A Novel BEM for Modeling and Simulation of 3T Nonlinear Generalized Anisotropic Micropolar-Thermoelasticity Theory with Memory Dependent Derivative

The main aim of this paper is to propose a new memory dependent derivative(MDD)theory which called threetemperature nonlinear generalized anisotropic micropolar-thermoelasticity.The system of governing equations of the problems associated with the proposed theory is extremely difficult or impossible to solve analytically due to nonlinearity,MDD diffusion,multi-variable nature,multi-stage processing and anisotropic properties of the considered material.Therefore,we propose a novel boundary element method(BEM)formulation for modeling and simulation of such system.The computational performance of the proposed technique has been investigated.The numerical results illustrate the effects of time delays and kernel functions on the nonlinear three-temperature and nonlinear displacement components.The numerical results also demonstrate the validity,efficiency and accuracy of the proposed methodology.The findings and solutions of this study contribute to the further development of industrial applications and devices typically include micropolar-thermoelastic materials.

A New BEM for Fractional Nonlinear Generalized Porothermoelastic Wave Propagation Problems

The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependent functionally graded anisotropic(FGA)structures.The system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity,fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous structures.Therefore,an efficient boundary element method(BEM)has been proposed to overcome this difficulty,where,the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the Cartesian transformation method(CTM).The generalized modified shift-splitting(GMSS)iteration method was used to solve the linear systems resulting from BEM,also,GMSS reduces the iterations number and CPU execution time of computations.The numerical findings show the effects of fractional order parameter,anisotropy and functionally graded material on the nonlinear porothermoelastic stress waves.The numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.

A New BEM Modeling Algorithm for Size-Dependent Thermopiezoelectric Problems in Smart Nanostructures

The main objective of this paper is to introduce a new theory called size-dependent thermopiezoelectricity for smart nanostructures.The proposed theory includes the combination of thermoelastic and piezoelectric influences which enable us to describe the deformation and mechanical behaviors of smart nanostructures subjected to thermal,and piezoelectric loadings.Because of difficulty of experimental research problems associated with the proposed theory.Therefore,we propose a new boundary element method(BEM)formulation and algorithm for the solution of such problems,which involve temperatures,normal heat fluxes,displacements,couple-tractions,rotations,force-tractions,electric displacement,and normal electric displacement as primary variables within the BEM formulation.The computational performance of the proposed methodology has been demonstrated by using the generalized modified shift-splitting(GMSS)iteration method to solve the linear systems resulting from the BEM discretization.GMSS advantages are investigated and compared with other iterative methods.The numerical results are depicted graphically to show the size-dependent effects of thermopiezoelectricity,thermoelasticity,piezoelectricity,and elasticity theories of nanostructures.The numerical results also show the effects of the sizedependent and piezoelectric on the displacement components.The validity,efficiency and accuracy of the proposed BEM formulation and algorithm have been demonstrated.The findings of the current study contribute to the further development of technological and industrial applications of smart nanostructures.