankel transform, Bessel function, Material thermal conductivity, young's modulus. Specific heat of constant strain.
Issue Date:
December 2011
Abstract:

In the present paper a problem for an infinite thermoelastic solid weakened by an internal penny-shaped crack has been solved. The solid that is assumed to be homogeneous and isotropic is subjected to temperature and stress distributions. A cylindrical system of coordinates is used, in which the plane = 0 is that of the crack and the z-axis is normal to it at the centre. In addition, the crack occupies the region = o, 0 £ r £ that is subjected to prescribed temperature and stress distributions which vary with the radial distance r. The boundary conditions of the problem give a set of two dual integral equations, which we have solved analytically. The problem is solved using the Hankel transform. The inversion of the transform is then obtained analytically. Numerical results for the temperature, stress and displacements distributions are shown graphically and then discussed. All the definite integrals involved were calculated using Romberg technique of numerical integration with the aid of a Fortran program compiled with Visual Fortran v.6.1 on a Pentium-IV pc with processor speed 2.0 GHz. 
 

Pages:
639-652
ISSN:
2319-8044 (Online) - 2231-346X (Print)
Source:
DOI:
jusps-A
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Copy the following to cite this article:

RAJESH KUMAR SAKALE and P. K. MATHUR* , "An Internal Penny-Shaped Crack Problem in an Infinite Thermoelastic Solid ", Journal of Ultra Scientist of Physical Sciences, Volume 23, Issue 3, Page Number 639-652, 2016

Copy the following to cite this URL:

RAJESH KUMAR SAKALE and P. K. MATHUR* , "An Internal Penny-Shaped Crack Problem in an Infinite Thermoelastic Solid ", Journal of Ultra Scientist of Physical Sciences, Volume 23, Issue 3, Page Number 639-652, 2016

Available from: https://www.ultrascientist.org/paper/724/

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