Journal of Solid Mechanics
Volume:12 Issue: 1, Winter 2020

This study is limited to study of buckling analysis of a sandwich cylindrical shell with functionally graded face sheets and homogenous core. High-order sandwich plate theory is improved by considering the in-plane stresses of the core that usually are ignored in the analysis of sandwich structures. Assume that all properties of the face sheets and the core are temperature dependent. Strain components are obtained by using the nonlinear Von-Karman type relations. The equilibrium equations are derived via principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich conical shells with functionally graded face sheets under axial in-plane compressive loads and in the temperature environments is performed by using Navier’s solution. The results show the critical dimensionless static axial loads are affected by the configurations of the constituent materials, compositional profile variations, temperature and the variation of the sandwich geometry. The comparisons show that the present results are in the good agreement with the numerical results.

In this paper, vibration analysis of rotary tapered axially functionally graded (AFG) Timoshenko nanobeam is investigated in a thermal environment based on nonlocal theory. The governing equations of motion and the related boundary conditions are derived by means of Hamilton’s principle based on the first order shear deformation theory of beams. The solution method is considered using generalized differential quadrature element (GDQE) method. The accuracy of results are validated by other results reported in other references. The effect of various parameters such as AFG index, rate of cross section change, angular velocity, size effect and boundary conditions on natural frequencies are discussed comprehensively. The results show that with increasing angular velocity, non-dimensional frequency is increased and it depends on size effect parameter. Also, in the zero angular velocity, it can be seen with increasing AFG index, the frequencies are reducing, but in non-zero angular velocity, AFG index shows complex behavior on frequency.

The effects of flexoelectricity on thermo-electro-mechanical behavior of a functionally graded electro-piezo-flexoelectric nano-plate are investigated in this paper using flexoelectric modified and the Kirchhoff classic theories. Moreover, using the variation method and the principle of minimum potential energy for the first time, the coupled governing nonlinear differential equations of the nano-plate and their associated boundary conditions are obtained.  The functionally graded nano-plate is modeled using a power law equation along the plate thickness direction. The nano-plate behavior is analyzed under mechanical, electrical, and thermal loadings with different boundary conditions. It should be noted that the direct and reverse flexoelectric effects under different loading conditions were investigated.  Finally, the important quantities such as: the nano-plate deflection, the induced electrical voltage for different values of the length parameter, the power index related to the functionally graded behavior model and the geometric ratio parameter are determined. The results indicate that in the presence of flexoelectricity, the rigidity of the nano-plate increases. Also, the deflection and the generated electric potential along nano-plate thickness decreases. Finally, induced polarization decreases as a linear temperature variation is applied on the nano-plate.

In this article, the time-dependent stress redistribution analysis of magneto-electro-elastic (MEE) thick-walled sphere subjected to mechanical, electrical, magnetic and uniform temperature gradient as well as moisture concentration gradient is presented. Combining constitutive equations of MEE with stress-strain relations as well as strain-displacement relations results in obtaining a differential equation in which there are the creep strains. At the first step, discounting creep strains in the mentioned equation, an analytical solution for the hygro-thermo-magneto-electro-elastic behavior is achieved at the initial state. After that, the creep stress rates can be achieved by keeping only the creep strains in the differential equation for the steady-state condition. The analysis is done by applying the Prandtl-Reuss equations as well as Norton’s law in creep behavior modeling. Finally, the history of stresses, displacement as well as magnetic and potential field, at any time, is achieved using an iterative method. Results show that the increase in tensile hoop stress resulted from creep progress must be considered in design progress. Also, the effect of hygrothermal loading is more extensive after creep evolution.

An approach of Green’s function is adopted to solve the inhomogeneous linear differential equations representing wave equations in piezo-composite materials. In particular, transference of horizontally polarised shear (SH) waves is considered in bedded structure comprising of porous-piezo electric layer lying over a heterogeneous half-space. Propagation of SH-waves is considered to be influenced by point source, situated in the heterogeneous substrate. A closed form analytical solution is obtained to establish the dispersion relation. Remarkable influence of different parameters (like elastic constant, piezoelectric constant, heterogeneity parameter, initial stress and layers thickness) on the phase and group velocity are shown graphically. Moreover, a special case of present study is shown by replacing the porous piezoelectric material with piezoelectric material. Some numerical examples are illustrated by taking the material constants of Lead Zirconate Titanate (PZT-1, PZT-5H and PZT-7) for the porous piezoelectric layer where the phase velocity of SH waves is high rather than that of piezoelectric layer.

In this study, the mechanical and thermal behavior of the nano-reinforced polymer composite reinforced by Montmorillonite (MMT) nanoparticles is investigated. Due to low cost of computations, the 3D representative volume elements (RVE) method is utilized using ABAQUS finite element commercial software. Low density poly ethylene (LDPE) and MMT are used as matrix and nanoparticle material, respectively. By using various geometric shapes and weight fractions of nanoparticle, the mechanical and thermal properties such as Young’s modulus, shear modulus, heat expansion coefficient and heat transfer coefficient are studied. Due to addressing the properties of interfacial zone between the matrix and nanoparticle, finite element modeling is conducted in two ways, namely, perfect bonding and cohesive zone. The results are validated by comparing with experimental results reported in literature and a reasonable agreement was observed. The prediction function for Young’s modulus is presented by employing Genetic Algorithm (GA) method. Also, Kerner and Paul approaches as theoretical models are used to calculate the Young’s modulus. It was finally concluded that the magnitude of the Young’s and shear modules increase by adding MMT nanoparticles. Furthermore, increment of MMT nanoparticles to polymer matrix nanocomposite decrease the heat expansion and heat transfer coefficients.

This paper investigates the moments and stress resultants from infinite FG laminates with different polygonal cutouts subject to uniaxial tensile load. The analytical solution used for the calculation of stress resultants and moments is the basis of the complex-variable method and conformal mapping function. The impact of various factors, namely cutout orientation angle, cutout aspect ratio as well as the cutout corner curve on stress distribution and moment resultants is studied. The effect of the aforementioned parameters around triangular, square, pentagonal and hexagonal cutout is analyzed. The mechanical characteristics of the graded plates are hypothesized to vary throughout the thickness exponentially. Finite element numerical solution is employed to examine the results of the present analytical solution. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes.

Dynamic behaviour of nonlinear free vibration of circular plate resting on two-parameters foundation is studied. The governing ordinary differential equation is solved analytically using hybrid Laplace Adomian decomposition method. The analytical solutions obtained are verified with existing results in literature. The analytical solutions are used to determine the influence of elastic foundation, radial and circumferential stress on natural frequency of the plate. Also, the radial and circumferential stress determined. From the results, it is observed that, increase in elastic foundation parameter increases the natural frequency of the plate. It is recorded that the modal radial and circumferential stress affect the extrema mode of the plate. It is hoped that the present study will contribute to the existing knowledge in the field of vibration analysis of engineering structures.

This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth order partial differential equations that govern the vibration of rotating SWCNTs are derived. To obtain the natural frequency and dynamic response of the nanorotor system, the equation of motion for the rotating SWCNTs are solved. It is found that there are two frequencies in the frequency spectrum. The positive rootintroduced as forward whirling mode, while the negative root represents backward whirling mode. The detailed mathematical derivations are presented while the emphasis is placed on investigating the effect of the several parameters such as, tube radius, angular velocity and small scale parameter on the vibration behavior of rotating nanotubes. It is explicitly shown that the vibration of a spinning nanotube is significantly influenced by these effects. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed. To the knowledge of authors, the vibration of rotating SWCNTs considering gyroscopic effect has not investigated analytically yet and then the results generated herein can be served as a benchmark for future works.

The surface tooth wear which occurs at the gear contact region due to inadequate contact strength of the tooth is one of the predominant modes of gear failures. Currently, higher contact ratio spur gears are increasingly used in power transmission applications such as aircraft, wind turbine, automobiles and compact tracked vehicles due to their high load carrying capacity.  In this work, the direct design is found to be one of the efficient gear design methods to reduce the tooth surface wear on high contact ratio asymmetric spur gears. Asymmetric gear tooth is defined as one whose tooth geometry of the drive and coast sides is not symmetric. Asymmetry between tooth sides is achieved by providing two different pressure angles at the respective coast and drive side pitch circles. The area of existence diagrams for normal and high contact ratio gears have been developed to select suitable design solution with the given variables of gear ratio, contact ratio and teeth number. The contact load capacity, wear resistance, power losses and mechanical efficiency have also been deduced for directly designing normal and high contact ratio asymmetric spur gears.

In this research paper, the formulation of a new three-dimensional sector element based on the strain approach is presented for plate bending problems and linear static analysis of circular structures. The proposed element has the three essential external degrees of freedom (Ur, Vθ and W) at each of the eight corner nodes. The displacements field of the present element is based on assumed functions for the different strains satisfying the compatibility equations. The effectiveness of the present element is applied through several tests related to plate bending problems and linear static analysis of circular structures. The results of the developed element have been compared with analytical and other numerical solutions available in the literature. The obtained results show the excellent performances and precision of the present element. It is found that the new three-dimensional sector element is more accurate and efficient than the three-dimensional classical element based on displacement approach.

In this article, the vibration and dynamic response of an orthotropic composite cylindrical shell under thermal shock loading and thermal field have been investigated. The problem is that the shell is initially located at a first temperature, and some tension caused by a mild heat field is created, then the surface temperature of the cylinder suddenly increases. The partial derivative equations of motion are in the form of couplings with the heat equations. First, the equations of motion are derived by the Hamilton principle, here first-order shear theory and considering strain-shift relations of Sanders are used. Then, the equation system including the equations of motion and energy equations by the Runge–Kutta fourth-order methodare solved. In this study, the effects of length, temperature, thickness and radius parameters on natural frequencies and intermediate layer displacement are investigated. The results show that the increase in external temperature decreases the natural frequency and increases the displacement of the system. Also, the results of radial transitions were evaluated with previous studies and it was found that it is in good agreement with the results of previous papers.

In this work, the nonlocal elastic waves in a fluid conveying armchair thermo elastic single walled carbon nanotube under moving harmonic load is studied using Eringen nonlocal elasticity theory via Euler Bernoulli beam equation. The governing equations that contains partial differential equations for single walled carbon nanotube is derived by considering thermal and Lorenz magnetic force. The small scale interactions induced by the nano tubes are simulated by the non-local effects. The time domain responses are obtained by using both modal super position method and Newmarks’s direct integration method.  The effect of nonlocal parameter, thermal load, magnetic field of the moving harmonic load on the dynamic displacement of SWCNT is discussed. The results obtained show that the dynamic displacement of fluid conveying SWCNT ratio is significantly affected by the load velocity and the excitation frequency. This type of results presented here, will provide useful information for researchers in structural nano science to understand the small scale response of elastic waves coupled with thermo elasticity and some field forces.

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel function we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. Both the two contact stresses under the punch and on the lower face of the layer are expressed as appropriate Chebyshev series. The effects of the radius of the disc with the rigid base and the layer thickness on the displacements, contact stresses as well as the shear stress and the stress singularity factor are discussed. A numerical application is also considered with some concluding results.

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cross-sections composed of non homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the polygonal plate using Fourier expansion collocation method. The complex roots of the frequency equations are obtained by secant method. The numerical computations are carried out for triangular, square, pentagon and hexagon cross sectional plates. Graphical representation is given for the various physical variables via gravity and different edge boundaries and its characteristics are discussed. This result can be applied for optimum design of concrete plates with polygonal cross sections.

A fuel cell is an electro-chemical tool capable of converting chemical energy into electricity. High operating temperature of solid oxide fuel cell, between 700oC to 1000oC, causes thermal stress. Thermal stress causes gas escape, structure variability and cease operation of the SOFC before its lifetime.The purpose of the current paper is to present a method that predicts the thermal stress distribution in an anisotropic porous anode of planar SOFC. The coupled governing non-linear differential equations, heat transfer, fluid flow, mass transfer, mass continuity, and momentum are solved numerically. A code based on computational fluid dynamics (CFD), computational structural mechanics and finite element method (FEM) is developed and utilized. The code uses the generated data inside the porous anode in order to detect the temperature and the stress distribution using the Darcy’s law and the Navier-Stokes equations. The numerical results used to govern the areas of high values of stresses were higher than the yield strength of materials. The results show that a highest thermal stress occurs at lower corners of the anode. The concentrated temperature occurs at the middle of the electrolyte-anode whereas the maximum pressure occurs at the middle of the upper and lower section of the anode.