Generalized Magneto-Thermo-Viscoelastic Problems of Rotating Functionally Graded Anisotropic Plates by the Dual Reciprocity Boundary Element Method

REFERENCES

• M. Biot , Thermoelasticity and Irreversible Thermo-Dynamics , J. Appl. Phys. , vol. 27 , pp. 249 – 253 , 1956 .
   Web of Science ®Google Scholar
• J. Duhamel , Some Memoire sur les Phenomenes Thermo-Mechanique , J. de l'Ecole Polytech. , vol. 15 , pp. 1 – 57 , 1837 .
   Google Scholar
• F. Neumann , Vorlesungen Uber die theorie der elasticitat , Meyer , Brestau , 1885 .
   Google Scholar
• H. W. Lord and Y. Shulman , A Generalized Dynamical Theory of Thermoelasticity , J. Mech. Phys. Solids , vol. 15 , pp. 299 – 309 , 1967 .
   Web of Science ®Google Scholar
• A. E. Green and K. A. Lindsay , Thermoelasticity , J. Elast. , vol. 2 , pp. 1 – 7 , 1972 .
   Google Scholar
• A. E. Green and P. M. Naghdi , On Undamped Heat Waves in an Elastic Solid , J. Therm. Stresses , vol. 15 , pp. 253 – 264 , 1992 .
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi , Thermoelasticity Without Energy Dissipation , J. Elast. , vol. 31 , pp. 189 – 208 , 1993 .
   Web of Science ®Google Scholar
• Y. Ochiai and R. Ishida , Unsteady Thermal Stress Analysis in Axisymmetric Problems By Means of Boundary Element Method, J. Therm. Stresses , vol. 15, pp. 507–518, 1992.
   Web of Science ®Google Scholar
• 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 Mass Transf. , vol. 39 , pp. 41 – 46 , 2002 .
   Web of Science ®Google Scholar
• A. M. El-Naggar , A. M. Abd-Alla , and M. A. Fahmy , The Propagation of Thermal Stresses in an Infinite Elastic Slab , Appl. Math. Comput. , vol. 157 , pp. 307 – 312 , 2004 .
   Web of Science ®Google Scholar
• X. Z. Zhang , S. Kitipornchai , K. M. Liew , C. W. Lim , and L. X. Peng , Thermal Stresses Around a Circular Hole in a Functionally Graded Plate , J. Therm. Stresses , vol. 26 , pp. 379 – 390 , 2003 .
   Web of Science ®Google Scholar
• A. M. Abd-Alla , A. M. El-Naggar , and M. A. Fahmy , Magneto-Thermoelastic Problem in Non-Homogeneous Isotropic Cylinder , Heat Mass Transf. , vol. 39 , pp. 625 – 629 , 2003 .
   Web of Science ®Google Scholar
• 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. , vol. 78 , pp. 135 – 148 , 2008 .
   Web of Science ®Google Scholar
• M. Das , I. Guven , and E. Madenci , Coupled BEM and FEM Analysis of Functionally Graded Material Layers , J. Therm. Stresses , vol. 29 , pp. 263 – 287 , 2006 .
   Web of Science ®Google Scholar
• M. Ohmichi and N. Noda , Plane Thermoelastic Problem in a Functionally Graded Plate with an Oblique Boundary to the Functional Graded Direction , J. Therm. Stresses , vol. 30 , pp. 779 – 799 , 2007 .
   Web of Science ®Google Scholar
• 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. , vol. 78 , pp. 431 – 442 , 2008 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Thermoelastic Stresses in a Rotating Non-Homogeneous Anisotropic Body , Numer. Heat Transfer, Part A , vol. 53 , pp. 1001 – 1011 , 2008 .
   Web of Science ®Google Scholar
• D. Nardini and C. A. Brebbia , A New Approach to Free Vibration Analysis Using Boundary Elements , Appl. Math. Model. , vol. 7 , pp. 157 – 162 , 1983 .
   Web of Science ®Google Scholar
• C. A. Brebbia , J. C. F. Telles , and L. Wrobel , Boundary Element Techniques in Engineering , Springer-Verlag , New York , 1984 .
   Google Scholar
• L. C. Wrobel and C. A. Brebbia , The Dual Reciprocity Boundary Element Formulation for Nonlinear Diffusion Problems , Comput. Methods Appl. Mech. Eng. , vol. 65 , pp. 147 – 164 , 1987 .
   Web of Science ®Google Scholar
• P. W. Partridge and C. A. Brebbia , Computer Implementation of the BEM Dual Reciprocity Method for the Solution of General Field Equations , Commun. Appl. Numer. Meth. , vol. 6 , pp. 83 – 92 , 1990 .
   Web of Science ®Google Scholar
• P. W. Partridge , C. A. Brebbia , and L. C. Wrobel , The Dual Reciprocity Boundary Element Method , Computational Mechanics Publications , Boston , Southampton , 1992 .
   Google Scholar
• M. A. Fahmy , A Three-Dimensional Generalized Magneto-Thermo-Viscoelastic Problem of a Rotating Functionally Graded Anisotropic Solids With and Without Energy Dissipation , Numer. Heat Transf., Pt. A. , vol. 63 , pp. 1 – 21 , 2013 .
   Web of Science ®Google Scholar
• M. A. Fahmy , A Time-Stepping DRBEM for Magneto-Thermo-Viscoelastic Interactions in a Rotating Nonhomogeneous Anisotropic Solid , Int. J. Appl. Mech. , vol. 3 , pp. 1 – 24 , 2011 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Implicit-Explicit Time Integration DRBEM for Generalized Magneto-Thermoelasticity Problems of Rotating Anisotropic Viscoelastic Functionally Graded Solids , Eng. Anal. Boundary Elem. , vol. 37 , pp. 107 – 115 , 2013 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Transient Magneto-Thermoviscoelastic Plane Waves in a Non-Homogeneous Anisotropic Thick Strip Subjected to a Moving Heat Source , Appl. Math. Model. , vol. 36 , pp. 4565 – 4578 , 2012 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Numerical Modeling of Transient Magneto-Thermo-Viscoelastic Waves in a Rotating Nonhomogeneous Anisotropic Solid under Initial Stress , Int. J. Model. Simul. Sci. Comput. , vol. 3 , pp. 125002 , 2012 .
   Google Scholar
• C. Farhat , K. C. Park , and Y. Dubois-Pelerin , An Unconditionally Stable Staggered Algorithm for Transient Finite Element Analysis of Coupled Thermoelastic Problems, Comput. Meth. Appl. Mech. Eng. , vol. 85, pp. 349–365, 1991.
   Web of Science ®Google Scholar
• M. A. Fahmy , The Effect of Rotation and Inhomogeneity on the Transient Magneto-Thermo-Visco-Elastic Stresses in an Anisotropic Solid , ASME J. Appl. Mech. , vol. 79 , pp. 051015 , 2012 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Transient Magneto-Thermo-Elastic Stresses in an Anisotropic Viscoelastic Solid with and without Moving Heat Source , Numer. Heat Transf., Pt. A. , vol. 61 , pp. 547 – 564 , 2012 .
   Web of Science ®Google Scholar
• L. Gaul , M. Kögl , and M. Wagner , Boundary Element Methods For Engineers and Scientists , Springer-Verlag , Berlin , 2003 .
   Google Scholar
• 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. , vol. 36 , pp. 335 – 345 , 2012 .
   Web of Science ®Google Scholar
• A. V. Ekhlakov , O. M. Khay , Ch. Zhang, J. Sladek, and V. Sladek, A BDEM for Transient Thermoelastic Crack Problems in Functionally Graded Materials Under Thermal Shock , Comput. Mater. Sci. , vol. 57 , pp. 30 – 37 , 2012 .
   Web of Science ®Google Scholar