6. Conclusion

The main aim of this article is to introduce a new fractional-order theory called nonlinear uncoupled magneto-thermoelasticity theory involving three temperatures for FGA structures and new boundary element technique for solving problems related to the proposed theory. Since the nonlinear three temperatures radiative heat conduction equation is independent of the displacement field, we first determine the temperature field using the BEM, then based on the known temperature field, the displacement field is obtained by solving the move equation using the BEM. It can be seen from the numerical results that the graded parameter had a significant effect on the temperatures and displacements through the thickness of the functionally graded structures. Since there are no available results for the considered problem. So, some literatures may be considered as special cases from the considered problem based on replacing the heat conduction by three temperatures radiative heat conduction. The numerical results demonstrate the validity and accuracy of our proposed model. From the proposed BEM technique that has been performed in the present paper, it is possible to conclude that the proposed BEM should be applicable to any FGM uncoupled magneto-thermoelastic problem with three-temperature. BEM is more efficient, accurate and easy to use than FDM or FEM, because it only needs to solve the unknowns on the boundaries and BEM users need only to deal with real geometry boundaries. Also, BEM is reducing the computational cost of its solver. The present numerical results for our complex problem may provide interesting information for computer scientists, designers of new FGM materials and researchers in FGM science as well as for those working on the development of new functionally graded structures.

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