Mohamed Abdelsabour Fahmy, Mathematics Department, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia; Basic Sciences Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.

Saleh Manea Al-Harbi, Mathematics Department, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia.

Badr Hamedy Al-Harbi, Mathematics Department, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia.

A. M. Abd-Alla, A. M. El-Naggar, and M. A. Fahmy, "Magneto-thermoelastic problem in non-homogeneous isotropic cylinder," Heat Mass Transfer 39, 625-629 (2003).

A. M. Abd-Alla, T. M. El-Shahat, and M. A. Fahmy Thermoelastic stresses in inhomogeneous anisotropic solid in the presence of body force. Int. J. Heat Technol. 25, 111-118 (2007).

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 J. Appl. Math. 27, 499-516 (2007).

A. M. El-Naggar, A. M. Abd-Alla, and M. A. Fahmy, and S. M. Ahmed, "thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder," Heat Mass Transfer 39, 41-46 (2002).

A. M. El-Naggar, A. M. Abd-Alla, M. A. Fahmy, "The propagation of thermal stresses in an infinite elastic slab," Appl. Math. Comput. 157, 307-312 (2004).

M. A. Fahmy and T. M. El-Shahat, "The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid," Arch. Appl. Mech. 78, 431-442 (2008).

A. N. Abd-Alla, and F. A. Alsheikh, “Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses,” Arch. Appl. Mech. 79, 843–857 (2009).

M. A. Fahmy, “Shape design sensitivity and optimization for two-temperature generalized magneto-thermoelastic problems using time-domain DRBEM,” J. Therm. Stresses 41, 119–138 (2018).

P. Singh, I. Couckuyt, K. Elsayed, D. Deschrijver, and T. Dhaene, “Shape optimization of a cyclone separator using multi-objective surrogate-based optimization,” Appl. Math. Modell. 40, 4248-4259 (2016).

Computerized boundary element solutions for thermoelastic problems: Applications to functionally graded anisotropic structures, edited by M. A. Fahmy (LAP Lambert Academic Publishing, Saarbrücken, Germany, 2017), Chaps. 2 and 3.

A. Montoya, and H. Millwater, “Sensitivity analysis in thermoelastic problems using the complex finite element method,” J. Therm. Stresses 40, 302-321 (2017).

M. A. Biot, "Mechanics of incremental deformation," Wiley, New York 1966.

M. A. Fahmy, "Effect of initial stress and inhomogeneity on magneto-thermo-elastic stresses in a rotating anisotropic solid," JP J. Heat Mass Transfer Transfer 1, 93-112 (2007).

M. A. Fahmy, "Thermoelastic stresses in a rotating non-homogeneous anisotropic body," Numer. Heat Transfer, Part A, 53, 1001-1011 (2008).

A new approach to free vibration analysis using boundary elements, edited by D. Nardini and C. A. Brebbia (Springer, Berlin, 1982), Chaps. 1 and 2.

The dual reciprocity boundary element formulation for transient heat conduction, edited by L. C. Wrobel, C. A. Brebbia, and D. Nardini (Springer, Berlin, 1986), Chaps. 2 and 3.

P. W. Partridge and L. C. Wrobel, "The dual reciprocity boundary element method for spontaneous ignition," Int. J. Numer. Methods Eng. 30, 953–963 (1990).

The dual reciprocity boundary element method, edited by P. W. Partridge, C. A. Brebbia, and L. C. Wrobel (Computational Mechanics Publications, Southampton, 1992), Chap. 2.

T. T. Yamada and L. C. Wrobel, "A new approach to magnetic field analysis by the dual reciprocity boundary element method," Int. J. Numer. Methods Eng. 36, 2073–2085 (1993).

Boundary element methods for engineers and scientists, edited by L. Gaul, M. Kögl, and M. Wagner (Springer-Verlag, Berlin 2003), Chap. 10.

B. I. Yun and W. T. Ang, "A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a non-homogeneous solid," Eng. Anal. Boundary Elem. 34, 697-706 (2010).

M. A. Fahmy Application of DRBEM to non-steady state heat conduction in non-homogeneous anisotropic media under various boundary elements. Far East J. Math. Sci. 43, 83-93 (2010).

M. A. Fahmy, “Transient magneto-thermoviscoelastic plane waves in a non-homogeneous anisotropic thick strip subjected to a moving heat source,” Applied Mathematical Modelling, 36, 4565-4578 (2012).

M. A. Fahmy, “Numerical modeling of transient magneto-thermo-viscoelastic waves in a rotating nonhomogeneous anisotropic solid under initial stress,” International Journal of Modeling, Simulation and Scientific Computing, 3, 1250002 (1-24) (2012).

M. A. Fahmy, “The effect of rotation and inhomogeneity on the transient magneto-thermoviscoelastic stresses in an anisotropic solid,” ASME Journal of Applied Mechanics, 79, 1015 (2012).

M. A. Fahmy, “Transient magneto-thermo-viscoelastic stresses in a rotating nonhomogeneous anisotropic solid with and without a moving heat source,” Journal of Engineering Physics and Thermophysics, 85, 950-958 (2012).

M. A. Fahmy, “Transient magneto-thermo-elastic stresses in an anisotropic viscoelastic solid with and without moving heat source," Numerical Heat Transfer, Part A: Applications, 61, 547-564 (2012).

M. A. Fahmy, “Implicit-Explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids,” Engineering Analysis with Boundary Elements, 37, 107-115 (2013).

M. A. Fahmy, “Generalized magneto-thermo-viscoelastic problems of rotating functionally graded anisotropic plates by the dual reciprocity boundary element method,” Journal of Thermal Stresses, 36, 1-20 (2013).

M. A. Fahmy, “A three-dimensional generalized magneto-thermo-viscoelastic problem of a rotating functionally graded anisotropic solids with and without energy dissipation,” Numerical Heat Transfer, Part A: Applications, 63, 713-733 (2013).

M. A. Fahmy, “A 2-D DRBEM for generalized magneto-thermo-viscoelastic transient response of rotating functionally graded anisotropic thick strip,” International Journal of Engineering and Technology Innovation, 3, 70-85 (2013).

M. A. Fahmy, “The DRBEM solution of the generalized magneto-thermo-viscoelastic problems in 3D anisotropic functionally graded solids,” I. Idelsohn, M. Papadrakakis, B. Schrefler (eds.), 5th International conference on coupled problems in science and engineering (Coupled Problems 2013), Ibiza, Spain, June 17-19, pp. 862-872 (2013).

M. A. Fahmy, A. M. Salem, M. S. Metwally and M. M. Rashid, “Computer Implementation of the DRBEM for Studying the Generalized Thermoelastic Responses of Functionally Graded Anisotropic Rotating Plates with One Relaxation Time,” International Journal of Applied Science and Technology, 3, 130-140 (2013).

M. A. Fahmy, A. M. Salem, M. S. Metwally and M. M. Rashid, “Computer Implementation of the DRBEM for Studying the Classical Uncoupled Theory of Thermoelasticity of Functionally Graded Anisotropic Rotating Plates,” International Journal of Engineering Research and Applications, 3, 1146-1154 (2013).

M. A. Fahmy, “A Computerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures,” Latin American Journal of Solids and Structures, 11, 386-409 (2014).

M. A. Fahmy (2014), A. M. Salem, M. S. Metwally and M. M. Rashid, “Computer Implementation of the Drbem for Studying the Classical Coupled Thermoelastic Responses of Functionally Graded Anisotropic Plates,” Physical Science International Journal, 4, 674-685 (2014).

M. A. Fahmy, A. M. Salem, M. S. Metwally and M. M. Rashid, “Computer Implementation of the DRBEM for Studying the Generalized Thermo Elastic Responses of Functionally Graded Anisotropic Rotating Plates with Two Relaxation Times,” British Journal of Mathematics & Computer Science, 4, 1010-1026 (2014).

M. A. Fahmy, “A 2D time domain DRBEM computer model for magneto-thermoelastic coupled wave propagation problems,” International Journal of Engineering and Technology Innovation, 4, 138-151 (2014).

M. A. Fahmy, “Boundary Element Solution of 2D Coupled Problem in Anisotropic Piezoelectric FGM Plates,” Proceedings of the, B. Schrefler, E. Oñate and M. Papadrakakis (eds.), 6th International Conference on Computational Methods for Coupled Problems in Science and Engineering (Coupled Problems 2015), Venice. Italy, May 18-20, pp. 382-391 (2015).

M. A. Fahmy (2016), Numerical Modeling of Coupled Thermoelasticity with relaxation times in Rotating FGAPs Subjected to a Moving Heat Source, Physical Science International Journal, Vol. 9, Issue 4, pp. 1-13.

M. A. Fahmy, “3D DRBEM Modeling for Rotating initially stressed Anisotropic functionally graded piezoelectric Plates,” 7th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2016) M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.), Crete Island, Greece, June 5–10 (2016).

M. A. Fahmy, "A time-stepping DRBEM for Magneto-thermo-viscoelastic interactions in a rotating nonhomogeneous anisotropic solid," Int. J. Appl. Mech. 3, 1-24 (2011).

M. A. Fahmy, "A time-stepping DRBEM for the transient magneto-thermo-visco-elastic stresses in a rotating non-homogeneous anisotropic solid," Eng. Anal. Boundary Elem. 36, 335-345 (2012).

M. A. Fahmy, "Finite difference algorithm for transient magneto-thermo-elastic stresses in a non-homogeneous solid cylinder," Int. J. Mater. Eng. Technol. 3, 87-93 (2010).

M. A. Fahmy, "Influence of inhomogeneity and initial stress on the transient magneto-thermo-visco-elastic stress waves in an anisotropic solid," World J. Mech. 1, 256-265 (2011).

A. M. Abd-Alla, M. A. Fahmy, and T. M. El-Shahat, "Magneto-thermo-elastic problem of a rotating non-homogeneous anisotropic solid cylinder," Arch. Appl. Mech. 78, 135-148 (2008).

Sladek, V. Sladek, P. Solek, and Ch. Zhang, "Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG," Int. J. Solids and Struct. 47, 1381-1391 (2010).