Mohamed Abdelsabour Fahmy

By Mohamed Abdelsabour Fahmy

In this chapter, we propose a new theory called nonlinear generalized thermoelasticity involving three temperatures. Because of strong nonlinearity of the proposed theory, therefore, it is much more difficult to develop analytical solution for solving problems related with the proposed theory. So, we propose a new computerized boundary element model for the solution of such problems and obtaining the three-temperature nonlinear generalized thermoelastic stresses in anisotropic circular cylindrical plate structures problems which are related with the proposed theory, where we used two-dimensional three temperature nonlinear radiative heat conduction equations coupled with electron, ion and phonon temperatures. The numerical results of the current study show the temperatures effects on the thermal stresses. Also, these numerical results demonstrate the validity and accuracy of our proposed model.

Part of the book: Dynamical Systems Theory

By Mohamed Abdelsabour Fahmy

The main objective of this chapter is to introduce a new theory called three-temperature nonlinear generalized micropolar thermoviscoelasticity. Because of strong nonlinearity of simulation and optimization problems associated with this theory, the numerical solutions for problems related with the proposed theory are always very difficult and require the development of new numerical techniques. So, we propose a new boundary element technique for simulation and optimization of such problems based on genetic algorithm (GA), free form deformation (FFD) method and nonuniform rational B-spline curve (NURBS) as the shape optimization technique. In the formulation of 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). The numerical results verify the validity and accuracy of our proposed technique.

Part of the book: Metastable, Spintronics Materials and Mechanics of Deformable Bodies

By Mohamed Abdelsabour Fahmy

The main objective of this paper is to introduce a new fractional-order theory called nonlinear fractional generalized photo-thermoelasticity involving three temperatures. Due to strong nonlinearity, it is very difficult to solve the wave problems related to this theory analytically. Therefore, we propose a new boundary element algorithm and technique for simulation and optimization of the considered problems related to this theory. The genetic algorithm (GA) as an optimization method has been applied based on free form deformation (FFD) technique to improve the performance of our proposed technique. In the formulation of the considered problem, the profiles of the considered objects are determined by FFD technique, where the FFD control point positions are treated as genes, and then the chromosome profiles are defined with the gene sequence. The population is established by a number of individuals (chromosomes), where the objective functions of individuals are achieved by the boundary element method (BEM). A nonuniform rational B-spline curve (NURBS) was used to model optimized boundary where it reduces the number of control points and provides the flexibility to design several different shapes for solving the considered photo-thermoelastic wave problems. The numerical results verify the validity and accuracy of our proposed boundary element technique.

Part of the book: Recent Trends in Computational Intelligence

By Mohamed Abdelsabour Fahmy

The principal aim of this chapter is to introduce a new theory called acoustic wave propagation of three-temperature nonlinear generalized magneto-thermoelasticity, and we propose a new boundary element model for solving problems of initially stressed multilayered functionally graded anisotropic (ISMFGA) structures using laser ultrasonics, which connected with the proposed theory. Since there are no available analytical or numerical solutions for the considered nonlinear wave propagation problems in the literature, we propose a new boundary element modeling formulation for the solution of such problems. The numerical results are depicted graphically to show the propagation of three temperatures and displacement waves. The results also show the effects of initial stress and functionally graded material on the displacement waves and confirm the validity and accuracy of our proposed theory and solution technique.

Part of the book: Noise and Environment

By Mohamed Abdelsabour Fahmy

The main objective of this chapter is to introduce a novel memory-dependent derivative (MDD) model based on the boundary element method (BEM) for solving transient three-temperature (3T) nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures. The governing equations of the considered study are nonlinear and very difficult if not impossible to solve analytically. Therefore, we develop a new boundary element scheme for solving such equations. The numerical results are presented highlighting the effects of the MDD on the temperatures and nonlinear thermal stress distributions and also the effect of anisotropy on the nonlinear thermal stress distributions in FGA smart structures. The numerical results also verify the validity and accuracy of the proposed methodology. The computing performance of the proposed model has been performed using communication-avoiding Arnoldi procedure. We can conclude that the results of this chapter contribute to increase our understanding on the FGA smart structures. Consequently, the results also contribute to the further development of technological and industrial applications of FGA smart structures of various characteristics.

Part of the book: Advanced Functional Materials

By Mohamed Abdelsabour Fahmy

The main purpose of this chapter, which represents one of the chapters of a fractal analysis book, is to propose a new boundary element method (BEM) formulation based on time fractional order theory of thermoelasticity for modeling and optimization of three temperature (3T) multi-material initially stressed multilayered functionally graded anisotropic (ISMFGA) structures subjected to moving heat source. Fractional order derivative considered in the current chapter has been found to be an accurate mathematical tool for solving the difficulty of our physical and numerical modeling. Furthermore, this chapter shed light on the practical application aspects of boundary element method analysis and topology optimization of fractional order thermoelastic ISMFGA structures. Numerical examples based on the multi-material topology optimization algorithm and bi-evolutionary structural optimization method (BESO) are presented to study the effects of fractional order parameter on the optimal design of thermoelastic ISMFGA structures. The numerical results are depicted graphically to show the effects of fractional order parameter on the sensitivities of total temperature, displacement components and thermal stress components. The numerical results also show the effects of fractional order parameter on the final topology of the ISMFGA structures and demonstrate the validity and accuracy of our proposed technique.

Part of the book: Fractal Analysis

By Mohamed Abdelsabour Fahmy

In this chapter, we introduce a new theory called acoustic wave propagation of three-temperature fractional nonlinear generalized micropolar poro-thermoelasticity and we propose a new boundary element technique for modeling and simulation of laser-generated ultrasonic wave propagation problems of functionally graded anisotropic (FGA) structures which are linked with the proposed theory. Since it is very difficult to solve general acoustic problems of this theory analytically, we need to develop and use new computational modeling techniques. So, we propose a new boundary element technique for solving such problems. The numerical results are shown graphically to depict the effects of three temperatures on the thermal stress waves propagation. The validity, accuracy, and efficiency of our proposed theory and the technique are examined and demonstrated by comparing the obtained outcomes with those previously reported in the literature as special cases of our general study.

Part of the book: Modeling and Simulation in Engineering

By Mohamed Abdelsabour Fahmy

The main purpose of this chapter is to propose a new boundary element formulation for the modeling and optimization of three-temperature nonlinear generalized magneto-thermoelastic functionally graded anisotropic (FGA) composite microstructures’ problems, which is the gap of this study. Numerical results show that anisotropy and the functionally graded material have great influences on the nonlinear displacement sensitivities and nonlinear thermal stress sensitivities of composite microstructure optimization problem. Since, there are no available data for comparison, except for the problems with one-temperature heat conduction model, we considered the special case of our general study based on replacing three-temperature radiative heat conductions with one-temperature heat conduction. In the considered special case, numerical results demonstrate the validity and accuracy of the proposed technique. In order to solve the optimization problem, the method of moving asymptotes (MMA) based on the bi-evolutionary structural optimization method (BESO) has been implemented. A new class of composite microstructures problems with holes or inclusions was studied. The two-phase magneto-thermoelastic composite microstructure which is studied in this chapter consists of two different FGA materials. Through this chapter, we investigated that the optimal material distribution of the composite microstructures depends strongly on the heat conduction model, functionally graded parameter, and shapes of holes or inclusions.

Part of the book: Composite Materials

By Mohamed Abdelsabour Fahmy

The main purpose of this chapter is to propose a novel boundary element modeling and simulation algorithm for solving fractional bio-thermomechanical problems in anisotropic soft tissues. The governing equations are studied on the basis of the thermal wave model of bio-heat transfer (TWMBT) and Biot’s theory. These governing equations are solved using the boundary element method (BEM), which is a flexible and effective approach since it deals with more complex shapes of soft tissues and does not need the internal domain to be discretized, also, it has low RAM and CPU usage. The transpose-free quasi-minimal residual (TFQMR) solver are implemented with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner to solve the linear systems arising from BEM. Numerical findings are depicted graphically to illustrate the influence of fractional order parameter on the problem variables and confirm the validity, efficiency and accuracy of the proposed BEM technique.

Part of the book: Recent Developments in the Solution of Nonlinear Differential Equations