Influence of Inhomogeneity and Initial Stress on the Transient Magneto-Thermo-Visco-Elastic Stress Waves in an Anisotropic Solid — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
Influence of Inhomogeneity and Initial Stress on the Transient Magneto-Thermo-Visco-Elastic Stress Waves in an Anisotropic Solid
The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses in a non-ho- mogeneous anisotropic solid under initial stress. The system of fundamental equations is solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are presented graphically to show the effects of initial stress and inhomogeneity on the displacement components and thermal stress components.
KeywordsMagneto-Thermoviscoelastic StressesInitial StressInhomogeneityAnisotropicDual Reciprocity Boundary Element Method
[1] A. M. El-Naggar, A. M. Abd-Alla and M. A. Fahmy, “The Propagation of Thermal Stresses in an Infinite Elastic Slab,” Applied Mathematics and Computation, Vol. 157, No. 2, 2004, pp. 307-312. doi:10.1016/j.amc.2003.08.116
A. M. El-Naggar, A. M. Abd-Alla, M. A. Fahmy and S. M. Ahmed, “thermal Stresses in a Rotating Non-Homogeneous Orthotropic Hollow Cylinder,” Heat and Mass Transfer, Vol. 39, No. 1, 2002, pp. 41-46. doi:10.1007/s00231-001-0285-4
C. A. Brebbia and D. Nardini, “Dynamic Analysis in Solid Mechanics by an Alternative Boundary Element Procedure,” International Journal of Soil Dynamics and Earthquake Engineering, Vol. 2, No. 4, 1983, pp. 228-233. doi:10.1016/0261-7277(83)90040-2
L. C. Wrobel and C. A. Brebbia, “The Dual Reciprocity Boundary Element Formulation for Nonlinear Diffusion Problems,” Computer Methods in Applied Mechanics and Engineering, Vol. 65, No. 2, 1987, pp. 147-164. doi:10.1016/0045-7825(87)90010-7
P. W. Partridge, C. A. Brebbia and L. C. Wrobel, “The Dual Reciprocity Boundary Element Method,” Computational Mechanics Publications, Southampton, 1992.
E. A. Divo and A. J. Kassab, “Boundary Element Methods for Heat Conduction: With Applications in Non-Homogeneous Media,” WIT Press, Southampton, 2003.
L. Gaul, M. K?gl and M. Wagner, “Boundary Element Methods for Engineers and Scientists,” Springer-Verlag, Berlin, 2003.
T. Matsumoto, A. Guzik and M. Tanaka, “A Boundary Element Method for Analysis of Thermoelastic Deformations in Materials with Temperature Dependent Properties,” International Journal for Numerical Methods in Engineering, Vol. 64, No. 11, 2005, pp. 1432-1458. doi:10.1002/nme.1412
M. A. Fahmy, “Thermoelastic Stresses in a Rotating Non- homogeneous Anisotropic Body,” Numerical Heat Transfer, Part A: Applications, Vol. 53, No. 9, 2008, pp. 1001- 1011. doi:10.1080/10407780701789179
M. A. Fahmy, “Application of DRBEM to Non-Steady State Heat Conduction in Non-Homogeneous Anisotropic Media under Various Boundary Elements,” Far East Journal of Mathematical Sciences, Vol. 43, 2010, pp. 83-93.
M. A. Fahmy, “A Time-Stepping DRBEM for the Transient Magneto-Thermo-Visco-Elastic Stresses in a Rotating Non-Homogeneous Anisotropic Solid,” Engineering Analysis with Boundary Elements, Vol. 36, 2012, pp. 335- 345. doi:10.1016/j.enganabound.2011.09.004
G. Davì and A. Milazzo, “A Regular Variational Boundary Model for Free Vibrations of Magneto-Electro-Elastic Structures,” Engineering Analysis with Boundary Elements, Vol. 35, No. 3, 2011, pp. 303-312. doi:10.1016/j.enganabound.2010.10.004
M. A. Fahmy and T. M. El-Shahat, “The Effect of Initial Stress and Inhomogeneity on the Thermoelastic Stresses in a Rotating Anisotropic Solid,” Archive of Applied Mechanics, Vol. 78, No. 6, 2008, pp. 431-442. doi:10.1007/s00419-007-0150-0
C. A. Brebbia, J. C. F. Telles and L. Wrobel, “Boundary Element Techniques in Engineering,” Springer-Verlag, New York, 1984.
P. W. Partridge and L. C. Wrobel, “The Dual Reciprocity Boundary Element Method for Spontaneous Ignition,” International Journal for Numerical Methods in Engineering, Vol. 30, No. 5, 1990, pp. 953-963. doi:10.1002/nme.1620300502
D. Nardini and C. A. Brebbia, “A New Approach to Free Vibration Analysis Using Boundary Elements,” Boundary Element Methods, In: C. A. Brebbia, Ed., Springer- Verlag, Berlin, 1982, pp. 312-326.
E. L. Albuquerque, P. Sollero and M. H. Aliabadi, “Dual Boundary Element Method for Anisotropic Dynamic Fracture Mechanics,” International Journal for Numerical Methods in Engineering, Vol. 59, No. 9, 2004, pp. 1187-1205. doi:10.1002/nme.912
H. A. Cho, M. A. Golberg, A. S. Muleshkov and X. Li, “Trefftz Methods for Time Dependent Partial Differential Equations,” CMC―Computers, Materials & Continua, Vol. 1, 2004, pp. 1-37.
M. Guiggiani and A. Gigante, “A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method,” Journal of Applied Mechanics, ASME, Vol. 57, 1990, pp. 906-915. doi:10.1115/1.2897660
V. Manti?, “A New Formula for the C-Matrix in the Somigliana Identity,” Journal of Elasticity, Vol. 33, 1993, pp. 191-201. doi:10.1007/BF00043247
G. H. Golub and C. F. Van Loan, “Matrix Computations,” North Oxford Academic, Oxford, 1983.
K. J. Bathe, “Finite Element Procedures,” Prentice-Hall, Englewood Cliffs, 1996.
N. Ahmed, “Visco-Elastic Boundary Layer Flow Past a Stretching Plate and Heat Transfer with Variable Thermal Conductivity,” World Journal of Mechanics, Vol. 1, No. 3, 2011, pp. 15-20. doi:10.4236/wjm.2011.12003
S. Kanaun, “An Efficient Numerical Method for Calculation of Elastic and Thermo-Elastic Fields in a Homogeneous Medium with Several Heterogeneous Inclusions,” World Journal of Mechanics, Vol. 1, No. 2, 2011, pp. 31-43. doi:10.4236/wjm.2011.12005
M. D. Monsia, “A Simplified Nonlinear Generalized Maxwell Model for Predicting the Time Dependent Behavior of Viscoelastic Materials,” World Journal of Mechanics, Vol. 1, No. 3, 2011, pp. 158-167. doi:10.4236/wjm.2011.13021
A. M. Abd-Alla, T. M. El-Shahat and M. A. Fahmy, “Thermoelastic Stresses in Inhomogeneous Anisotropic Solid in the Presence of Body Force,” International Journal of Heat & Technology, Vol. 25, No. 1, 2007, pp. 111-118.
A. M. Abd-Alla, M. A. Fahmy and T. M. El-Shahat, “Magneto-Thermo-Elastic Stresses in Inhomogeneous Anisotropic Solid in the Presence of Body Force,” Far- East Journal of Applied Mathematics, Vol. 27, No. 3, 2007, pp. 499-516.
A. M. Abd-Alla, M. A. Fahmy and T. M. El-Shahat, “Magneto-Thermo-Elastic Problem of a Rotating Non-Ho- mogeneous Anisotropic Solid Cylinder,” Archive of Applied Mechanics, Vol. 78, No. 2, 2008, pp. 135-148. doi:10.1007/s00419-007-0147-8
J. Sladek, V. Sladek, P. Solek and Ch. Zhang, “Fracture Analysis in Continuously Nonhomogeneous Magneto- Electro-Elastic Solids under a Thermal Load by the MLPG,” International Journal of Solids and Structures, Vol. 47, No. 10, 2010, pp. 1381-1391. doi:10.1016/j.ijsolstr.2010.01.025