A.H. Akbarzadeh

Snapping Mechanical Metamaterials under Tension

A snapping mechanical metamaterial is designed, which exhibits a sequential snap-through behavior under tension. The tensile response of this mechanical metamaterial can be altered by tuning the architecture of the snapping segments to achieve a range of nonlinear mechanical responses, including monotonic, S-shaped, plateau, and non-monotonic snap-through behavior.

THERMOPIEZOELECTRIC ANALYSIS OF A FUNCTIONALLY GRADED PIEZOELECTRIC MEDIUM

The thermopiezoelectrical behavior of a functionally graded piezoelectric medium (FGPM) is investigated in the present work. For the special case, the dynamic response of an FGPM rod excited by a moving heat source is studied. The material properties of the FGPM rod are assumed to vary exponentially through the length, except for specific heat and thermal relaxation time which are held constant for simplicity. The governing differential equations in terms of displacement, temperature, and electric potential are obtained in a general form that includes coupled and uncoupled thermoelasticity. The coupled formulation considers classical thermoelasticity as well as generalized thermoelasticity. Employing the Laplace transform and successive decoupling method, unknowns are given in the Laplace domain. Employing a numerical Laplace inversion method, the solutions are gained in the time domain. Numerical examples for the transient response of the FGPM rod are displayed to clarify the differences among the result...

The thermo-electromagnetoelastic behavior of a rotating functionally graded piezoelectric cylinder

In this paper, the dynamic response of a rotating radially polarized functionally graded piezoelectric hollow cylinder is investigated. The cylinder is placed in a constant magnetic field and subjected to a thermo-electro-mechanical loading. All material properties are taken to follow a power law along the radial direction of the cylinder. The temperature distribution through the thickness of the cylinder is obtained by solving the heat conduction equation. The two coupled differential equations in terms of the displacement and electric potential accounting for the effects of the thermal and magnetic fields are solved directly. Numerical examples of the analytical results are given to illustrate the effects of non-homogeneity parameter, angular velocity, temperature gradient, magnetic field, and different boundary conditions on the thermo-electromagnetoelastic behavior of the hollow cylinder. The results in the absence of the thermo-magnetic loading are verified with those reported in the literature.

Coupled thermopiezoelectric behaviour of a one- dimensional functionally graded piezoelectric medium based on C-T theory

In this article, the transient thermopiezoelectric behaviour of a one-dimensional (1D) functionally graded piezoelectric medium subjected to a moving heat source is investigated. The formulation is given based on the Chandrasekhariah and Tzou (C–T) generalized thermoelasticity theory to consider the details of energy transport in the material in comparison with the Lord–Shulman (L–S) generalized theory. All material properties are taken to vary exponentially along the length of the medium except for phase lags, the relaxation time, and the specific heat, which are taken to be constant. The governing partial differential equations are given in the three coupled fields of displacement, temperature, and electric potential based on the C–T theory. Using Laplace transform to eliminate the time dependency of the problem, an analytical method is presented to obtain the coupled fields in the Laplace domain. The solutions are then derived in time domain by employing the fast Laplace inversion technique. Numerical results are shown to display the effects of discontinuities on the temperature and stress distribution, non-homogeneity index and the phase-lag constants of heat flux and temperature gradient on the wave propagation of temperature and stress fields based on the dual-phase-lag model of the C–T. Furthermore, the results are compared between the C–T and L–S thermoelasticity theories. Finally, the results are validated with those reported in the literature.

Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading

In this paper, the magnetoelectroelastic responses of radially polarized and magnetized hollow and solid magnetoelectroelastic cylinders subjected to hygrothermal loading are obtained by a straightforward analytical method. The transversely isotropic and homogeneous cylinders are embedded with a Winkler-type elastic foundation on the inner and/or outer surfaces. The cylinders are assumed to be infinitely long. To obtain the temperature and moisture concentration distributions within the thicknesses of the cylinders, the steady state, axisymmetric heat conduction and moisture diffusion equations are solved. For uniform temperature and moisture concentration rise, the temperature and moisture dependence of the elastic stiffness coefficients are considered in the analysis. The coupled ordinary differential equations in terms of displacement, electric potential and magnetic potential are solved exactly by the successive decoupling method. Numerical results are shown to clarify the effects of hygrothermal loading, elastic foundation and temperature and moisture dependence of the elastic coefficients on the magnetoelectroelastic behavior of the cylinders. The results for magnetic, electrical and mechanical loadings are verified by those available in the literature.

Mechanical behaviour of functionally graded plates under static and dynamic loading

This article presents an analytical solution for the mechanical behaviour of rectangular plates made of functionally graded materials (FGMs) based on the first-order shear deformation theory (FSDT) and the third-order shear deformation theory (TSDT). The FGM plate is assumed to be graded across the thickness. The material properties of the FGM plate are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituent materials, except Poissons ratio, which is assumed to be constant. The plate is subjected to a lateral mechanical load on its upper surface. The equations of motion are written based on displacement fields. The partial differential equations have been solved by the Fourier series expansion. Using the Laplace transform, unknown variables are obtained in the Laplace domain. The resulting formulations enable one to perform the static, dynamic, and free vibration analysis for both FSDT and TSDT plates. Employing the analytical Laplace inversion method and numerical time integration technique based on the Newmark method, time function solution of the problem is obtained and the unknown parameters are derived for a dynamic loading situation. Finally, the natural frequencies of the plate are obtained and dynamic responses are presented in the form of combinations of different frequencies. The results are verified with those reported in the literature.

Thermo-Magneto-Electro-Elastic Responses of Rotating Hollow Cylinders

Analytical solutions are obtained for multiphysical responses of a functionally graded, thermomagnetoelastic, rotating hollow cylinder as well as a homogeneous orthotropic thermo-magnetoelectroelastic cylinder. The cylinders are subjected to a combination of thermo-magneto-electro-mechanical loading. The material properties of the functionally graded hollow cylinder are assumed to obey a power law along the radial direction. The coupled differential equations are solved in an exact form using the successive decoupling method. Numerical results are displayed to clarify the effects of the temperature gradient, angular velocity, magneto-electro-mechanical boundary conditions, and non-homogeneity. Finally, the results are verified with those reported in the literature.

Static Analysis of Functionally Graded Piezoelectric Beams under Thermo-Electro-Mechanical Loads

This paper presents the analysis of static bending of beams made of functionally graded piezoelectric materials (FGPMs) under a combined thermo-electro-mechanical load. The Euler Bernoulli theory (EBT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) were employed to compare the accuracy and the reliability of each theory in applications. The material properties vary continuously through the thickness direction. The material compositions were selected from the PZT family. The governing equations were derived from Hamiltons principle and solved using the finite element method and Fourier series method. Cubic Hermit interpolation shape function was used for estimating the transverse deflection, and the linear interpolation function was used for the axial displacement and the shear rotation as well. Fourier series expansion, based on the boundary conditions, were employed to solve the governing equations analytically. The accuracy of the method was validated by comparing the results with the previous studies. Finite element results were compared with the analytical results presented in this paper. A comprehensive parametric study is conducted to show the influence of the voltage, shear deformation, material composition, end supports, and the slenderness ratio on the thermo-electro-mechanical characteristic.

Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys

The present paper deals with the nonlinear thermal instability of geometrically imperfect sandwich cylindrical shells under uniform heating. The sandwich shells are made of a shape memory alloy (SMA)-fiber-reinforced composite and functionally graded (FG) face sheets (FG/SMA/FG). The Brinson phenomenological model is used to express the constitutive characteristics of SMA fibers. The governing equations are established within the framework of the third-order shear deformation shell theory by taking into account the von Karman geometrical nonlinearity and initial imperfection. The material properties of constituents are assumed to be temperature dependent. The Galerkin technique is utilized to derive expressions of the bifurcation points and bifurcation paths of the sandwich cylindrical shells. Using the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of the SMA fiber volume fraction, SMA pre-strain, core thickness, non-homogeneity index, geometrical imperfection, geometry parameters of sandwich shells and temperature dependency of materials on the stability of shells. The results reveal that proper application of SMA fibers postpones the thermal bifurcation point and dramatically decreases thermal post-buckling deflection. Moreover, the induced tensile recovery stress of SMA fibers could also stabilize the geometrically imperfect shells during the inverse martensite phase transformation.

DUAL PHASE LAG HEAT CONDUCTION IN FUNCTIONALLY GRADED HOLLOW SPHERES

In the present work, the dual phase lag heat conduction in functionally graded hollow spheres is investigated under spherically symmetric and axisymmetric thermal loading. The heat conduction equation is given based on the dual phase lag theory to consider the details of energy transport in the material in comparison with the non-Fourier hyperbolic heat conduction. All the material properties of the sphere are taken to vary continuously along the radial direction following a power-law with arbitrary non-homogeneity indices except the phase lags which are assumed to be constant for simplicity. The specified spherically symmetric and axisymmetric boundary conditions of the sphere lead to a 1D and 2D heat conduction problem, respectively. Employing the Laplace transform to eliminate the time dependency of the problem, analytical solutions are obtained for the temperature and heat flux. The final results in the time domain are obtained by a numerical Laplace inversion method. The speed of thermal wave in the functionally graded sphere based on the dual phase lag is compared with that of the hyperbolic heat conduction. Furthermore, the numerical results are shown to clarify the effects of phase lags and non-homogeneity indices on the thermal response. The current results are verified with those reported in the literature.