A Three-Dimensional Generalized Magneto-Thermo-Viscoelastic Problem of a Rotating Functionally Graded Anisotropic Solids with and Without Energy Dissipation

Abstract

A numerical model based on the dual reciprocity boundary element method (DRBEM) is extended to study the generalized magneto-thermo-viscoelastic problem in a rotating solid of functionally graded material (FGM) in the context of the Green and Naghdi theory of type III. The material properties of the solid have a gradient in the thickness direction and are anisotropic in the plane of the solid. An implicit-implicit staggered strategy was developed and implemented for use with the DRBEM to obtain a solution for the displacement and temperature fields. The accuracy of the proposed method was examined and confirmed by comparing the obtained results with those known previously. In the case of three-dimensional, a numerical scheme for the implementation of the method is presented and the numerical computations are presented graphically to show the effect of the energy dissipation on the temperature and displacement components.

Acknowledgments

The author is grateful to Professor Dr. A. M. El-Naggar, Professor of Applied Mathematics, Faculty of Science, Banha University, Banha, Egypt, Professor Dr. F. S. Ibrahim, Professor of Applied Mathematics, Faculty of Science, Assiut University, Assiut, Egypt, and Professor Dr. M. Elsayed Waheed, Dean of Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt for their kind encouragement during this work.