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

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

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.

Keywords: mode-I crack Lord-?ulman theory thermoelasticity normal mode analysis.

Received: 03 April 2011
Revised: 30 June 2011
Accepted manuscript online:

PACS:

42.65.Hf

Cite this article:

Kh. Lotfy Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem 2012 Chin. Phys. B 21 014209

[1]	Belfield A J, Rogers T G and Spencer A J M 1983 J. Mech. Phys. Solids 31 25
[2]	Verma P D S and Rana O H 1983 Mech. Materials 2 353
[3]	Verma P D S 1986 Int. J. Eng. Sci. 24 1067
[4]	Singh S J 2002 S adhan a 27 1
[5]	Sengupta P R and Nath S 2001 S adhan a 26 363
[6]	Hashin Z and Rosen W B 1964 J. Appl. Mech. 31 223
[7]	Singh B and Singh S J 2004 S adhan a 29 249
[8]	Chattopadhyay A and Choudhury S 1990 Int. J. Eng. Sci. 28 485
[9]	Chaudhary S, Kaushik V P and Tomar S K 2004 Acta Geoph. Polonica 52 219
[10]	Chattopadhyay A and Choudhury S 1995 Int. J. Num. Anal. Meth. Geomech. 19 289
[11]	Pradhan A S, Samal K and Mahanti N C 2003 Tamkang J. Sci. Eng. 6:3 173
[12]	Chattopadhyay A, Venkateswarlu R L K and Saha S 2002 S adhan a 27 613
[13]	Lord H W and cSulman Y A 1967 J. Mech. Phys. Solid 15 299
[14]	Green A E and Lindsay K A 1972 J. Elasticity 2 1
[15]	Roy Choudhuri S K and Debnath L 1983 Int. J. Eng. Sci. 21 155
[16]	Roy Choudhuri S K and Debnath L 1983 J. Appl. Mech. 50 283
[17]	Othman M I A 2005b Int. J. Solids Struct. 41 2939
[18]	Othman M I A 2005 Acta Mechanica 174 129
[19]	Othman M I A and Singh B 2007 Int. J. Solids Stru. 44 2748
[20]	Othman M I A and Song Y 2008 Appl. Math. Modelling 32 811
[21]	Othman M I A and Song Y 2007 Int. J. Sol. Stru. 44 5651
[22]	Verma P D S, Rana O H and Verma M 1988 Indian J. Pure Appl. Math. 19 713
[23]	Singh B 2006 Arch. Appl. Mech. 75 513
[24]	Othman M I A and Lotfy KH 2009 MMMS 5 235
[25]	Othman M I A, Lotfy KH and Farouk R M 2009 Acta Physica Polonica A 116 186
[26]	Othman M I A and Lotfy KH 2010 Int. Commun. in Heat and Mass Transfer 37 192
[27]	Othman M I A and Lotfy KH 2009 Int. J. of Ind. Math. 2 87
[28]	Othman M I A and Lotfy KH 2010 Eng. Anal. with Boundary Elements 34 229
[29]	Dhaliwal R 1980 External Crack due to Thermal Effects in an Infinite Elastic Solid with a Cylindrical Inclusion. Thermal Stresses in Server Environments (New York: Plenum Press) pp. 665-692
[30]	Hasanyan D, Librescu L, Qin Z and Young R 2005 J. Thermal Stresses 28 729
[31]	Ueda S 2003 J. Thermal Stresses 26 311
[32]	Elfalaky A and Abdel-Halim A A 2006 J. Applied Sciences 6 598
[33]	Othman M I A 2002 J. Thermal stresses 25 1027
[34]	Ezzat M, Othman M I A and El-Karamany A S 2001 J. Thermal Stresses 24 1159
[35]	Ezzat M, Othman M I A and El-Karamany A S 2001 J. Thermal Stresses 24 411
[36]	Othman M I A and Singh B 2007 Int. J. Solids and Structures 44 2748
[37]	Othman M I A and Kumar R 2009 Int. Comm. in Heat and Mass Transfer 36 513

[1]	Reflection of thermoelastic wave on the interface of isotropic half-space and tetragonal syngony anisotropic medium of classes 4, 4/m with thermomechanical effect Nurlybek A Ispulov, Abdul Qadir, M A Shah, Ainur K Seythanova, Tanat G Kissikov, Erkin Arinov. Chin. Phys. B, 2016, 25(3): 038102.
[2]	The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium Ahmed E. Abouelregal, Ashraf M. Zenkour. Chin. Phys. B, 2013, 22(10): 108102.
[3]	The effect of rotation on plane waves in generalized thermo-microstretch elastic solid with one relaxation time for a mode-I crack problem Kh. Lotfy and Mohamed I. A. Othman. Chin. Phys. B, 2011, 20(7): 074601.
[4]	Thermoelasticity of CaO from first principles Liu Zi-Jiang(刘子江), Qi Jian-Hong(祁建宏), Guo Yuan(郭媛), Chen Qi-Feng(陈其峰), Cai Ling-Cang(蔡灵仓), and Yang Xiang-Dong(杨向东). Chin. Phys. B, 2007, 16(2): 499-505.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention