Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

doi:10.1088/1674-1056/21/1/014209

中国物理B ›› 2012, Vol. 21 ›› Issue (1): 14209-014209.doi: 10.1088/1674-1056/21/1/014209

Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

Kh. Lotfy

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, Egypt; Department of Mathematics, Faculty of Science and Arts, Al-mithnab, Qassim University, P.O. Box 931, Buridah 51931, Al-mithnab, Kingdom of Saudi Arabia

收稿日期:2011-04-03 修回日期:2011-06-30 出版日期:2012-01-15 发布日期:2012-01-20

Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

Kh. Lotfy

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, Egypt; Department of Mathematics, Faculty of Science and Arts, Al-mithnab, Qassim University, P.O. Box 931, Buridah 51931, Al-mithnab, Kingdom of Saudi Arabia

Received:2011-04-03 Revised:2011-06-30 Online:2012-01-15 Published:2012-01-20

摘要/Abstract

摘要： A general model of the equations of the Lord-Şulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode-I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.

关键词: mode-I crack, Lord-Ş, ulman theory, thermoelasticity, normal mode analysis.

Abstract: A general model of the equations of the Lord-Şulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode-I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.

Key words: mode-I crack, Lord-?ulman theory, thermoelasticity, normal mode analysis.

中图分类号:

42.65.Hf

Kh. Lotfy. Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem[J]. 中国物理B, 2012, 21(1): 14209-014209.

Kh. Lotfy . Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem[J]. Chin. Phys. B, 2012, 21(1): 14209-014209.

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Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

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