IJPAM: Volume 47, No. 4 (2008)


A.V. Balueva$^1$, M. Matczynski$^2$
$^1$Department of Mathematics
Gainesville State College
P.O. Box 1358, Gainesville, Georgia, 30503, USA
$^2$Department of Mathematics
Kielce University of Technology
7, Al. Tysiaclecia Panstwa Polskiego, Kielce, 25-314, POLAND

Abstract.Considering durability of structures with cracks it is necessary to take into account a possibility of crack surfaces contact. Indeed, under arbitrary loading of structures there is no guarantee, that the cracks will be completely opened. The complete or partial closure can take place if the material is under compression [2]. The crack surfaces contacting leads to changing the stress and deformations within the structure and influences on the conditions of the crack growth and on life-time of structures.

Problem of partial opening of a penny-shaped crack due to the heat sources is considered. Analytical results are obtained by means of Hankel transforms and corresponding dual integral equations. The closed form solutions for heat flux across the crack surfaces and for the aperture of the crack are obtained. The solution is illustrated by several numerical results. The crack openings as functions of the distance between the heat sources and the crack for different initial openings of the crack are shown.

Received: September 1, 2008

AMS Subject Classification: 74B20

Key Words and Phrases: thermal stresses, elasticity, fracture

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4