Effect of Magnetic Field and a Mode-I Crack 3D-Problem in Micropolar Thermoelastic Cubic Medium Possessing Under Three Theories

Subject Areas : Engineering

Kh Lotfy ¹ , Y Yahia ²

1 - Department of Mathematics, Faculty of Science, Zagazig University--- Department of Mathematics, Faculty of Science and Arts, Al-mithnab, Qassim University
2 - Department of Mathematics, Faculty of Science and Arts, Al-mithnab, Qassim University

Received: 2013-05-13 Accepted : 2013-07-11 Published : 2013-09-30

Keywords:

References:

[1] Eringen A. C., Suhubi E. S., 1964, Nonlinear theory of simplemicropolar solids, International Journal of Engineering Science 2:1-18.

[2] Eringen A. C.,1966,Linear theory of micropolar elasticity, Journal of Applied Mathematics and Mechanics 15: 909-924.

[3] Biot M. A., 1956, Thermoclasticity and irreversible thermodynamics, Journal of Applied Physics 27:240-253.

[4] Lord H. W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15:299-306.

[5] Othman M. I. A., 2002, Lord-shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermo- elasticity, Journal of Thermal Stresses 25:1027-1045.

[6] Green A. E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2:1-7.

[7] Green A. E., Laws N., 1972, On the entropy production inequality, Archive for Rational Mechanics and Analysis45:47-53.

[8] Suhubi E. S., 1975, Thermoelastic Solids in Continuum Physics, Part 2, Chapter2, Academic Press, New York.

[9] Othman M. I. A., 2004, Relaxation effects on thermal shock problems in an elastic half-space of generalized magneto-thermoelastic waves, Mechanics and Mechanical Engineering 7:165-178.

[10] Iesan D., 1973, The plane micropolar strain of orthotropic elastic solids, Archives of Mechanics 25:547-561.

[11] Iesan D., 1974, Torsion of anisotropic elastic cylinders, Journal of Applied Mathematics and Mechanics 54:773-779.

[12] Iesan D., 1974, Bending of Orthotropic Micropolar Elastic Beams by Terminal Couples, An State University Lasi 20:411- 418.

[13] Nakamura S., Benedict R., Lakes R., 1984, Finite element method for orthotropic micropolar elasticity, International Journal of Engineering Science 22:319-330.

[14] Kumar R., Choudhary S., 2002, Influence and green's function for orthotropic micropolar containua, Archives of Mechanics 54:185-198.

[15] Kumar R., Choudhary S., 2002, Dynamical behavior of orthotropic micropolar elastic medium, Journal of vibration and control 5:1053- 1069.

[16] Kumar R., Choudhary S., 2002, Mechanical sources in orthotropic micropolar continua, Proceedings of the Indian Academy of Sciences 111(2):133-141.

[17] Kumar R., Choudhary S., 2003, Response of orthotropic micropolar elastic medium due to various sources, Meccanica 38:349- 368.

[18] Kumar R., Choudhary S., 2004, Response of orthotropic micropolar elastic medium due to time harmonic sources, Sadhana 29:83- 92.

[19] Singh B., Kumar R., 1998, Reflection of plane wave from a flat boundary of micropolar generalized thermoelastic half-space, International Journal of Engineering Science 36:865-890.

[20] Singh B., 2000, Reflection of plane sound wave from a micropolar generalized thermoelastic solid half-space, Journal of sound and vibration 235:685-696.

[21] Othman M.I. A., Lotfy KH., 2009, Two-dimensional Problem of generalized magneto-thermoelasticity under the Effect of temperature dependent properties for different theories, Multidiscipline Modeling in Materials and Structures 5:235-242.

[22] Othman M.I. A., Lotfy KH., Farouk R.M., 2009, Transient disturbance in a half-space under generalized magneto-thermoelasticity due to moving internal heat source , Acta Physica Polonica A 116:186-192.

[23] Othman M.I. A, Lotfy KH., 2010, On the plane waves in generalized thermo-microstretch elastic half-space, International Communication in Heat and Mass Transfer 37:192-200.

[24] Othman M.I. A, Lotfy KH., 2009, Effect of magnetic field and inclined load in micropolar thermoelastic medium possessing cubic symmetry, International Journal of Industrial Mathematics 1(2): 87-104.

[25] Othman M.I. A, Lotfy KH., 2010, Generalized thermo-microstretch elastic medium with temperature dependent properties for different theories, Engineering Analysis with Boundary Elements 34:229-237.
[26] Lotfy Kh., 2014, Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories, Applied Mathematics and Computation 227:871-888.

[27] Dhaliwal R., 1980, External Crack due to Thermal Effects in an Infinite Elastic Solid with a Cylindrical Inclusion, Thermal Stresses in Server Environments, Doi: 10.1007/978-1-4613-3156-8_41.

[28] Hasanyan D., Librescu L., Qin Z., Young R., 2005, Thermoelastic cracked plates carrying nonstationary electrical current, Journal of Thermal Stresses 28:729-745.

[29] Ueda S., 2003, Thermally induced fracture of a piezoelectric Laminate with a crack normal to interfaces, Journal of Thermal Stresses 26:311-323.

[30] Elfalaky A., Abdel-Halim A. A., 2006, A mode-i crack problem for an infinite space in thermoelasticity, Journal of Applied Sciences 6:598-606.