Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

Abstract

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step—generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

“…Let us consider a fibrous polymer nanomaterial in the 𝑥 1 𝑥 2 − plane, occupies the region 𝑉 that bounded by Γ, the governing equations of fractional size-and temperature-dependent polymer problems of nonlinear nonlocal elasticity can be expressed as [10,11] The force equilibrium equation 𝜎 ̃𝑖𝑗,𝑗 + 𝐹 𝑖 = 0 (1) The fractional-order temperature-dependent heat equation is…”

“…To solve the domain integrals in Eq. ( 35), we used the same process as Fahmy [11] and the techniques [35,36] to obtain the following system:…”

“…Graphite, for example, is employed as a lubricant and is somewhat soft on the bulk scale, whereas carbon nanotubes can have a structure with extremely high tensile strength on the nanoscale [7,8]. Fahmy suggested novel boundary element solutions to thermoelastic nanostructure problems [9][10][11].…”

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

“…Soleiman et al [12] examined the thermomechanical behaviour of functionally graded nanoscale beams under the fractional heat transfer model using a two-parameter Mittag-Leffler function. Fahmy proposed unique boundary element solutions to thermoelastic nanostructure problems [13,14].…”

“…Let us consider a fibrous polymer nanomaterial in the x 1 x 2 − plane, occupying the region V that is bounded by Γ. The governing equations of fractional size-and temperaturedependent polymer problems of nonlinear nonlocal elasticity can be expressed as the following [13,14]:…”