**6. Conclusion**

**Table 2** shows that our proposed BEM modeling of Michell-type structure dramatically reduces the computer resources necessary to calculate our proposed modeling in comparison with the calculated results based on the FDM and FEM.

*Solid State Physics - Metastable, Spintronics Materials and Mechanics of Deformable…*

*Comparison of computer resources needed for FDM, FEM and BEM modeling of Michell-type structure.*

**Figure 8.**

**Table 2.**

**200**

*Final Michell-type structure for BEM, FDM and FEM.*

In the present paper, we propose a new theory called nonlinear micropolar thermoviscoelasticity involving three temperatures. A new mathematical modeling of nonlinear generalized micropolar thermoviscoelasticity problem. A new boundary element technique for simulation and optimization problems of mechanics of solid deformable bodies is implemented based on genetic algorithm (GA), free form deformation (FFD) method and nonuniform rational B-spline curve (NURBS) as the global optimization technique for solving complex simulation and optimization problems associated with the proposed theory. FFD is an efficient and versatile parameterization technique for treating shape optimization problems with complex shapes. It is implemented for simulation and optimization of the shape. In the formulation of the considered problem, solutions are obtained for specific arbitrary parameters which are the control points positions in the considered problem, the profiles of the considered objects are determined by FFD method, where the FFD control points positions are treated as genes, and then the chromosomes profiles are defined with the genes sequence. The population is founded by a number of individuals (chromosomes), where the objective functions of individuals are determined by the boundary element method (BEM). Due to the large amount of computer resources required by the FDM and FEM, our proposed BEM model can be applied to a wide range of simulation and optimization problems related with our proposed theory. The numerical results demonstrate the validity, accuracy and efficiency of our proposed technique.
