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Effect of magnetic field and a mode-I crack problem in micropolar thermoelastic medium possessing under three theories

Khaled Lotfy (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt)
N. Yahia (Mathematics and Physics Department, Faculty of Engineering, Port Said Branch of Suez Canal University, Port Said, Egypt)
W. Hassan (Department of Mathematics, Faculty of Science and Arts, Qassim University, Buridah, Al-Mithnab, Kingdom of Saudi Arabia)

International Journal of Structural Integrity

ISSN: 1757-9864

Article publication date: 13 May 2014

100

Abstract

Purpose

A model of the equations of two-dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a mode-I crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half-space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lord-Shulman theory includes one relaxation time and Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory. The paper aims to discuss these issues.

Design/methodology/approach

The normal mode analysis is used to obtain the exact expressions for the displacement, microrotation, stresses and temperature distribution.

Findings

The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence of magnetic field.

Originality/value

A comparison is also made between the three theories for different depths in 3D plots.

Keywords

Citation

Lotfy, K., Yahia, N. and Hassan, W. (2014), "Effect of magnetic field and a mode-I crack problem in micropolar thermoelastic medium possessing under three theories", International Journal of Structural Integrity, Vol. 5 No. 2, pp. 86-106. https://doi.org/10.1108/IJSI-03-2013-0003

Publisher

:

Emerald Group Publishing Limited

Copyright © 2014, Emerald Group Publishing Limited

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