Showing papers in "Applied and Computational Mechanics in 2018"

Nonlinear Dynamic Response of Functionally Graded Porous Plates on Elastic Foundation Subjected to Thermal and Mechanical Loads

Abstract: In this paper, the first-order shear deformation theory is used to derive theoretical formulations illustrating the nonlinear dynamic response of functionally graded porous plates under thermal and mechanical loadings supported by Pasternak’s model of the elastic foundation. Two types of porosity including evenly distributed porosities (Porosity-I) and unevenly distributed porosities (Porosity-II) are assumed as effective properties of FGM plates such as Young’s modulus, the coefficient of thermal expansion, and density. The strain-displacement formulations using Von Karman geometrical nonlinearity and general Hooke’s law are used to obtain constitutive relations. Airy stress functions with full motion equations which is employed to shorten the number of governing equations along with the boundary and initial conditions lead to a system of differential equations of the nonlinear dynamic response of porous FGM plates. Considering linear parts of these equations, natural frequencies of porous FGM plates are determined. By employing Runge-Kutta method, the numerical results illustrate the influence of geometrical configurations, volume faction index, porosity, elastic foundations, and mechanical as well as thermal loads on the nonlinear dynamic response of the plates. Good agreements are obtained in comparison with other results in the literature.

Bending Response of Nanobeams Resting on Elastic Foundation

Abstract: In the present study, the finite element method is developed for the static analysis of nano-beams under the Winkler foundation and the uniform load The small scale effect along with Eringen's nonlocal elasticity theory is taken into account The governing equations are derived based on the minimum potential energy principle Galerkin weighted residual method is used to obtain the finite element equations The validity and novelty of the results for bending are tested and comparative results are presented Deflections according to different Winkler foundation parameters and small scale parameters are tabulated and plotted As it can be seen clearly from figures and tables, for simply-supported boundary conditions, the effect of small scale parameter is very high when the Winkler foundation parameter is smaller On the other hand, for clamped-clamped boundary conditions, the effect of small scale parameter is higher when the Winkler foundation parameter is high Although the effect of the small scale parameter is adverse on deflection for simply-supported and clamped-clamped boundary conditions

A review of size-dependent elasticity for nanostructures

Abstract: Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and nano-rodes are being investigated by Non-classical elasticity theories. This review includes the last researches on bending, buckling, and vibration of nano-plates, nano-beams, nanorods, and nanotubes which were investigated by non-local elasticity theory and nonlocal strain gradient theory. Great scholars have written valuable reviews in the field of nanomechanics. Therefore, given a large number of researches and the prevention of repetition, the articles in the past year are reviewed.

Stability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method

Abstract: In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the problem’s parameters. Based on the multiple scales homotopy perturbation method, a uniform second-order periodic solution having a damping part is formulated. Comparing these two approaches reveals the accuracy of using the second approach and further allows studying the stability behavior. Numerical simulations are carried out to validate the analytical finding.

Vibration Analysis of Material Size-Dependent CNTs Using Energy Equivalent Model

Abstract: This study presents a modified continuum model to investigate the vibration behavior of single and multi-carbon nanotubes (CNTs). Two parameters are exploited to consider size dependence; one derived from the energy equivalent model and the other from the modified couple stress theory. The energy equivalent model, derived from the basis of molecular mechanics, is exploited to describe size-dependent material properties such as Young and shear moduli for both zigzag and armchair CNT structures. A modified couple stress theory is proposed to capture the microstructure size effect by assisting material length scale. A modified kinematic Timoshenko nano-beam including shear deformation and rotary inertia effects is developed. The analytical solution is shown and verified with previously published works. Moreover, parametric studies are performed to illustrate the influence of the length scale parameter, translation indices of the chiral vector, and orientation of CNTs on the vibration behaviors. The effect of the number of tube layers on the fundamental frequency of CNTs is also presented. These findings are helpful in mechanical design of high-precision measurement nano-devices manufactured from CNTs.

Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory

Abstract: In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Karman and Hamilton's principle into account On the other hand, a viscoelastic matrix was modeled as a three-parameter foundation Furthermore, the differential quadrature method was applied by which the critical load was obtained Finally, since there was no research available for the dynamic buckling of a nanoplate, the static buckling was taken into consideration to compare the results and explain some significant and novel findings One of these results showed that for greater values of the nanoscale parameter, the small scale had further influences on the dynamic buckling

Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory

Abstract: The present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential equations are obtained using the Hamilton’s principle by considering the Von-Karman’s nonlinear strains. An analytical approach is applied to obtain exact results with different boundary conditions. Due to the fact that there is no research on the stability of micro/nano sandwich plates based on S-FSDT including the couple stress effect, the obtained results are compared with the FSDT studies which use the Eringen nonlocal elasticity.

A Review of Solar Energy Collectors: Models and Applications

Abstract: A current study and discussion in detail about many solar energy collectors of various types, components, classifications and configurations, through the analysis of their performance, is our aim through this review paper. The effects of the geometrical parameters of the solar air collectors as well as the functioning parameters on heat transfer and fluid flow processes were also discussed in detail. The numerical, analytical, and experimental analyses on different models of flat plate solar air collectors with various thermal transfer enhancement strategies were shown in various stages, i.e., modelling, control, measurement, and visualization of airfield, determination of heat transfer, control of friction loss and pressure drop, and evaluation of the thermal performance by the measurement of the augmentation in the temperature of the working fluid at a given solar irradiance and under given flow rate. We concluded this review by identifying the various applications possible for the solar air collectors such as heating and cooling of houses, drying agricultural food materials, and water desalination process.

Free Vibration Analysis of Nanoplates Made of Functionally Graded Materials Based On Nonlocal Elasticity Theory Using Finite Element Method

Abstract: In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesses according to a volume fraction power law distribution. The finite element method (FEM) is presented to model the functionally graded nanoplate and solve mathematical equations accurately. The finite element formulation for HSDT nanoplate is also presented. Natural frequencies of FG nanoplate with various boundary conditions are compared with available results in the literature. At the end some numerical results are presented to evaluate the influence of different parameters, such as power law index, nonlocal parameter, aspect ratio and aspect of length to thickness of nanoplate. In addition, all combinations of simply supported and clamped boundary conditions are considered.

Dynamic analysis of planar rigid multibody systems modeled using natural absolute coordinates

Abstract: This paper deals with the dynamic simulation of rigid multibody systems described with the use of two-dimensional natural absolute coordinates. The computational methodology discussed in this investigation is referred to as planar Natural Absolute Coordinate Formulation (NACF). The kinematic representation used in the planar NACF is based on a vector of generalized coordinates that includes two translational coordinates and four rotational parameters. In particular, the set of natural absolute coordinates is employed for describing the global location and the geometric orientation relative to the general configuration of a planar rigid body. The kinematic description utilized in the planar NACF is based on the separation of variable principle. Therefore, a constant symmetric positive-definite mass matrix and a zero inertia quadratic velocity vector associated with the centrifugal and Coriolis inertia effects enter in the formulation of the equations of motion. However, since a redundant set of rotational parameters is used in the kinematic description of the planar NACF for defining the geometric orientation of a rigid body, the introduction of a set of intrinsic normalization conditions is necessary for the mathematical formulation of the algebraic constraint equations. Thus, the intrinsic constraint equations associated with the natural absolute coordinates must be properly taken into account in addition to the extrinsic constraint equations that model the kinematic pairs which form the mechanical joints. This investigation discusses in details the mathematical derivation and the numerical implementation of the multibody system differential-algebraic equations of motion elaborated in the context of the planar NACF. For this purpose, simple geometric considerations are employed in the paper to develop the algebraic equations associated with the intrinsic and extrinsic constraints, whereas the fundamental principles of classical mechanics are utilized for the formal deduction of the dynamic equations. By using the augmented formulation, the index-three form of the differential-algebraic equations of motion is reduced to the corresponding index-one counterpart in order to be able to apply the Udwadia-Kalaba approach for the analytical calculation of the multibody system generalized acceleration vector. Furthermore, in the numerical implementation of the equations of motion based on the planar NACF, the direct correction method is utilized for stabilizing the algebraic constraint equations at both the position and velocity levels. The direct correction approach represents a new methodology recently developed in the field of multibody system dynamics for treating the algebraic constraint equations leading to physically correct and numerically stable dynamic simulations. A standard numerical integration algorithm is employed for obtaining an approximate solution of the nonlinear dynamic equations derived by using the planar NACF. The numerical implementation of a general-purpose multibody computer program based on the planar NACF is demonstrated in the paper considering four simple benchmark examples of rigid multibody systems.

Thermal Analysis of Convective-Radiative Fin with Temperature-Dependent Thermal Conductivity Using Chebychev Spectral Collocation Method

Abstract: In this paper, the Chebychev spectral collocation method is applied for the thermal analysis of convective-radiative straight fins with the temperature-dependent thermal conductivity. The developed heat transfer model was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conductivity (nonlinear) parameters on the thermal performance of the fin. The results of this study reveal that the rate of heat transfer from the fin increases as convective, radioactive, and magnetic parameters increase. This study finds good agreements between the obtained results using the Chebychev spectral collocation method and the results obtained using the Runge-Kutta method along with shooting, homotopy perturbation, and Adomian decomposition methods.

Inherent Irreversibility of Exothermic Chemical Reactive Third-Grade Poiseuille Flow of a Variable Viscosity with Convective Cooling

Abstract: In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.

Heat Transfer in Hydro-Magnetic Nano-Fluid Flow between Non-Parallel Plates Using DTM

Abstract: This study presents a computational investigation on heat and flow behaviors between non parallel plates with the influence of a transverse magnetic field when the medium is filled with solid nanoparticles. The nonlinear governing equations are treated analytically via Differential Transform Method (DTM). Thereafter, obtained DTM results are validate with the help of numerical fourth order Runge-Kutta (RK4) solution. The main aim of this research work is to analyze the influence of varying physical parameters, in particular Reynolds number, nanofluid volume fraction, and Hartmann number. It was found that the presence of solid nanoparticles in a water base liquid has a notable effect on the heat transfer improvement within convergent-divergent channels. The comparison of DTM results with numerical RK4 solution also shows the validity of the analytical DTM technique. In fact, results demonstrate that the DTM data match perfectly with numerical ones and those available in literature.

Longitudinal magnetic field effect on torsional vibration of carbon nanotubes

Abstract: Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gradient elasticity theory is used in the formulation. Fourth order nonlocal equation of motion is solved by utilizing differential quadrature method. Clamped-clamped and clamped-free nonlocal boundary conditions are considered. Nonlocal and axial magnetic field effects on torsional vibration of carbon nanotubes are investigated. The magnetic field has significant effects on the dynamics of carbon nanotubes and may lead to torsional buckling. Critical torsional buckling load reduces with nonlocal effects. Nonlocality shows softening effect on carbon nanotube’s lattice structure. Present results can be used in the design and analysis of nanoelectromechanical products like nano-motors.

Free Vibration Analysis of BNNT with Different Cross-Sections via Nonlocal FEM

Abstract: In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) and Carbon Nanotube (CNT) are calculated using the Nonlocal Elasticity Theory. Frequency values are found via both analytical and finite element method (FEM). Galerkin weighted residual method is used to obtain the finite element equations. BNNT and CNT are modeled as Euler - Bernoulli Beam and solutions are gained by using four different cross-section geometries with three boundary conditions. Selected geometries are circle, rectangle, triangle, and square. Frequency values are given in tables and graphs. The effect of cross-section, boundary conditions and length scale parameter on frequencies has been investigated in detail for BNNT.

Nonlinear free vibration of viscoelastic nanoplates based on modified couple stress theory

Abstract: In this paper, a new viscoelastic size-depended model developed based on a modified couple stress theory and the for nonlinear viscoelastic material in order to vibration analysis of a viscoelastic nanoplate. The material of the nanoplate is assumed to obey the Leaderman nonlinear constitutive relation and the von Karman plate theory is employed to model the system. The viscous parts of the classical and nonclassical stress tensors are obtained based on the Leaderman integral and the corresponding work terms are calculated. The viscous work equations are balanced by the terms of size-dependent potential energy, kinetic energy. Then the equations of motion are derived from Hamilton’s principle. The governing nonlinear integro-differential equations with coupled terms are solved by using the fourth-order Runge-Kutta method and Galerkin approach. The results are validated by carrying out the comparison with existing results in the literature when our model is reduced into an elastic case. In order to explore the vibrational characteristics, the influences of the thickness ratio, relaxation coefficient, and aspect ratio on the frequency and damping ratio were also examined. The results revealed that the frequency, vibration amplitude and damping ratio of viscoelastic nanoplate were significantly influenced by the relaxation coefficient of nanoplate material, and length scale parameter. Also, it was found that with increasing (h/l) the vibration frequency decreases and its amplitude and damping ratio increase.

Wave motion and stop-bands in pipes with helical characteristics using Wave Finite Element analysis

Abstract: Pipes are widely used in many industrial and mechanical applications and devices. Although there are many different constructions according to the specific application and device, these can show helical pattern, such as spiral pipes, wire-reinforced pipes/shells, spring-suspension, and so on. Theoretical modelling of wave propagation provides a prediction about the dynamic behavior, and it is fundamental in the design process of these structures/devices and in structural health monitoring techniques. However, standard approaches have limitations in terms of difficulties in modelling and impossible computational cost at higher frequencies. In this study, the wave characteristics in waveguides with helical patterns are obtained using a Wave Finite Element (WFE) method. The method is described for a 1D and 2D waveguide with helical properties and it is illustrated by numerical examples. These include the optimization of stop-bands for a fluid-filled pipe with concentrated masses and a cylindrical structure with helical orthotropy.

Performance, Thermal Stability and Optimum Design Analyses of Rectangular Fin with Temperature-Dependent Thermal Properties and Internal Heat Generation

Abstract: In this study, we analysed the thermal performance, thermal stability and optimum design analyses of a longitudinal, rectangular fin with temperature-dependent, thermal properties and internal heat generation under multi-boiling heat transfer using Haar wavelet collocation method. The effects of the key and controlling parameters on the thermal performance of the fin are investigated. The thermal stability criteria and optimum design parameter were established. From the investigation, the study reveals that the performance of the fin is enhanced as the boiling condition parameter or the exponent decreases. It is also established that the optimum fin length (at which Q/ζ reaches a maximum value) increases as the non-linear thermal conductivity term β, increases. Furthermore, the study shows that the optimum value of M can be obtained based on the value of the non-linear term. The computational results obtained in this study were compared with established numerical solutions and is found to be in good agreement with the standard numerical solutions.

Free vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach

Abstract: In this paper, wave propagation approach is used to analysis the free vibration and buckling analysis of the thick rectangular plates based on higher order shear deformation plate theory. From wave viewpoint, vibrations can be considered as traveling waves along structures. Waves propagate in a waveguide and reflect at the boundaries. It is assumed that the plate has two opposite edge simply supported while the other two edges may be simply supported or clamped. It is the first time that the wave propagation method is used for thick plates. In this study, firstly the matrices of propagation and reflection are derived and by combining them, the characteristic equation of the plate is obtained. Comprehensive results on dimensionless natural frequencies and dimensionless buckling loads of rectangular thick plates with different boundary conditions for various values of aspect ratio and thickness to length ratio are presented. It is observed that obtained results of wave propagation method with considerable accuracy are so close to obtained values by literature.

Ritz Method Application to Bending, Buckling and Vibration Analyses of Timoshenko Beams via Nonlocal Elasticity

Abstract: Bending, buckling and vibration behaviors of nonlocal Timoshenko beams are investigated in this research using a variational approach. At first, the governing equations of the nonlocal Timoshenko beams are obtained, and then the weak form of these equations is outlined in this paper. The Ritz technique is selected to investigate the behavior of nonlocal beams with arbitrary boundary conditions along them. To find the equilibrium equations of bending, buckling, and vibration of these structures, an analytical procedure is followed. In order to verify the proposed formulation, the results for the nonlocal Timoshenko beams with four classical boundary conditions are computed and compared wherever possible. Since the Ritz technique can efficiently model the nano-sized structures with arbitrary boundary conditions, two types of beams with general boundary conditions are selected, and new results are obtained.

Modelling of Suddenly Expanded Flow Process in Supersonic Mach Regime using Design of Experiments and Response Surface Methodology

Abstract: The present work is an attempt to model, analyze, and control the flow at the base of an abruptly expanded circular duct by using design of experiments (DOE) and response surface methodology (RSM). Tiny-jets in the form of orifice were positioned at an interval of 900, 6.5 mm from the primary axis of the main jet of the nozzle. Experiments were conducted to measure two responses namely, base pressure without the use of micro jets or active control (WoC) and base pressure with the use of micro jets or active control (WC). Mach number (M), nozzle pressure ratio (NPR), area ratio (AR) and length to diameter ratio (L/D) were considered as input variables (parameters), which control the outputs (i.e. base pressure). Non-linear regression models based on central composite design (CCD) and Box-Behnken design (BBD) have been developed in order to facilitate the input-output relationships. Moreover, the significance of main, square and interaction terms of the developed models have been tested by performing analysis of variance (ANOVA). The ANOVA and significance test results and their respective correlation coefficient values indicate that both the CCD and BBD regression models are statistically adequate for both the base pressure responses of without control and with control respectively. The performances of the nonlinear models have been validated for accuracy prediction by use of 15 test cases. The performance of BBD model is found to be better in forecasting base pressure for both cases of without control and with control when compared to the CCD model.

On the application of Sturm's theorem to analysis of dynamic pull-in for a graphene-based MEMS model

Abstract: A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.

Buckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams

Abstract: The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather than the classical power law distribution which permits gradually variation of stresses at the surface boundary and eliminates delamination. The Voigt model is proposed to homogenize micromechanical properties and to derive the effective material properties. The Euler-Bernoulli beam theory is selected to describe Kinematic relations. A finite element model is exploited to form stiffness and buckling matrices and solve the problem of eignivalue numerically. Numerical results present the effect of material graduations and elasticity ratios on the buckling behavior of FG beams. The proposed model is helpful in stability of mechanical systems manufactured from FGMs.

Buckling and Vibration Analysis of Tapered Circular Nano Plate

Abstract: In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simply supported and clamped boundary conditions. To verify the accuracy of the Ritz method, the differential transform method (DTM) was also used to drive the size-dependent natural frequencies of circular nanoplates. Both methods reported good results. The validity of solutions was performed by comparing the present results with those of the literature for both classical plate and nanoplate. The effects of nonlocal parameter, mode number, and taper parameter on the natural frequency were investigated. The results showed that increasing the taper parameter causes increasing of buckling load and natural frequencies, and its effects on the clamped boundary condition is more than the simply support.

Transient Natural Convection in an Enclosure with Variable Thermal Expansion Coefficient and Nanofluid Properties

Abstract: Transient natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity, and the thermal expansion coefficient of Al2O3-water nanofluid. The study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ ϕ ≤ 7%), the enclosure aspect ratio (AR =1), and temperature differences between the cold and hot walls (∆T= 30). Transient parameters such as development time and time-average Nusselt number along the cold wall are also presented as a non-dimensional form. Increasing the Rayleigh number shortens the non-dimensional time of the initializing stage. By increasing the volume fraction of nanoparticles, the flow development time shows different behaviors for various Rayleigh numbers. The non-dimensional development time decreases by enhancing the concentration of nanoparticles.

Transverse Sensing of Simply Supported Truncated Conical Shells

Abstract: Modal signals of transverse sensing of truncated conical shells with simply supported boundary condition at both ends are investigated. The embedded piezoelectric layer on the surface of conical shell is used as sensors and output voltages of them in considered modes are calculated. The Governing sensing signal displacement equations are derived based on the Kirchhoff theory, thin-shell assumption, piezoelectric direct effect, the Gauss theory and the open circuit assumption. A conical shell with fully covered piezoelectric layer is considered as a case study and the layer is segmented into 400 patches. Modal voltages of the considered model are calculated and evaluated. The ideal locations for sensor patches are in the middle of conical shell surface in the longitudinal direction and locations near the ends of the conical shell are not recommended. The longitudinal membrane strain signal has a leading role on the total signal in comparison with other strain signal components. The output signals of the sensor can be used as a controller input for later active vibration control or structural health monitoring.

On the level of computational model of a human skull: A comparative study

Abstract: In this study, different patient-specific computational models of the skull, which are often used in literature, were investigated, analysed and compared. The purpose of this study was to demonstrate the differences in computational model creation and results in case different computational models based on same computed tomography (CT) dataset are used. The selection of computational model directly influences the values of investigated parameters. The effort is to demonstrate, how the selection of the computational model influences the results of biomechanically relevant parameters. The comparison was based on total displacement of the skull and von Mises strain investigated around predefined paths around the skull. The strain values were evaluated according to criterion from literature. The results were obtained using finite element method. The values of the displacement of the skull were higher in case of considering cancellous bone tissue due to its poor material properties or heterogeneous material properties. The same situation occurred during the evaluation of strain. The values were higher in models which include cancellous bone tissue in the structure.

Magneto-Thermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation

Abstract: Article history:Received: 12 July 2018 Accepted: 1 September 2018 Available online In this paper, the mechanical vibration analysis of functionally graded (FG) nanoplate embedded in visco Pasternak foundation incorporating magnet and thermal effects is investigated. It is supposed that a uniform radial magnetic field acts on the top surface of the plate and the magnetic permeability coefficient of the plate along its thickness are assumed to vary according to the volume distribution function. The effect of in-plane pre-load, viscoelastic foundation, magnetic field and temperature change is studied on the vibration frequencies of functionally graded annular and circular nanoplate. Two different size dependent theories also are employed to obtain the vibration frequencies of the FG circular and annular nanoplate. It is assumed that a power-law model is adopted to describe the variation of functionally graded (FG) material properties. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a visco Pasternak foundation. The governing equation is derived for FG circular and annular nanoplate using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST). The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. Subsequently, the results are compared with valid results reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the magnetic field, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are scrutinized. According to the results, the application of radial magnetic field to the top surface of plate gives rise to change the state of stresses in both tangential and radial direction as well as the natural frequency. Also, The temperature changes play significant role in the mechanical analysis of FG annular and circular nanoplate. This study can be useful to product the sensors and devices at the nanoscale with considering the thermally and magnetically vibration properties of the nanoplate.

Time-Discontinuous Finite Element Analysis of Two-Dimensional Elastodynamic Problems using Complex Fourier Shape Functions

Abstract: This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in complex space as well as the polynomial ones simultaneously, that make them a better choice than classic Lagrange shape functions, which only can satisfy polynomial function field. To investigate the validity and accuracy of the proposed method, three numerical examples are provided and the results obtained from the present method (complex Fourier-based TD-FEM) and the classic Lagrange-based TD-FEM are compared with the exact analytical solutions. According to them, using complex Fourier functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM.

On the Thermal Conductivity of Carbon Nanotube/Polypropylene Nanocomposites by Finite Element Method

Abstract: In this paper, finite element method is used to obtain thermal conductivity coefficients of single-walled carbon nanotube reinforced polypropylene. For this purpose, the two-dimensional representative volume elements are modeled. The effect of different parameters such as nanotube dispersion pattern, nanotube volume percentage in polymer matrix, interphase thickness between nanotube and surrounded matrix and nanotube aspect ratio on the thermal conductivity coefficient of nanotube/polypropylene nanocomposite are investigated. For the dispersion pattern, three different algorithms, including random dispersion, regular dispersion along the temperature difference and regular dispersion perpendicular to the temperature difference are employed. Furthermore, the temperature is considered in the range of 0°C to 200°C. The nanotube volume percentage in the polymer matrix is selected as 1%, 3% and 5%. It is shown that the polypropylene matrix reinforced by the regular distribution of nanotubes directed parallel to the temperature difference leads to the largest thermal conductivity coefficients. Besides, the nanocomposites with larger volume percentages of carbon nanotubes possess larger thermal conductivity coefficients.