5. Numerical results and discussion

The BEM that has been used in the current chapter can be applicable to a wide variety of plate structures problems associated with the proposed theory of three temperatures nonlinear generalized thermoelasticity. In order to evaluate temperatures effects on the thermal stresses, the numerical results are carried out and depicted graphically for electron, ion and phonon temperatures.

Figure 4 shows the distributions of the three temperatures Te, Ti, Tp and total temperature T T ¼ Te þ Ti þ Tp along the radial distance r. It was shown from this figure that the three temperatures are different and they may have great effects on the connected fields.

Figure 4. Variation of the temperatures Te,Ti,Tp and T along the radial distance r.

Figure 5. Variation of the thermal stress σ<sup>11</sup> with radial distance r.

A New Computerized Boundary Element Model for Three-Temperature Nonlinear Generalized… DOI: http://dx.doi.org/10.5772/intechopen.90053

Figure 6.

Variation of the thermal stress σ<sup>12</sup> with radial distance r.

Figure 7. Variation of the thermal stress σ<sup>22</sup> with radial distance r.

Figures 5–7 show the distributions of the thermal stresses σ11, σ<sup>12</sup> and σ<sup>22</sup> respectively, with the radial distance r for the three temperatures Te, Ti, Tp and total temperature. It was noticed from these figures that the three temperatures have great effects on the thermal stresses.

Figure 8 shows the distributions of the thermal stresses σ11, σ12, σ<sup>22</sup> and total temperature T with the radial distance r for BEM results and finite element method (FEM) results of COMSOL Multiphysics software version 5.4 to demonstrate the validity and accuracy of our proposed model based on replacing heat conduction with three-temperature heat conduction.

Figure 8. Thermal stresses and total temperature variations with r.
