فهرست مطالب

Applied and Computational Mechanics - Volume:5 Issue: 1, 2019
  • Volume:5 Issue: 1, 2019
  • تاریخ انتشار: 1397/10/23
  • تعداد عناوین: 15
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  • Mohammad Kazem Moayyedi * Pages 1-12
    In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynamical system was improved using a calibration method based on a least-square optimization process. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least- square procedure is a combination of POD method and the solution of an optimization problem. The obtained model can predict accurate time variations of flow field with high speed. For long time periods, the calibration term can be computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has recently been proposed by the authors. The results obtained from the calibrated reduced order model show close agreements to the benchmark DNS data, proving high accuracy of our model.
    Keywords: Proper orthogonal decomposition, Galerkin projection, Reduced order model, Calibration strategy, Incompressible flow, Fourier modes
  • Gbeminiyi Sobamowo* Pages 13-39
    In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed. The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. The resulting systems of fully-coupled nonlinear ordinary differential equations are solved using a differential transformation method - Padé approximant technique. The accuracy of the developed approximate analytical methods is verified by comparing the results of the differential transformation method - Padé approximant technique with those of previous works as presented in the literature. Thereafter, the analytical solutions are used to investigate the effects of the Prandtl number, the nanoparticles volume-fraction, the shape and the type on the flow and heat transfer behaviour of various nanofluids over the flat plate. It is observed that as the Prandtl number and volume-fraction of the nanoparticles in the basefluid increase, the velocity of the nanofluid decreases while the temperature increases. Also, the maximum decrease in velocity and the maximum increase in temperature are recorded in lamina-shaped nanoparticles, followed by platelets, cylinders, bricks, and sphere-shaped nanoparticles, respectively. Using a common basefluid for all nanoparticle types, it is established that the maximum decrease in velocity and the maximum increase in temperature are recorded in TiO2 followed by CuO, Al2O3 and SWCNTs nanoparticles, respectively. It is hoped that the present study will enhance the understanding of free convection boundary-layer problems as applied in various industrial, biological and engineering processes.
    Keywords: Free convection, Boundary layer, Prandtl number, Nanofluid, Differential transformation method, Padé-approximant technique
  • Mario Freitas*, Lineu Pedroso Pages 40-45
    This study targets the behavior of shear buildings equipped with tuned liquid column dampers (TLCD) which attenuate dynamic load-induced vibrations. TLCDs are a passive damping system used in tall buildings. This kind of damper has proven to be very efficient, being an excellent alternative to mass dampers. A dynamic analysis of the structure-damper system was made using the software DynaPy, developed in the research process. The software solves the equations of motion through numeric integration using the central differences method. The simulations results obtained with DynaPy showed that the use of TLCD can reduce the dynamic response significantly for both harmonic excitations and random excitations.
    Keywords: TLCD, Structure dynamics, DynaPy, Numeric integration
  • Dang Hieu *, N.Q. Hai Pages 46-57
    In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, which are compared with the previous analytical solutions and the exact solutions. Comparisons show the accuracy of the present solutions. The impact of nonlinear terms on the dynamical behavior of beams and the effect of the initial amplitude on frequencies of beams are investigated. Furthermore, the effect of the axial force and the length of beams on frequencies are studied.
    Keywords: Equivalent linearization method, Weighted averaging, Non-linear vibration, Euler-Bernoulli beam
  • Ahmed A. Hamoud*, Kirtiwant P. Ghadle Pages 58-69
    This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on their reliability and reduction in the size of the computational work. This study provides an analytical approximate to determine the behavior of the solution. It proves the existence and uniqueness results and convergence of the solution. In addition, it brings an example to examine the validity and applicability of the proposed techniques.
    Keywords: Modified Adomian Decomposition Method, Modified Variational Iteration Method, Caputo Fractional Volterra-Fredholm Integro-Differential Equation
  • Endalew Getnet Tsega* , Vinod Kumar Katiyar Pages 70-76
    At high altitudes, the air pressure is much lower than it is at sea level and contains fewer oxygen molecules and less oxygen is taken in at each breath. This requires deeper and rapid breathing to get the same amount of oxygen into the blood stream compared to breathing in air at sea level. Exercises increase the oxygen demand and make breathing more difficult at high altitude. In this study, a numerical simulation of inspiratory airflow in a three-dimensional bifurcating human airways model (third to sixth generation) during exercise at sea level and at high altitude was performed. The computational fluid dynamics (CFD) solver FLUENT was used to solve the governing equations for unsteady airflow in the model. Flow velocity, pressure, and wall shear stress were obtained from the simulations with the two breathing conditions. The result of this study quantitatively showed that performing exercise with a given work rate at high altitude increased inspiratory airflow velocity, pressure, and wall shear stress more than that at sea level in the airway model. The ranges of the airflow fields were also higher at high altitude than sea level. The simulation results showed that there were no significant differences in flowing pattern for the two breathing conditions.
    Keywords: Computational fluid dynamics, Airway model, Flow fields, Exercise, Sea level, High altitude, Numerical Simulation
  • Ali Zargaripoor, Ali Reza Daneshmehr* , Mansour Nikkhah Bahrami Pages 77-90
    In this paper, the wave propagation approach is presented to analyze the vibration and wave power reflection in FG rectangular plates based on the first order shear deformation plate theory. The wave propagation is one of the useful methods for analyzing the vibration of structures. This method gives the reflection and propagation matrices that are valuable for the analysis of mechanical energy transmission in devices. It is assumed that the plate has two opposite edges 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 functionally graded plates. In this study, firstly, the matrices of reflection and propagation are derived. Second, these matrices are combined to provide an exact method for obtaining the natural frequencies. It is observed that the obtained results of the wave propagation method are in a good agreement with the obtained values in literature. At the end, the behavior of reflection coefficients for FG plates are studied for the first time.
    Keywords: Rectangular FG plate, Propagation matrix, Reflection matrix, Vibration analysis, FSDT
  • Raziyeh Gharechahi, Maryam Arab Ameri *, Morteza Bisheh, Niasar Pages 91-102
    In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the presented methods are efficient and applicable for lower and upper solutions.
    Keywords: Bratu-type equations, Compact finite difference methods, Lower, upper solutions, Convergence
  • Mohammad Malikan * Pages 103-112
    In the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear correction factors. The equilibrium equation is formulated by the nonlocal elasticity theory in order to predict small-scale effects. The equation is solved by Navier’s approach by which critical buckling loads are obtained for simple boundary conditions. Finally, to approve the results of the new beam theory, some available well-known references are compared.
    Keywords: Buckling analysis, Single-walled carbon nanotubes, A new refined beam theory, nonlocal elasticity theory, Navier’s approach
  • Breno Vincenzo de Almeida* , Renato Pavanello Pages 113-127
    Due to developments in additive manufacturing, the production of piezoelectric materials with complex geometries is becoming viable and enabling the manufacturing of thicker harvesters. Therefore, in this study a piezoelectric harvesting device is modelled as a bimorph cantilever beam with a series connection and an intermediate metallic substrate using the plain strain hypothesis. On the other hand, the thickness of the harvester’s piezoelectric material is structurally optimized using a discrete topology optimization method. Moreover, different optimization parameters are varied to investigate the algorithm’s convergence. The results of the optimization are presented and analyzed to examine the influence of the harvester's geometry and its different substrate materials on the harvester’s energy conversion efficiency.
    Keywords: Piezoelectric, Harvester, Structural optimization
  • Mehdi Bohlooly, Keramat Malekzadeh Fard* Pages 128-140
    This research presents the modeling and analysis for the buckling and postbuckling behavior of sandwich plates under thermal and mechanical loads. The lay-up configurations of plates are laminated composite with concentric stiffener and surface mounted piezoelectric actuators. The plates are in contact with a three-parameter elastic foundation including softening and/or hardening nonlinearity. Several types of grid shapes of stiffeners are studied such as ortho grid, angle grid, iso grid, and orthotropic grid. The equations of structures are formulated based on the classical lamination theory incorporating nonlinear von-Karman relationships. The stress function and Galerkin procedure are applied to derive explicit formulations of the equilibrium paths. New results are introduced to give the influences of voltage through the thickness of piezoelectric actuators, different stiffeners, and nonlinear elastic foundations.
    Keywords: Buckling, composite, Stiffener, Piezoelectric, Foundation
  • Lizbeth Cuba, RA Arciniega, J.L. MANTARI* Pages 141-149
    The present study introduces a generalized 2-unknown’s higher order shear deformation theory (HSDT) for isotropic and orthotropic plates. The well-known Shimpi’s two-unknown's HSDT is reproduced as a special case. Reddy’s shear strain shape function (SSSF) is also adapted to the present generalized theory. The results show that both Shimpi and the adapted Reddy’ HSDT are essentially the same, i.e., both present the same static results. This is due to the fact that both theories use polynomial SSSFs. This study presents a new optimized cotangential SSSF. The generalized governing equation obtained from the principle of virtual displacement is solved via the Navier closed-form solution. Results show that transverse shear stresses can be improved substantially when non-polynomial SSSFs are utilized. Finally, this theory is attractive and has the potential to study other mechanical problems such as bending in nanoplates due to its reduced number of unknown’s variables.
    Keywords: Layered structures, Plates, Elasticity, Analytical modeling
  • Nehad Ali Shah *, Najma Ahmed, Thanaa Elnaqeeb, Mohammad Mehdi Rashidi Pages 150-161
    The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with the thermal memory and the ordinary fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t. Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction.
    Keywords: Free convection, Porous medium, Inclined magnetic field, Caputo time-fractional derivatives
  • Hossein Hatami *, Mojtaba Hosseini Pages 162-173
    This study derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering elastic-plastic idealizations. The interaction relations can predict strains, which is not possible in a rigid perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-section is considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations are suggested.
    Keywords: Elastic-Plastic Analysis, Mild Steel, T–Section, M-P interaction, Bending Moment
  • Alborz Mirzabeigy* , Reza Madoliat Pages 174-180
    In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner layer does not affect higher modes significantly and mainly affects the first frequency. Then, equation of motion in the presence of cubic nonlinearity in the inner layer is derived and transformed to the form of Duffing equation. Using an analytical solution, the effect of nonlinearity on the frequency for simply-supported and clamped boundary conditions is analyzed. Results show that the nonlinearity effect is not significant and, in small amplitude free vibration analysis of a double-beam system, the material nonlinearity of the inner layer could be neglected.
    Keywords: Double-beam system, Frequency, Nonlinearity, Duffing equation, Analytical solution