فهرست مطالب
Journal of Applied and Computational Mechanics
Volume:7 Issue: 4, Autumn 2021
 تاریخ انتشار: 1400/07/28
 تعداد عناوین: 30


Pages 18621877In this article, the thermal buckling behavior of orthotropic circular bilayer graphene sheets embedded in the Winkler–Pasternak elastic medium is scrutinized. Using the nonlocal elasticity theory, the bilayer graphene sheets are modeled as a nonlocal double–layered plate that contains small scale effects and van der Waals (vdW) interaction forces. The vdW interaction forces between the layers are simulated as a set of linear springs using the Lennard–Jones potential model. Using the principle of virtual work, the set of equilibrium equations are obtained based on the firstorder shear deformation theory (FSDT) and nonlocal differential constitutive relation of Eringen. Differential quadrature method (DQM) is employed to solve the governing equations for simplysupported and clamped boundary conditions. Finally, the effects of the small scale parameter, vdW forces, aspect ratio, elastic foundation, and boundary conditions are considered in detail.Keywords: Thermal buckling, Bilayer graphene sheets, elastic medium, Nonlocal elasticity, van der Waals forces, Firstorder shear deformation theory, Differential quadrature method

Pages 18781891In this paper, the nonlinear forced vibration of isotropic viscoelastic/ piezoelectric EulerBernoulli nanobeam is investigated. For this purpose, the consistent couple stress theory is utilized for modeling the viscoelastic/piezoelectric nanobeam. Hamilton’s principle is also employed to obtain the governing equations of motion. Further, the Galerkin method is used in order to convert the governing partial differential equations to a nonlinear secondorder ordinary differential one, and then multiple scale method is used to solve motion equation.Keywords: Nonlinear forced vibration, Piezoelectric, Viscoelastic, Consistent couple stress theory, Multiple scale method

Pages 18921906The current paper aims to explain the peristaltic mechanism of a Bingham fluid with varying viscosity. The fluid is considered to flow within a porous medium and subjected to a magnetic field with significant inclination. Heat transfer characteristics are studied with convective conditions and variable thermal conductivity. The solution is obtained by the perturbation technique, where small values of variable liquid properties are utilized. The graphs plotted indicate that variation in viscosity as well as thermal conductivity actively contribute to reduce the pressure gradient. Further, for a higher radius of the plug flow region, a higher pressure rise occurs. The magnetic parameter and Grashof number influence the trapping phenomenon by reducing the dimensions of the bolus.Keywords: Biot number, Darcy number, Grashof number, Inclined magnetic field, Plug flow

Pages 19071915Recently, the application of porous bionanocomposites has been considered by many researchers for orthopedic application. Since experimental tests for obtaining the mechanical and physical properties of these nanostructured biomaterials are very expensive and timeconsuming, it is highly recommended to model and simulate these bionanoscale materials to predict their mechanical and physical properties. In this study, threephase porous bionanocomposite membranes were fabricated with Titanium oxide (TiO2), Hydroxyapatite (HA) and Polycaprolactone (PCL) polymer. HA and TiO2 are both biocompatible and biodegradable. The samples were fabricated with various amounts of titanium oxide and the materials characterization has been performed on selected sample. The molecular dynamics technique (MD) have been used to predict the mechanical performance of the nanocomposite models. The MD simulations were performed for single phase material and the developed for two phases equivalent components as a new approach in using MD simulation results. The results indicated the close relationship between the experimental data and simulation values for the selected sample. Moreover, phase and morphology of these nanostructures have been investigated using SEM results. Therefore, based on the proposed approach, MD simulation can be applicable for predicting the properties of porous bionanocomposite membrane.Keywords: Molecular dynamics, Polycaprolactone, Hydroxyapatite, Mechanical performance, Nanocomposite membrane

Pages 19161924An important equation usually used in modeling neuronal dynamics is cable equation. In this work, a numerical method for the fractional cable equation which involves two RiemannLiouville fractional derivatives is proposed. Our computational technique is based on collocation idea where a combination of Bernoulli polynomials and Sinc functions are used to approximate the solution to this problem. The constructed approximation by our method convert the fractional cable equation into a set of algebraic equations. Also, we provide two numerical examples to confirm the accuracy and effectiveness of the present method.Keywords: Fractional cable equation, Bernoulli polynomials, RiemannLiouville fractional derivative, Sinc function, Numerical solution

Pages 19251930
In this paper, the influence of the transverse magnetic field is unraveled on the development of steady flow regime for an incompressible fluid in the boundary layer limit of a semiinfinite vertical plate. The sensitivity of real fluids to changes in temperature suggests a variable thermal conductivity modeling approach. Using appropriate similarity variables, solutions to the governing nonlinear partial differential equations are obtained by numerical integration. The approach used here is based on using the shooting method together with the RungeKuttaFehlberg integration scheme. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skinfriction coefficient and the rate of heat transfer are also calculated for different parameter values. Pertinent results are displayed graphically and discussed. It is found that the heat transfer rate improves with an upsurge in a magnetic field but lessens with an elevation in the fluid thermal conductivity.
Keywords: MHD, Blasius flow, variable thermal conductivity, heat transfer 
Pages 19311943Forcedconvection heat transfer of pure airfluid inside an open channel as a section of a shellandtube heat exchanger is evaluated numerically. Sshaped obstacles are used in the mentioned channel. Airflow inside the channel is considered as a turbulence flow. Governing equations are solved throughout the computational Finite Volume Method (FVM). These equations are analyzed using the standard kε model. The results are designed based on the geometry of Sshaped obstacles. Mentioned results are shown in the form of turbulent kinetic energy (k), turbulent intensity (TI), turbulent viscosity (μt), temperature (T), Nusselt numbers (Nux local, and Nu average), friction coefficients (Cf local, and f average), and the thermal aerodynamic performance factor (TEF), for a Reynolds number (Re) of 12,000 to 32,000. This type of analysis is very useful in many industries and engineeringrelated problems for getting a good idea about the physical model whenever the analytic solution is out of reach.Keywords: Shellandtube heat exchanger, Thermal performance, Fluid mechanics, Turbulent Flow, Numerical simulation

Pages 19441955In this work, turbulent indoor airflow was considered by Large Eddy Simulation (LES) based on Multi Relaxation Time Lattice Boltzmann Method (MRTLBM). The Lagrangian approach was utilized to investigate the effect of inlet air location on transport and concentration of different sizes of particles (110 µm) in a modeled room. Simulation results showed that for the displacement ventilation system with the inlet air register on the floor, the number of 10µm particles that exit through the outlet is more than the case for the mixing ventilation system with the inlet register on the ceiling. Also, for the latter case, when the inlet air is on the ceiling, the number of suspended 10µm particles in the room is less than for the displacement ventilation system with inlet register on the floor. In addition, the results showed that the location of the inlet air register does not have a considerable effect on the small 1µm particle motion, and the numbers of the particles that remain suspended in the room are roughly the same for both ventilation systems.Keywords: MRTLBM, LES, Particle motion, Inlet air position, Particle concentration

Pages 19561963Nowadays, researches on different kinds of renewable energies including photovoltaic technology are developing rapidly. It is proved that the output power of a PV cell is reduced by increasing the temperature. In this paper, mounting aluminum fins at the back surface of the PV module is proposed as a simple and lowcost method to decrease the PV cell temperature. It was found that using aluminum fins caused more than 7°C reduction in the cell temperature. Besides, it was shown that the entropy generation of the PV module with fin, was 3.5% lower than the conventional one. Also, the positive environmental impacts of using fins at the back surface of the PV module were estimated by RETScreen software, so that it, leads to enhance the performance of the PV power plant by more than 25 %, from an environmental viewpoint.Keywords: Photovoltaic, Entropy, Environmental impacts, Fin

Pages 19641972The significance of inconstant gravity force and uniform throughflow on the start of convective movement in an anisotropic porous matrix is investigated numerically utilizing largeterm Galerkin procedure. The porous layer is acted to uniform upright throughflow and inconstant downward gravitational force which changes with the height from the layer. In this study, two types of gravity field digression were examined: (a) linear and (b) parabolic. It is found that the throughflow parameter Pe, the thermal anisotropy parameter η and gravity deviation parameter λ postpone the beginning of convective activity, whereas the mechanical anisotropy parameter ξ rapids the onset of convective activity. The dimension of the convection cells enhances on enhancing the thermal anisotropy parameter η, the mechanical anisotropy parameter ξ and gravity deviation parameter λ while, the throughflow parameter Pe decreases the extent of the convective cells. It is also noted that the structure with linear variation of gravity force is more stable.Keywords: Convective instability, Throughflow, Inconstant gravity, Anisotropic porous medium

Pages 19731986The magnetoconvection influenced by a gyrotactic behavior of algal suspensions along with rotation in the nanoliquid layer is investigated. Linear theory based on normal mode analysis is used to find out the inquisitive results of the problem for rigidfree and rigidrigid boundaries. Both Galerkinmethod (Number of terms (N) > 6) and shooting method (by taking forcing condition) are utilized to find the critical value of the Rayleigh number (both thermal and bio) in case of nonoscillatory stability. Both thermal and bio Rayleigh numbers are dependent on each other, thus advance or delay the convection. Rotation and magnetic field slow down the convective motion of microorganisms across the layer and destabilizes the system.Keywords: Microorganism, Bioconvection, Nanofluid, Rayleigh number, Galerkin method, Shooting method

Pages 19871998In this research study, the numerical Galerkin Finite Element Method (GFEM) is used for forced laminar convection heat transfer of Cuwater nanofluid in a divergent wavy channel including a rotating cylinder turbulator. The above boundary of the channel is in low temperatures and the bottom boundary is in hot temperatures as well as the cylinder wall temperature. It is assumed that the cylinder rotates in the cavity and makes vortexes to enhance heat transfers. The dimensionless governing equations including velocity, pressure, and temperature formulation are solved by the Galerkin finite element method. The results are discussed based on the governing factors such as nanoparticle volume fraction, Reynolds number, cylinder diameter and rotating velocity. As a main result, among the all studied parameters (Re, u, Φ and r), increasing the Re number has the most effect on heat transfer which has 4.8 and 1.6 Average Nu for the cylinder wall and wavy wall, respectively.Keywords: Turbulator, Nusselt number, Forced Convection, Nanofluid, GFEM

Pages 19992009Theoretical investigation of variable mass diffusivity, thermal conductivity, and viscosity on unsteady squeezed flow of dissipative Casson fluid is presented. Physically, for any effective heat and mass transfer process, a proper account of thermophysical properties in such a system is required to attain the desired production output. The magnetized free convective flow of unsteady Casson fluid encompassing Joule dissipation, radiation, and chemical reactive influence is induced as a result of squeezing property. The governing model assisting the magnetized flow is formulated and transformed via an appropriate similarity transformation. The resulting set of ordinary differential equations is solved numerically using Chebyshev based Collocation Approach (CCA). However, variable viscosity, thermal conductivity, and mass diffusivity effects are seen to diminish the fluid flow velocities, temperature, and concentration respectively along with the lower plate. Heat and mass transfer coefficient, skin friction downsized to an increasing value of variable thermal and mass diffusivity parameters while variable viscosity pronounces the skin friction coefficient. Furthermore, the present analysis is applicable in polymer processing, such as injection molding, extrusion, thermoforming among others.Keywords: Casson Fluid, Chebyshev Collocation Method, Squeezing flow, MHD, Thermophysical properties

Pages 20102023A computational analysis on waterAl2O3 nanofluid turbulent forced convection is performed to analyze heat transfer and entropy production in a channel containing heated blocks, cooled by impinging jets. The two phase mixture model (TPMM) is used. The increase in the Reynolds number (Re) and the volume fraction of nanoparticles (φ), the decrease in spacing between the heated block (Db) and moving the location of the second jet (J2) to the first jet (J1) contribute to increasing the heat transfer rate (HTR).In addition, the TPMM gives higher values of average Nusselt number (Nu) ̅ than the singlephase model (SPM). The thermal (𝑆𝑔̇ ,𝑡ℎ), frictional (𝑆𝑔̇ ,𝜈) and total (𝑆𝑔̇ ,𝑡) entropy generation values increase with Re and φ. When Db is reduced, 𝑆𝑔̇,𝑡 increases. However, 𝑆𝑔̇ ,𝑡 increases when the jet position vary from J2 to J1. Different correlations are proposed for Nu ̅. Our results are compared with data available in the literature.Keywords: heat transfer, Turbulent Flow, Entropy generation, Nanofluid, impinging jets, heated blocks

Pages 20242039A study on the effects of gyrotactic microorganism and nanoparticles in the bioconvection magnetohydrodynamic flow of Casson fluid at the nonlinear stretching boundary is investigated. Irregular heat source/sink, Joule and viscous dissipations, Brownian motion, and thermophoresis are included in the energy equation. The model outlining the flow system is nondimensionalised and retained in the same form. The equations are worked out by pairing, i.e. first pair momentum and gyrotactic microorganism density equation and second pair energy and nanoparticle concentration equation. This technique is termed as a paired quasilinearisation method (PQLM). Convergence and accuracy of PQLM are shown. Obtained numerical results are depicted in graphs in order to observe further insight into the flow pattern. Interesting aspects of various controlling parameters in flow, heat, nanoparticle concentration and microorganism density are discussed.Keywords: Casson Nanofluid, Magnetic field, Nonlinear stretching sheet, Gyrotactic microorganism, Paired quasilinearisation method

Pages 20402048The effects of viscous dissipation, chemical reaction and activation energy on the twodimensional hydromagnetic convective heat and mass transfer flow of a Casson nanofluid fluid over a stretching sheet with thermal radiation, have been discussed in detail. The formulated highly nonlinear equations for the abovementioned flow are converted into firstorder ordinary differential equations (ODEs). The shooting method along with AdamsBash forth Moulton method is used to solve the BVP by using the Fortran language program. The numerical results are computed by choosing different values of the involved physical parameters and compared with earlier published results and excellent validation of the present numerical results has been achieved for local Nusselt number and local Sherwood number. The graphical numerical results of different physical quantities of interest are presented to analyze their dynamics under the varying physical quantities. From the results, it has been remarked that the heat transfer rate escalates for the large values of radiation parameter, viscous dissipation for the Casson nanofluid.Keywords: Casson Nanofluid, Viscous dissipation, Chemical reaction, Brownian motion, Thermophoresis, stretching Sheet

Pages 20492063In this paper, the numerical manifold method (NMM) with a 9node quadrilateral element and a 10node triangular element is developed. Furthermore, complex Fourier shape functions are used to improve the 9node quadrilateral NMM. Also, the two approaches of higherorder NMM construction are compared, increasing the order of weight functions or local approximation ones; for this purpose, sixnode triangular and threenode triangular using secondorder and thirdorder NMM is used. For validation of the suggested method, one free vibration and two forced vibration numerical examples are assessed. The results show that the proposed methods are more accurate than conventional NMM. In addition, the superiority of complex Fourier shape functions compared to classical Lagrange ones in improving accuracy is perceived.Keywords: Numerical manifold method, Ninenode complex Fourier shape functions, Complex Fourier radial basis functions, Free vibrations, Forced vibrations, Tennode shape functions

Pages 20642083In this paper, laminar natural convection of copper/water nanofluid in an openended Lshaped cavity is investigated by Lattice Boltzmann Model (LBM). The results are compared by previous studies that are in good agreement. Influences of Rayleigh number (Ra = 103, 104, 105, 106), cavity aspect ratio (AR = 0.2, 0.4, 0.6) and volume concentration of Cu nanoparticles (0 ≤ Φ ≤ 0.1) on the momentum, thermal ﬁelds and heat transfer in the enclosure are studied. Also, the effect of changing the boundary conditions, on the heat transfer rate has been investigated. It is observed that maximum heat transfer enhancement by adding the nanoparticles for Ra = 106 with AR = 0.4 (32.76%) occurs. Results illustrate that increasing the cavity aspect ratio decreases heat transfer rate for Ra = 103 and Ra = 104. The least and most heat transfer rate for Ra = 105 occurs in enclosures by aspect ratios of 0.2 and 0.4 respectively, while it was observed at Ra = 106 for minimum and maximum rate of heat transfer the opposite behavior that at Ra = 105 occurs.Keywords: Lattice Boltzmann method, Natural convection, Nanofluid, Openended Lshaped cavity, Aspect ratio

Pages 20842095A major goal in the design of architected structures for low frequency vibration applications (also called mechanical metamaterials, metastructures, elastic metamaterials, auxetic structures) is the creation of regions in the frequency domain where vibration amplitudes are minimal, regardless of the source of excitation. The idea is to provide vibration suppression in manmade structures. The proposed effort is to examine approaches to produce straightforward methods of designing a given mechanical metamaterial to have a specified gap in the frequency spectrum by adjusting its local mass and stiffness values of the individual cells. Previous work in mechanical metamaterial design has focused on using optimization procedures concerned with global vibration suppression. Here our efforts are focused on frequency separation using two direct approaches by interpreting techniques from the areas of model updating and inverse eigenvalue solutions. Rather than examining the overall suppression of vibration, creating specific bandgaps eliminates the possibility of resonance occurring in a given range of excitation frequencies.Keywords: inverse eigenvalue problems, model updating, frequency separation, vibration suppression, metastructures

Pages 20962112Unsteady magnetohydrodynamic mixed convection flow of an incompressible hybrid nanofluid (CuAl2O3/water) past an isothermal cylinder with thermal radiation effect has been studied. Appropriate nondimensional variables are initiated to reduce the governing equations into a convenient form. By utilizing the procedure of finite difference, reduced equations are then solved for all time. Besides, series solutions are obtained using perturbation technique for short time and asymptotic method for long time which agree with the acquired numerical solution up to a good accuracy. When the mixed convection parameter Ri, radiation conduction parameter Rd, magnetic field parameter M and the volume fractions of nanoparticles ϕ1 and ϕ2 are increased, the local skin friction coefficient and the local Nusselt number are found to increase. Results revealed that the hybrid nanofluid (CuAl2O3/water) enhances the heat transfer about 28.28% in comparison to the Al2O3water nanofluid and about 51.15% than the pure fluid. Contrary to this, the heat transfer of hybrid nanofluid is augmented about 41.76% than the Cuwater nanofluid and 71.41% than the base fluid. The streamlines and isotherms reveal that higher values of Ri, M and Rd delay the boundary layer separation and accordingly shrink the vortices. Moreover, the thermal boundary layer is thickened for the increment of aforesaid quantities. The surface temperature parameter augments the local skin friction coefficient, however, the reverse characteristic is observed for the local Nusselt number.Keywords: Hybrid nanofluid, Mixed convection, Isothermal cylinder, Boundary layer separation, Thermal radiation

Pages 21132119An artificial Earth satellite with an electric charge and an intrinsic magnetic moment is considered. Due to the geomagnetic field, the satellite experiences the influence of the Lorentz and magnetic torques. To set the angular position of the satellite, we introduce natural coordinate system associated with the directions of geomagnetic induction vector and Lorentz force vector which is orthogonal both to the geomagnetic induction and relative velocity of the satellite. It is shown that such a natural magnetovelocity coordinate system is convenient for attitude stabilization of a satellite operating in the mode of scanning the Earth's surface. The properties of the trajectory of the satellite axis on the Earth's surface are analysed. The rotation tensor connecting the natural magnetovelocity and the orbital coordinate systems is obtained. The angular velocity of the natural magnetovelocity trihedron is found. Kinematic differential equations for the unit vectors of the natural magnetovelocity coordinate system are derived.Keywords: artificial Earth satellite, geomagnetic field, electric charge, intrinsic magnetic moment, attitude control

Pages 21202128We consider the motion of a magnetized satellitegyrostat in a circular orbit due to the combined influence of uniform gravity and magnetic fields. Based on the Lagrangian equations, the necessary conditions for the existence of regular precessions are determined in which the axis of precession is perpendicular to the orbital plane. All possible regular precessions and permanent rotations are determined and classified. We show the usage of Lagrange equations taking Eulerian angles as generalized coordinates for determining the regular precessions is more effective and accurate than utilization of EulerPoisson equations.Keywords: Satellite, Gyrostat, Principal axes, Regular precessions, Permanent rotations, Magnetic field

Pages 21292148This paper presents a methodology that allows the numerical simulation of realistic sea waves, called WaveMIMO methodology, which is based on the imposition of transient discrete data as prescribed velocity on a finite volume computational model developed in Fluent software. These transient data are obtained by using the spectral wave model TOMAWAC, where the wave spectrum is converted into a series of free surface elevations treated and processed as wave propagation velocities in the horizontal (x) and vertical (z) directions. The processed discrete transient data of wave propagation velocity are imposed as boundary conditions of a wave channel in Fluent, allowing the numerical simulation of irregular waves with realistic characteristics. From a case study that reproduces the sea state occurring on March 31st, 2014, in Ingleses Beach, in the city of Florianópolis, state of Santa Catarina, Brazil, it was concluded that the WaveMIMO methodology can properly reproduce realistic conditions of a sea state. In sequence, the proposed methodology was employed to numerically simulate the incidence of irregular realistic waves over an oscillating water column (OWC) wave energy converter (WEC). From these results, the WaveMIMO methodology has proved to be a promising technique to numerically analyze the fluiddynamic behavior of WECs subjected to irregular waves of realistic sea state on any coastal region where the device can be installed.Keywords: ocean waves, irregular waves, computational modeling, Fluent, TOMAWAC

Pages 21492158The fracture and size effect properties of the unidirectional (UD) laminae were investigated based on the fracture energy analysis. The crack propagations on inclined fiber orientation may result in different energy release mechanisms. Therefore, the size effect behavior of these types of failures may vary according to the fracture parameters of the UD composites. This study aims to develop a fracture analysis of UD plies with inclined fibers relative to the loading axis. A numerical work with a developed material model was conducted to predict the size effect trends. The size effect law was used to fit the strength reduction with increasing size. The fundamentals of the quasibrittle fracture mechanics are shown to be applicable to analyze these types of structures. It is shown that the composite structures as quasibrittle materials, can exhibit a significant size effect.Keywords: Size effect, fiber composite, quasibrittle fracture, inclined cracking

Pages 21592170In this paper, a highaccuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lamé system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes.Keywords: Elasticity problem with a crack, Weighted finite element method, body of optimal parameters

Pages 21712178The doubly salient permanent magnet generator (DSPMG) is widely known as an efficient machine for electrical production from renewable energy. In this paper, we aim to improve the output power of the DSPMG using a structural modification, which is targeted for lowspeed electrical generations. Structural parameters including the stator pole depth, thickness of permanent magnet, stator pole arc, and number of winding turns were adjusted, then an optimal value of those parameters was selected based on the characteristics of the generator tested during noload and onload conditions. Simulations were based on the finite element method. The generator was targeted to be used for the rated power of 200 W. It was found that the optimally designed generator had a higher electromotive force of 36.1%, a lower cogging torque of 20%, and a higher output power of 12.2% than the conventional structure. The leakage flux of the proposed structure was also improved from the conventional one. Thus, the generator designed in this work could be another capable choice for electrical generation from renewable energy. The proposedly modified technique can also be adapted for output profile improvement of the doubly salient permanent magnet machines which are extensively used for renewable energy production nowadays.Keywords: Rotating machines, Permanent magnet machine, Permanent magnet generator, Doubly salient permanent magnet generator

Pages 21792184We consider the problem of the motion of a rigid bodygyrostat immersed in an incompressible ideal fluid. Based on Yehia's study [1, 2], the equations of the motion of the problem are introduced and they are reduced to the orbital equation. This reduced equation may be used to study the stability of certain motions of the body [3] and to obtain solutions for the classical problems in rigid body dynamics [4]. Using the orbital equation, a single new solution of the considered problem is obtained in which the angle between the body axis of symmetry and the vertical axis is constant.Keywords: Rigid body dynamics, Motion of a rigid body in a liquid, Particular solutions, The reduced equation

Pages 21852195Creating new fracture networks in coal seams with natural fractures through hydraulic fracturing techniques is an effective method for exploiting coalbed methane. In this paper, a continuumdiscontinuum element method (CDEM) is developed for simulating and assessing hydraulic fracture propagation in coal seams. An elasticdamagefracture model is proposed for capturing the deformation and cracking processes of fractured coal. A stressfracture percolation relation is implemented to simulate the hydromechanical coupling processes. The influence of Xdirection angles, mechanical strengths, distances and lengths of natural fractures are analyzed in detail. The results are potentially useful to optimize the fracturing design.Keywords: Continuumdiscontinuum element method (CDEM), Hydraulic fracturing, Fractured coal, Hydromechanical coupling

Pages 21962220In this paper, it is aimed to analyze the linear vibrational behavior of functionallygraded (FG) sizedependent circular nanoplates using the integral form of the nonlocal strain gradient (NSG) model. The linear axisymmetric vibration of the circular FG nanoplates based on the nonlocal strain gradient (NSG) model is the focal point of this study. In this regard, the nonlocal elasticity theory (NET) and strain gradient (SG) models are used in conjunction with Hamilton's principle to obtain the governing equations. Discretization of the obtained governing equations is performed with the help of generalized differential quadrature rule (GDQR) and Galerkin weighted residual method (GWRM). The analysis is focused on the effect of nonlocal and material parameters, as well as the aspect ratio, heterogeneity index of FG material, different boundary conditions, and frequency number on the overall behavior of nanoplate. On using the Galerkin method, a system of linear differential equations is obtained and solved to determine the natural linear frequencies and mode shapes. The obtained results are then compared with the existing results in the literature. On using the proposed procedure in this paper, the dynamic behavior of nanoplate under different boundary conditions can be well described. In addition, the existing deficiencies in other nonlocal theories can be eliminated. The results of this investigation can be considered as a turning point in the improvement of theoretical results for achieving a better prediction of vibrational behavior in nanostructures.Keywords: Size effect, vibrational response, Functionally graded material, circular nanoplate, nonlocal strain gradient theory

Pages 22212237This work analyses the homogeneous isotropic turbulence by means of the equivalence between Euler and Lagrange representations of motion, adopting the bifurcation rates associated with NavierStokes and kinematic equations, and an appropriate hypothesis of fully developed chaos. The equivalence of these motion descriptions allows to show that kinetic and thermal energy cascade arise both from the convective term of Liouville equation. Accordingly, these phenomena, of nondiffusive nature, correspond to a transport in physical space linked to the trajectories divergence. Both the bifurcation rates are properly defined, where the kinematic bifurcation rate is shown to be much greater than NavierStokes bifurcation rate. This justifies the proposed hypothesis of fully developed chaos where velocity field and particles trajectories fluctuations are statistically uncorrelated. Thereafter, a specific ergodic property is presented, which relates the statistics of fluid displacement to that of velocity and temperature fields. A detailed analysis of separation rate is proposed which studies the statistics of radial velocity component along the material separation vector. Based on previous elements, the closure formulas of von KarmanHowarth and Corrsin equations are finally achieved. These closures, of nondiffusive kind, represent a propagation phenomenon, and coincide with those just presented by the author in previous works, corroborating the results of these latter. This analysis applies also to any passive scalar which exhibits diffusivity.Keywords: Turbulence, Lagrange description, Euler description, Bifurcation rate, Liouville theorem