Modeling of Variable Lamé's Modulii for a FGM Generalized Thermoelastic Half Space

Abstract

In this work we consider a problem in the context of the generalized theory of thermoelasticity for a half space. The material of the half space is functionally graded in which Lamé's modulii are functions of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lamé's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

New fractional model for 2 dimensional half space problem with in the theory of generalized thermoelastic diffusion

“…Some comparisons square measure shown in figures to estimate the impact of the fractional order parameter all told the fields studied. All numerical results are fully agreement with previous work of thermoelastic theories (see, as an example, [24][25][26][27][28][29][30][31]). General sketch for a half area downside is shown in Figure 1.…”

Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

“…These novel nonhomogeneous materials have excellent thermo-mechanical properties and have broad applications to vital structures, for example, atomic reactors, pressure vessels, chemicals plants, aviation, and channels, and so on. The problems of a functionally graded elastic half-space are considered by many researchers [4][5][6][7][8][9].…”

Effect of Initial Stress on a Thermoelastic Functionally Graded Material with Energy Dissipation

“…For these properties (FGM) has a widely applications in industry and engineering applications as we mentioned such as aerospace, nuclear reactors, pressure vessels and pipes. Kumar et al discussed the influence of rotation, magnetic on (FGM) subjected to mechanical load [9], Mohamed H. Hendy discussed the application of fractional order theory to a functionally graded perfect conducting thermoelastic half space with variable Lame's Modulii [10], Vel and Batra, and Qian and Batra studied the three dimensional steady or transient thermal stress problems of functionally graded rectangular plate [11] "sadek", Javaheri and Eslami studied thermal bulking of functionally graded plates [12], Sherief and Abd El-Latief discussed modeling of variable Lamé's modulii for a FGM generalized thermoelastic half Space [13]. Abd-Alla et al [14] discussed Propagation of Rayleigh waves in magneto-thermoelastic half-space of a homogenous orthotropic material under the effect of rotation, initial stress and gravity field.…”