2020
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A New Adaptive Extended Kalman Filter for a Class of Nonlinear Systems
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2
This paper proposes a new adaptive extended Kalman filter (AEKF) for a class of nonlinear systems perturbed by noise which is not necessarily additive. The proposed filter is adaptive against the uncertainty in the process and measurement noise covariances. This is accomplished by deriving two recursive updating rules for the noise covariances, these rules are easy to implement and reduce the number of noise parameters that need to be tuned in the extended Kalman filter (EKF). Furthermore, the AEKF updates the noise covariances to enhance filter stability. Most importantly, in the worst case, the AEKF converges to the conventional EKF. The AEKF performance is determined based on the mean square error (MSE) performance measure and the stability is proven. The results illustrate that the proposed AEKF has a dramatic improved performance over the conventional EKF, the estimates are more stable with less noise.
1

1
12


Iyad
Hashlamon
Department of Mechanical Engineering, Palestine Polytechnic University, Hebron, Palestine
Department of Mechanical Engineering, Palestine
Iran
iyad@ppu.edu
Extended Kalman filer
Aadaptive extended Kalman filter
Covariance matching
Quaternion
[[1] Z. Zhou, J. Wu, Y. Li, C. Fu, and H. Fourati, Critical issues on Kalman filter with colored and correlated system noises, Asian Journal of Control, 19(6), 2017, 19051919.##[2] C. Fraser and S. Ulrich, An Adaptive Kalman Filter for Spacecraft Formation Navigation using Maximum Likelihood Estimation with Intrinsic Smoothing, in 2018 Annual American Control Conference (ACC), 2018, 58435848.##[3] X. Tong, Z. Li, G. Han, N. Liu, Y. Su, J. Ning, et al., Adaptive EKF Based on HMM Recognizer for Attitude Estimation Using MEMS MARG Sensors, IEEE Sensors Journal, 18(8), 2018, 32993310.##[4] Y. Xi, X. Zhang, Z. Li, X. Zeng, X. Tang, Y. Cui, et al., Doubleended travellingwave fault location based on residual analysis using an adaptive EKF, IET Signal Processing, 12(8), 2018, 10001008.##[5] M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice Using MATLAB, 2nd ed., John Wiley & Sons. New York, USA, 2001.##[6] S. Ulrich and J. Z. Sasiadek, Extended Kalman filtering for flexible joint space robot control, in American Control Conference (ACC), 2011, 10211026.##[7] V. A. Bavdekar, A. P. Deshpande, and S. C. Patwardhan, Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter, Journal of Process Control, 21(4), 2011, 585601.##[8] R. JassemiZargani and D. Necsulescu, Extended Kalman filterbased sensor fusion for operational space control of a robot arm, IEEE Transactions on Instrumentation and Measurement, 51(6), 2002, 12791282.##[9] E. Hedberg, J. Norén, M. Norrlöf, and S. Gunnarsson, Industrial Robot Tool Position Estimation using Inertial Measurements in a Complementary Filter and an EKF, IFACPapersOnLine, 50(1), 2017, 1274812752.##[10] U. Bussi, V. Mazzone, and D. Oliva, Control strategies analysis using EKF applied to a mobile robot, in Workshop on Information Processing and Control (RPIC), 2017, 16.##[11] Y. Xu, Y. S. Shmaliy, C. K. Ahn, G. Tian, and X. Chen, Robust and accurate UWBbased indoor robot localisation using integrated EKF/EFIR filtering, IET Radar, Sonar & Navigation, 12(7), 2018, 750756.##[12] D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches,Wiley & Sons. Hoboken, New Jersey, USA, 2006.##[13] P. S. Maybeck, Stochastic models, estimation and control,Academic Press. New York, USA, 1982.##[14] H. Heffes, The effect of erroneous models on the Kalman filter response, IEEE Transactions on Automatic Control, 11(3), 1966, 541543.##[15] R. J. Fitzgerald, Divergence of the Kalman filter, IEEE Transactions on Automatic Control, 16(6), 1971, 736747.##[16] A. Mohamed and K. Schwarz, Adaptive Kalman filtering for INS/GPS, Journal of Geodesy, 73(4), 1999, 193203.##[17] K. Myers and B. D. Tapley, Adaptive sequential estimation with unknown noise statistics, IEEE Transactions on Automatic Control, 21(4), 1976, 520523.##[18] W. Ding, J. Wang, C. Rizos, and D. Kinlyside, Improving adaptive Kalman estimation in GPS/INS integration, Journal of navigation, 60(3), 2007, 517.##[19] E. Shi, An improved realtime adaptive Kalman filter for lowcost integrated GPS/INS navigation, in IEEE 2012 International Conference on Measurement, Information and Control (MIC) Harbin, 2012, 10931098.##[20] C. Hide, T. Moore, and M. Smith, Adaptive Kalman filtering for lowcost INS/GPS, Journal of Navigation, 56(1), 2003, 143152.##[21] R. Mehra, On the identification of variances and adaptive Kalman filtering, IEEE Transactions on Automatic Control, 15(2), 1970, 175184.##[22] P. R. Bélanger, Estimation of noise covariance matrices for a linear timevarying stochastic process, Automatica, 10(3), 1974, 267275.##[23] M. Oussalah and J. D. Schutter, Adaptive kalman filter for noise identification, in Proceedings of the international Seminar on Modal Analysis, Kissimmee, Florida, 2001, 12251232.##[24] B. J. Odelson, M. R. Rajamani, and J. B. Rawlings, A new autocovariance leastsquares method for estimating noise covariances, Automatica, 42(2), 2006, 303308.##[25] H. Raghavan, A. K. Tangirala, R. Bhushan Gopaluni, and S. L. Shah, Identification of chemical processes with irregular output sampling, Control Engineering Practice, 14(5), 2006, 467480.##[26] B. J. Odelson, A. Lutz, and J. B. Rawlings, The autocovariance leastsquares method for estimating covariances: application to modelbased control of chemical reactors, IEEE Transactions on Control Systems Technology, 14(3), 2006, 532540.##[27] X. Wang, Vehicle health monitoring system using multiplemodel adaptive estimation, MSc Thesis, Electrical Engineering, University of Hawaii at Manoa, Manoa, 2003.##[28] X. Rong Li and Z. Youmin, Multiplemodel estimation with variable structure part V: Likelymodel set algorithm, IEEE Transactions on Aerospace and Electronic Systems, 36(2), 2000, 448466.##[29] M. Karasalo and X. Hu, An optimization approach to adaptive Kalman filtering, Automatica, 8(47), 2011, 17851793.##[30] Y. Yang and W. Gao, An Optimal Adaptive Kalman Filter, Journal of Geodesy, 80(4), 2006, 177183.##[31] I. Hashlamon and K. Erbatur, An improved realtime adaptive Kalman filter with recursive noise covariance updating rules, Turkish Journal of Electrical Engineering & Computer Sciences, 24(2), 2016, 524540.##[32] C. Biçer, E. K. Babacan, and L. Özbek, Stability of the adaptive fading extended Kalman filter with the matrix forgetting factor, Turkish Journal of Electrical Engineering & Computer Sciences, 20(5), 2012, 819833.##[33] E. K. Babacan, L. Ozbek, and M. Efe, Stability of the extended Kalman filter when the states are constrained, IEEE Transactions on Automatic Control, 53(11), 2008, 27072711.##[34] H. K. Khalil, Nonlinear Systems, 3rd ed.,Prentice Hall. New Jersy, 2000.##[35] R.M. Murray, Z. Li , and S. Satry, A mathematical introduction to robotic manipulation, CRC Press, 1994.##[36] L. Yinan, Research on Joint Orientation Algorithm of Multi Sensor and Distributed Localization based on Quaternion EKF, Revista de la Facultad de Ingeniería, 32(12), 2017, 341347.##[37] K. Feng, J. Li, X. Zhang, C. Shen, Y. Bi, T. Zheng, et al., A New QuaternionBased Kalman Filter for RealTime Attitude Estimation Using the TwoStep GeometricallyIntuitive Correction Algorithm, Sensors, 17(9), 2017, 2146.##[38] I. Hashlamon and K. Erbatur, Experimental verification of an orientation estimation technique for autonomous robotic platforms, Master Thesis, Sabanci University, Istanbul, 2010.##[39] A. Kim and M. F. Golnaraghi, A quaternionbased orientation estimation algorithm using an inertial measurement unit, IEEE. New York, 2004.##[40] P. Bauer and J. Bokor, Development and hardwareintheloop testing of an Extended Kalman Filter for attitude estimation, in 11th International Symposium on Computational Intelligence and Informatics (CINTI) 2010, 5762.##[41] D. Roetenberg, "Inertial and magnetic sensing of human motion," PhD, University of Twente, Enschede, NL, 2006.##[42] E. J. Lefferts, F. L. Markley, and M. D. Shuster, Kalman Filtering for Spacecraft Attitude Estimation, Journal of Guidance, Control, and Dynamics, 5(5), 1982, 417429.##[43] D. Simon, Kalman filtering with state constraints: a survey of linear and nonlinear algorithms, Control Theory & Applications, IET, 8(4), 2009, 13031318.##[44] A. J. Calise, Enforcing an Algebraic Constraint in Extended Kalman Filter Design, Journal of Guidance, Control, and Dynamics, 40(9), 2017, 22292236.##[45] V. Bonnet, R. Dumas, A. Cappozzo, V. Joukov, G. Daune, D. Kulić, et al., A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise, Journal of Biomechanics, 62, 2017, 140147.##[46] V. Mahboub and D. Mohammadi, A Constrained Total Extended Kalman Filter for Integrated Navigation, Journal of Navigation, 71(4), 2018, 971988.##[47] I. Hashlamon, A constrained quaternion extended Kalman filter, in Sixth Palestinian Conference on Modern Trends in Mathematics and Physics, Palestine, 2018.##]
Sequential Implicit Numerical Scheme for Pollutant and Heat Transport in a PlanePoiseuille Flow
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A sequential implicit numerical scheme is proposed for a system of partial differential equations defining the transport of heat and mass in the channel flow of a variableviscosity fluid. By adopting the backward difference scheme for time derivative and the central difference scheme for the spatial derivatives, an implicit finite difference scheme is formulated. The variablecoefficient diffusive term in each equation is first expanded by differentiation. The next step of the sequential approach consists of providing a solution of the temperature and concentration, before providing a solution for the velocity. To verify the numerical scheme, the results are compared with those of a Matlab solver and a good agreement are found. We further conduct a numerical convergence analysis and found that the method is convergent. The numerical results are investigated against the model equations by studying the time evolution of the flow fields and found that the data, such as the boundary conditions, are perfectly verified. We then study the effects of the flow parameters on the flow fields. The results show that the Solutal and thermal Grashof numbers, as well as the pressure gradient parameter, increase the flow, while the Prandtl number and the pollutant injection parameter both decrease the flow. The conclusion of the study is that the sequential scheme has high numerical accuracy and convergent, while a change in the pollutant concentration leads to a small change in the flow velocity due to the opposing effects of viscosity and momentum source.
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13
25


Chinedu
Nwaigwe
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria
Department of Mathematics, Rivers State University
Iran
nwaigwe.chinedu@ust.edu.ng
Finite difference methods
Fluid flows
Sequential implicit method
Pollutant dispersion
Experimental order of convergence
[[1] G.V. Ramana Reddy, N. Bhaskar Reddy, R.S.R. Gorla, Radiation and chemical reaction effects on mhd flow along a moving vertical porous plate. International Journal of Applied Mechanics and Engineering, 21(1), 2016, 157–168.##[2] T. Chinyoka, O.D., Makinde, Analysis of nonlinear dispersion of a pollutant ejected by an external source into a channel flow. Mathematical Problems in Engineering, 2010, Article ID 827363, 17 p.##[3] O.D. Makinde, T. Chinyoka, Numerical investigation of transient heat transfers to hydromagnetic channel flow with radiative heat and convective cooling. Communications in Nonlinear Science and Numerical Simulation, 15(12), 2010, 3919–3930.##[4] J.C. Umavathi, M.A. Sheremet, S. Mohiuddin, Combined effect of variable viscosity and thermal conductivity on mixed convection flow of a viscous fluid in a vertical channel in the presence of first order chemical reaction. European Journal of MechanicsB/Fluids, 58, 2016, 98–108.##[5] J.C. Umavathi, J.P. Kumar, M.A. Sheremet, Heat and mass transfer in a vertical double passage channel filled with electrically conducting fluid. Physica A: Statistical Mechanics and its Applications, 465, 2017, 195–216.##[6] R. Bhargava, R. Sharma, O.A. Beg, Oscillatory chemicallyreacting mhd free convection heat and mass transfer in a porous medium with soret and dufour effects  finite element modelling. International Journal of Applied Mathematics and Mechanics, 5(6), 2009, 15–37.##[7] P. Mebine, Radiation effects on mhd couette flow with heat transfer between two parallel plates. Journal of Pure Applied Mathematics, 3(2), 2007, 191–202.##[8] C. IsraelCookey, E. Amos, C. Nwaigwe, Mhd oscillatory couette flow of a radiating viscous fluid in a porous medium with periodic wall temperature. American Journal of Scientific and Industrial Research, 1(2), 2010, 326–331.##[9] C. IsraelCookey, C. Nwaigwe, Unsteady mhd flow of a radiating fluid over a moving heated porous plate with timedependent suction. American Journal of Scientific and Industrial Research, 1(1), 2010, 88–95.##[10] C. Nwaigwe, Mathematical modelling of ground temperature with suction velocity and radiation. American Journal of Scientific and Industrial Research, 1(2), 2010, 238–241.##[11] R.K. Selvi, R. Muthuraj, Mhd oscillatory flow of a jeffrey fluid in a vertical porous channel with viscous dissipation. Ain Shams Engineering Journal, 9(4), 2018, 25032516.##[12] T. Hayat, M. Mustafa, S. Asghar, Unsteady flow with heat and mass transfer of third grade fluid over a stretching surface in the presence of chemical reaction. Nonlinear Analysis, Real World Application, 11, 2010, 3186– 3197.##[13] K. Kavita, P.K., Ramakrishna, K.B., Aruna, Influence of heat transfer on mhd oscillatory flow of jeffrey fluid in a channel. Advanced Applied Scientific Research, 3, 2012, 2312–2325.##[14] R. Muthuraj, S. Srinivas, A.K. Shukla, T.R. Ramamohan, Effects of thermaldiffusion, diffusionthermo and space porosity on mhd mixed convection flow of micropolar fluid in a vertical channel with viscous dissipation. Asian Research, 43, 2014, 561–578.##[15] J.K. Singh, N. Joshi, S.G. Begum, Unsteady hydromagnetic heat and mass transfer natural convection flow past an exponentially accelerated vertical plate with hall current and rotation in the presence of thermal and mass diffusions. Frontiers in Heat and Mass Transfer, 7(24), 2016, 112.##[16] J.C. Umavathi, M.A. Sheremet, Mixed convection flow of an electrically conducting fluid in a vertical channel using robin boundary conditions with heat source/sink. European Journal of MechanicsB/Fluids, 55, 2016, 132–145.##[17] S.M. Ibrahim, G. Lorenzini, P.V. Kumar, C.S.K. Raju, Influence of chemical reaction and heat source on dissipative mhd mixed convection flow of a casson nanofluid over a nonlinear permeable stretching sheet. International Journal of Heat and Mass Transfer, 111, 2017, 346–355.##[18] L.N. Moresi, V.S. Solomatov, Numerical investigation of 2d convection with extremely large viscosity variations. Physics of Fluids, 7(9), 1995, 2154–2162.##[19] T. Chinyoka, O.D. Makinde, Computational dynamics of unsteady flow of a variable viscosity reactive fluid in a porous pipe. Mechanics Research Communications, 37(3), 2010, 347–353.##[20] J.C. Umavathi, M.A. Sheremet, Influence of temperature dependent conductivity of a nanofluid in a vertical rectangular duct. International Journal of NonLinear Mechanics, 78, 2016, 17–28.##[21] O.D. Makinde, T. Chinyoka, Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration. Computers and Mathematics with Applications, 60, 2010, 642–652.##[22] R.A Van Gorder, K. Makowski, K. Mallory, K. Vajravelu, Selfsimilar solutions for the nonlinear dispersion of a chemical pollutant into a river flow. Journal of Mathematical Chemistry, 53(7), 2015, 1523–1536.##[23] O.D. Makinde, R.J. Moitsheki, B.A. Tau, Similarity reductions of equations for river pollution. Applied Mathematics and Computation, 188(2), 2007, 1267–1273.##[24] R.J. Moitsheki, O.D. Makinde, Symmetry reductions and solutions for pollutant diffusion in a cylindrical system. Nonlinear Analysis: Real World Applications, 10(6), 2009, 3420–3427.##[25] O.D. Makinde, P. Olanrewaju, W.M. Charles, Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture. Journal of African Mathematical Union, 22, 2011, 65–78.##[26] C. Nwaigwe, Coupling Methods for 2D/1D Shallow Water Flow Models for Flood Simulations. PhD thesis, University of Warwick, United Kingdom, 2016.##[27] T. Chinyoka, O.D. Makinde, Analysis of transient generalized couette flow of a reactive variable viscosity thirdgrade liquid with asymmetric convective cooling. Mathematical and Computer Modelling, 54(12), 2011, 160–174.##]
Analysis of Transient RivlinEricksen Fluid and Irreversibility of Exothermic Reactive Hydromagnetic Variable Viscosity
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2
This study analyzes the unsteady RivlinEricksen fluid and irreversibility of exponentially temperature dependent variable viscosity of hydromagnetic twostep exothermic chemical reactive flow along the channel axis with walls convective cooling. The nonNewtonian HeleShaw flow of RivlinErickson fluid is driven by bimolecular chemical kinetic and unvarying pressure gradient. The reactive fluid is induced by periodic changes in magnetic field and time. The Newtons law of cooling is satisfied by the constant heat coolant convection exchange at the wall surfaces with the neighboring regime. The dimensionless nonNewtonian reactive fluid equations are numerically solved using a convergent and consistence semiimplicit finite difference technique which are confirmed stable. The response of the reactive fluid flow to variational increase in the values of some entrenched fluid parameters in the momentum and energy balance equations are obtained. A satisfying equations for the ratio of irreversibility, entropy generation and Bejan number are solved with the results presented graphically and discussed quantitatively. From the study, it was obtained that the thermal criticality conditions with the right combination of thermofluid parameters, the thermal runaway can be prevented. Also, the entropy generation can minimize at low dissipation rate and viscosity.
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Rasaq
Kareem
Department of Mathematics, Lagos State Polytechnic, Ikorodu, Nigeria
Department of Mathematics, Lagos State Polytechnic
Iran
kareem.r@mylaspotech.edu.ng


Salawu
Olakunle
Department of Mathematics, Landmark University, Omuaran, Nigeria
Department of Mathematics, Landmark University,
Iran
kunlesalawu2@gmail.com


Yubin
Yan
Department of Mathematics, University of Chester, Chester, UK
Department of Mathematics, University of
Iran
y.yan@chester.ac.uk
NonNewtonian
Hydromagnetic
Convective cooling
Irreversibility
Viscosity
[[1] Hassan, A.R., Gbadeyan, J.A., Salawu, S.O., The effects of thermal radiation on a reactive hydromagnetic internal heat generating fluid flow through parallel porous plates. Springer Proceedings in Mathematics & Statistics, 259, 2018.##[2] Salawu, S.O., Fatunmbi, E.O., Inherent irreversibility of hydromagnetic thirdgrade reactive poiseuille flow of a variable viscosity in porous media with convective cooling. Journal of the Serbian Society for Computational Mechanics, 11, 2017, 4658.##[3] Kim Y.J., Unsteady MHD convective heat transfer past a semiinfinite vertical porous moving plate with variable suction. International Journal of Engineering Science, 38, 2000, 83345.##[4] Muthtamilselvan, M., Prakash, D., Doh, D.H., Effect of nonuniform heat generation on unsteady MHD nonDarcian flow over a vertical stretching surface with variable properties. Journal of Applied Fluid Mechanics, 7(3), 2014, 425434.##[5] Ravikumar, V., Raju, M.C., Raju, G.S.S., Combined effects of heat absorption and MHD on convective RivlinEricksen flow past a semiinfinite vertical porous plate with variable temperature and suction. Ain Shams Engineering Journal, 5, 2014, 867875.##[6] Dada, M.S., Agunbiade, S.A., Radiation and chemical reaction effects on convective Rivlin Ericksen flow past a porous vertical plate. Ife Journal of Science, 18(3), 2016, 655667.##[7] Daleep, K., Sharma, A.S., Banyal. S.K., Bounds for complex growth rate in thermosolutal convection in Rivlin–Ericksen viscoelastic fluid in a porous medium. Internationa Journal of Engineering Science and Advanced Technology, 2(6), 2012, 15641571.##[8] Noushima, H., Ramana, M.V., Reddy, C.K., Rafiuddin, M., Ramu, A., Rajender, S., Hydromagnetics free convective Rivlin–Ericksen flow through a porous medium with variable permeability. International Journal of Computational and Applied Mathematics, 5(3), 2010, 267275.##[9] Rana, G.C., Thermal instability of compressible RivlinEfficksen rotating fluid permeated with suspended dust particles in porous medium. International Journal of Applied Mathematics and Mechanics, 8(4), 2012, 97110.##[10] Sharma, R.C., Sunil, S.C., Hall effects on thermal instability of Rivlin–Ericksen fluid. Indian Journal of Pure and Applied Mathematics, 3(1), 2000, 4959.##[11] Nidhish, K.M., Effect of RivlinEricksen fluid on MHD fluctuating flow with heat and mass transfer through a porous medium bounded by a porous plate. International Journal of Mathematics Research, 8(3), 2016, 143154.##[12] Seth, G.S., Ansari, Md.S., Nandkeolyar, R., MHD natural convection flow with radiative heat transfer past an impulsively moving plat with ramped wall temperature. Journal of Heat and Mass Transfer, 47(5), 2013, 551561.##[13] Ramya, E., Muthtamilselvan, M., Doh, D.H., Absorbing/emitting radiation and slanted hydromagnetic effects on micropolar liquid containing gyrostatic microorganisms. Applied Mathematics and Computation, 324, 2018, 6981. ##[14] Aziz, A., Entropy generation in pressure gradient assisted Couette flow with different thermal boundary conditions. Entropy, 8(2), 2006, 5062.##[15] AbuHijleh, B., Natural convection and entropy generation from a cylinder with high conductivity fins. Numerical Heat Transfer Part A, 39(4), 2004, 405432.##[16] Ibanez, G., Cuevas, S., de Haro M.L., Minimization of entropy generation by asymmetric convective cooling. International Journal of Heat and Mass Transfer, 46(8), 2003, 13211328.##[17] Makinde, O.D., Irreversibility analysis for a gravity driven nonNewtonian liquid film along an inclined isothermal plate. Physica Scripta, 74(6), 2006, 642645.##[18] Makinde, O.D., HermitePade approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate. Physica A, 381(12), 2007, 17.##[19] Salawu, S.O., Oke, I.S., Inherent irreversibility of exothermic chemical reactive thirdgrade poiseuille flow of a variable viscosity with convective cooling. Journal of Applied and Computational Mechanics, 4(3), 2018, 167174.##[20] Tasnim S.H., Mahmud, S., Entropy generation in a vertical concentric channel with temperature dependent viscosity. International Communications in Heat and Mass Transfer, 29(7), 2017, 907918.##[21] Adesanya, S.O., Makinde, O.D., Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface, Physica A, 432, 2015, 222229.##[22] Makinde, O.D., Olanrewaju, P.O., Titiloye, E.O., Ogunsola A.W., On thermal stability of a twostep exothermic chemical reaction in a slab. Journal of Mathematical Sciences, 13, 2013, 115.##[23] Salawu, S.O., Ogunseye, H.A., Olanrewaju, A.M., Dynamical analysis of unsteady poiseuille flow of twostep exothermic nonNewtonian chemical reactive fluid with variable viscosity. International Journal of Mechanical Engineering and Technology, 9(12), 2018, 596605.##[24] Chinyoka T., Computational dynamics of a thermally decomposable viscoelastic lubricant under shear. Journal of Fluids Engineering, 130(12), 2008, 121201(7p).##[25] Salawu, S.O., Oladejo, N.K., Dada, M.S., Analysis of unsteady viscous dissipative poiseuille fluid flow of twostep exothermic chemical reaction through a porous channel with convective cooling. Ain Shams Engineering Journal, doi.org/10.1016/j.asej.2018.08.006.##]
Buckling and Free Vibration Analysis of Fiber Metallaminated Plates Resting on Partial Elastic Foundation
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2
This research presents, buckling and free vibration analysis of fiber metallaminated (FML) plates on a total and partial elastic foundation using the generalized differential quadrature method (GDQM). The partial foundation consists of multisection Winkler and Pasternak type elastic foundation. Taking into consideration the firstorder shear deformation theory (FSDT), FML plate is modeled and its equations of motion and boundary conditions are derived using Hamilton's principle. The formulations include Heaviside function effects due to the nonhomogeneous foundation. The novelty of this study is considering the effects of partial foundation and inplane loading, in addition to considering the various boundary conditions of FML plate. A computer program is written using the present formulation for calculating the natural frequencies and buckling loadings of composite plates without contacting with elastic foundation and composite plates resting on partial foundations. The validation is done by comparison of continuous element model with available results in the literature. The results show that the constant of total or partial spring, elastic foundation parameter, thickness ratio, frequency mode number and boundary conditions play an important role on the critical buckling load and natural frequency of the FML plate resting on partial foundation under inplane force.
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Horae
Moraveji Tabasi
University Complex of Materials and Manufacturing Technology, Malek Ashtar University of Technology, Lavizan, Tehran, Iran
University Complex of Materials and Manufacturing
Iran
horamoraveji1988t@gmail.com


Jafar
Eskandari Jam
Department of Mechanical Engineering, Malek Ashtar University of Technology, Lavizan, Tehran, Iran
Department of Mechanical Engineering, Malek
Iran
jafar.eskandarijam@gmail.com


Keramat
Malekzadeh Fard
Department of Mechanical Engineering, Malek Ashtar University of Technology, Lavizan, Tehran, Iran
Department of Mechanical Engineering, Malek
Iran
k.malekzdeh@gmail.com


Mohsen
Heydari Beni
University Complex of Materials and Manufacturing Technology, Malek Ashtar University of Technology, Lavizan, Tehran, Iran
University Complex of Materials and Manufacturing
Iran
mohsenheydari1371@gmail.com
Partial elastic foundation
FML composite plate
Free vibration
Buckling
GDQ method
[[1] Winkler, E., Die Lehre von der Elasticitaet und Festigkeit: mit besonderer Rücksicht auf ihre Anwendung in der Technik für polytechnische Schulen, Bauakademien, Ingenieue, Maschinenbauer, Architecten, etc. Dominicus, 1867.##[2] Pasternak, P., On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, 1954.##[3] Timoshenko, S., Theory of Elastic Stability 2e. Tata McGrawHill Education, 1970.##[4] Vlasov, V.Z., Beams, plates and shells on elastic foundations. 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Applied Mathematics and Computation, 218(6), 2011, 27722784.##[25] Sobhy, M., Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions, Composite Structures, 99, 2013, 7687.##[26] Dehghany, M., Farajpour, A., Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and threedimensional solution, Engineering Solid Mechanics, 2(1), 2014, 2942.##[27] Thinh, T.I., Nguyen, M.C., Ninh, D.G., Dynamic stiffness formulation for vibration analysis of thick composite plates resting on nonhomogenous foundations, Composite Structures, 108, 2014, 684695.##[28] Mantari, J.L., Free vibration of advanced composite plates resting on elastic foundations based on refined nonpolynomial theory, Meccanica, 50(9), 2015, 23692390.##[29] Gupta, A., Talha, M., Seemann, W., Free vibration and flexural response of functionally graded plates resting on Winkler–Pasternak elastic foundations using nonpolynomial higher order shear and normal deformation theory, Mechanics of Advanced Materials and Structures, 25(6), 2018, 523538.##[30] MoradiDastjerdi, R., MomeniKhabisi, H., Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotubereinforced face sheets resting on Pasternak elastic foundation, Journal of Vibration and Control, 24(11), 2018, 23272343.##[31] Mansouri, M.H., Shariyat, M., Differential quadrature thermal buckling analysis of general quadrilateral orthotropic auxetic FGM plates on elastic foundations, ThinWalled Structures, 112, 2017, 194207.##[32] Reddy, J.N., Mechanics of laminated composite plates and shells: theory and analysis. 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McGrawHill Companies, 1974.##[35] Bracewell, R., Heaviside's Unit Step Functio, The Fourier Transform and Its Applications, 2000, 6165.##[36] Bellman, R., Casti, J., Differential quadrature and longterm integration, Journal of Mathematical Analysis and Applications, 34(2), 1971, 235238.##[37] Bellman, R., Kashef, B., Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, 10(1), 1972, 4052.##[38] Shu, C., Differential quadrature and its application in engineering, Springer Science & Business Media, 2012.##[39] Shu, C., Richards, R.E., Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations, International Journal for Numerical Methods in Fluids, 15(7), 1992, 791798.##[40] Khdeir, A., Free vibration and buckling of symmetric crossply laminated plates by an exact method, Journal of Sound and Vibration, 126(3), 1988, 447461.##[41] Aiello, M.A., Ombres, L., Buckling and vibrations of unsymmetric laminates resting on elastic foundations under inplane and shear forces, Composite Structures, 44(1), 1999, 3141.##]
Melting Heat Transfer Analysis on Magnetohydrodynamics Buoyancy Convection in an Enclosure: A Numerical Study
2
2
The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra), melting parameter (M) and Hartmann number (Ha) are graphically illustrated. As melting parameter and Rayleigh number increase, the rate of fluid flow and temperature gradients also increase. And in the presence of magnetic field, the temperature gradient reduces and hence, the conduction mechanism is dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with nonuniform case. The average Nusselt number reduces with increasing magnetic parameter in the both cases of heating of bottom wall.
1

52
62


K.
Venkatadri
Department of Mathematics, VEMU Institute of Technology, P. Kothakota, India
Department of Mathematics, VEMU Institute
Iran
venkatadri.venki@gmail.com


Shaik
Abdul Gaffar
Department of Information Technology, Mathematics Section, Salalah College of Technology, Salalah, Oman
Department of Information Technology, Mathematics
Iran
abdulsgaffar0905@gmail.com


M.
Suryanarayana Reddy
Department of Mathematics, JNTUA College of Engineering, Pulivendula, India
Department of Mathematics, JNTUA College
Iran
abdulsgaffar143@gmail.com


V.
Ramachandra Prasad
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India
Department of Mathematics, School of Advanced
Iran
rcpmaths@gmail.com


B. Md. Hidayathulla
Khan
Department of Mathematics, Sir Vishveshwaraiah Institute of Science and Technology, Madanapalle, India
Department of Mathematics, Sir Vishveshwaraiah
Iran
bmdhkh@gmail.com


Osman
Anwar Beg
Magnetohydrodynamics, Biological Propulsion and Energy Research, Aeronautical and Mechanical Engineering Division, University of Salford, M5 4WT, UK
Magnetohydrodynamics, Biological Propulsion
Iran
gortoab@gmail.com
Natural convection
Square enclosure
Finite difference method
Incompressible flow
Melting heat transfer
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Ed., 30(9), 2009, 1113–1120.##[23] Rahman, M.M., Öztop, H.F., Saidur, R., Naim, A.G., AlSalem, K.S., Ibrahim, T.A., Magnetohydrodynamic timedependent computational natural convection flow, heat and mass transfer in inclined semicircular enclosures, International Journal of Numerical Methods for Heat & Fluid Flow, 26(8), 2016, 23102330.##[24] Doostani, A., Ghalambaz, M., Chamkha, A.J, MHD natural convection phase‑change heat transfer in a cavity: analysis of the magnetic field effect, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(7), 2017, 2831–2846. ##[25] Arun, S., Satheesh, A., Mesoscopic analysis of MHD double diffusive natural convection and entropy generation in an enclosure filled with liquid metal, Journal of the Taiwan Institute of Chemical Engineers, 95, 2019, 155173.##[26] Saravanan, S., Sivaraj, C., Natural convection in an enclosure with a localized nonuniform heat source on the bottom wall, International Journal of Heat and Mass Transfer, 54, 2011, 2820–2828.##[27] Saravanan, S., Sivaraj, C., Combined natural convection and thermal radiation in a square cavity with a nonuniformly heated plate, Computers & Fluids, 117, 2015, 125–138.##[28] Uddin, M.B., Rahman, M.M., Khan, M.A.H., Saidur, R., Ibrahim, T.A., Hydromagnetic doublediffusive mixed convection in trapezoidal enclosure due to uniform and nonuniform heating at the bottom side: Effect of Lewis number, Alexandria Engineering Journal, 55, 2016, 1165–1176.##[29] Ghaffarpasand, O., Numerical study of MHD natural convection inside a sinusoidally heated liddriven cavity filled with Fe3 O4 water nanofluid in the presence of Joule heating, Applied Mathematical Modelling, 40, 2016, 9165–9182.##[30] Sheikholeslami, M., Oztop, H.F., MHD free convection of nanofluid in a cavity with sinusoidal walls by using CVFEM, Chinese Journal of Physics, 55, 2017, 2291–2304.##[31] Cheong, H.T., Siri, Z., Sivasankaran, S., Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition, International Communications in Heat and Mass Transfer, 45, 2013, 75–85.##[32] Hussain, S.H., Analysis of heatlines and entropy generation during doublediffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure, Engineering Science and Technology, an International Journal, 19, 2016, 926–945.##[33] Agyenim, F., Hewitt, N., Eames, P., Smyth, M., A review of materials, heat transfer and phase change problem formulation for latent heat thermal energy storage systems (LHTESSs), Renewable & Sustainable Energy Reviews, 14, 2010, 615–28.##[34] Sharma, R.K., Ganesan, P., Tyagi, V.V., Metselaar, H.S.C., Sandaran, S.C., Developments in organic solid–liquid phase change materials and their applications in thermal energy storage, Energy Conversion and Management, 95, 2015, 193–228.##[35] Shalaby, S.M., Bek, M.A., Experimental investigation of a novel indirect solar dryer implementing PCM as energy storage medium, Energy Conversion and Management, 83, 2014, 1–8.##[36] Memon, S.A., Phase change materials integrated in building walls: a state of the art review, Renewable & Sustainable Energy Reviews, 31, 2014, 870–906.##[37] Xu, H.T., Wang, T.T., Qu, Z.G., Chen, J., Li, B.B., Lattice Boltzmann simulation of the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium, International Communications in Heat and Mass Transfer, 81, 2017, 104115.##[38] Ren, Q., Chan, C.L., GPU accelerated numerical study of PCM melting process in an enclosure with internal fins using lattice Boltzmann method, International Journal of Heat and Mass Transfer, 100, 2016, 522535.##[39] Ren, Q., Meng, F., Guo, P., A comparative study of PCM melting process in a heat pipeassisted LHTES unit enhanced with nanoparticles and metal foams by immersed boundarylattice Boltzmann method at porescale, International Journal of Heat and Mass Transfer, 121, 2018, 12141228.##[41] Jiang, Z.Y., Qu, Z.G., Lithium–ion battery thermal management using heat pipe and phase change material during discharge–charge cycle: A comprehensive numerical study, Applied Energy, 242, 2019, 378392.##[41] Zhu, Z.Q., Huang, Y.K., Hu, N., et al. Transient performance of a PCMbased heat sink with a partially filled metal foam: Effects of the filling height ratio, Applied Thermal Engineering, 128, 2018, 966972.##[42] Ren, Q., Enhancement of nanoparticlephase change material melting performance using a sinusoidal heat pipe, Energy Conversion and Management, 180, 2019, 784795.##[43] Sathiyamoorthy, M., Chamkha, A.J., Natural convection flow under magnetic field in a square cavity for uniformly (or) linearly heated adjacent walls, International Journal of Numerical Methods for Heat & Fluid Flow, 22, 2012, 677–98.##[44] Gibanov, N.S., Sheremet, M.A., Pop, I., Free convection in a trapezoidal cavity filled with a micropolar fluid, International Journal of Heat and Mass Transfer, 99, 2016, 831–838.##[45] Sheikholeslami, M., Rokni, H.B., Melting heat transfer influence on nanofluid flow inside a cavity in existence of magnetic field, International Journal of Heat and Mass Transfer, 114, 2017, 517–526.##[46] Erturk, E., Gokcol, C., Fourthorder compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids, 50, 2006, 421–436##]
Nonlocal Elasticity Effect on Linear Vibration of Nanocircular Plate Using Adomian Decomposition Method
2
2
In this study, the small scale effect on the linear freefield vibration of a nanocircular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theory was extracted from Hamilton principle while the inertial effect, as well as the shear stresses effect was ignored. Effect of nonlocal parameter is investigated by solving the governing equation using Adomian decomposition method (ADM) for the clamped and simply supported boundary conditions. By using this method, the first five axisymmetric natural frequencies and displacements of nanocircular plate are obtained one at a time and some numerical results are given to illustrate the influence of nonlocal parameters on the natural frequencies and displacements of the nanocircular plate. For the purpose of comparison, the linear equations were solved by the analytical method. Excellent agreements were observed between the two methods. This indicates that the latter method can be applied to seek the linear solution of nanocircular plates with high accuracy while simplifying the problem.
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63
76


Mohammad
Shishesaz
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Golestan Blvd., Ahvaz, 6135743337, Iran
Mechanical Engineering Department, Faculty
Iran
mshishehsaz@scu.ac.ir


Mojtaba
Shariati
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Golestan Blvd., Ahvaz, 6135743337, Iran
Mechanical Engineering Department, Faculty
Iran
mojtabashariati@stu.scu.ac.ir


Amin
Yaghootian
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Golestan Blvd., Ahvaz, 6135743337, Iran
Mechanical Engineering Department, Faculty
Iran
a.yaghootian@scu.ac.ir
Linear free vibration
Nanocircular plates
Nonlocal elasticity
Adomian decomposition method
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Applied Mathematics and Computation. 217(7), 2010, 342941.##[44] Mao Q, Pietrzko S. Free vibration analysis of a type of tapered beams by using Adomian decomposition method. Applied Mathematics and Computation. 219(6), 2012, 326471.##[45] Jamali M, Shojaee T, Kolahchi R, Mohammadi B. Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials. Steel and Composite Structures. 22(3), 2016, 691712.##[46] Karlicic D, Murmu T, Adhikari S, McCarthy M. Nonlocal structural mechanics: John Wiley & Sons; 2015.##[47] Wang Q, Han Q, Wen B. Estimate of material property of carbon nanotubes via nonlocal elasticity. Advances in Theoretical and Applied Mechanics. 1(1), 2008, 110.##[48] Wang Q, Wang C. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology. 18(7), 2007, 075702.##[49] Duan W, Wang C, Zhang Y. Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics. Journal of Applied Physics. 101(2), 2007, 024305.##[50] Li C, Lai S, Yang X. On the nanostructural dependence of nonlocal dynamics and its relationship to the upper limit of nonlocal scale parameter. Applied Mathematical Modelling. 69, 2019, 12741.##[51] Shodja H, Ahmadpoor F, Tehranchi A. Calculation of the additional constants for fcc materials in second strain gradient elasticity: behavior of a nanosize BernoulliEuler beam with surface effects. Journal of Applied Mechanics. 79(2), 2012, 021008.##[52] Timoshenko SP, WoinowskyKrieger S. Theory of plates and shells: McGrawhill; 1959.##[53] Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis: CRC press; 2004.##[54] Wazwaz AM. A reliable modification of Adomian decomposition method. Applied Mathematics and Computation. 102(1), 1999, 7786.##[55] Wazwaz AM. Partial differential equations and solitary waves theory: Springer Science & Business Media; 2010.##[56] Leissa AW. Vibration of Plates, Office of Technology Utilization. National Aeronautics and Space Administration, Washington, DC. 1969.##]
Exploration of the Significance of Autocatalytic Chemical Reaction and CattaneoChristov Heat Flux on the Dynamics of a Micropolar Fluid
2
2
During the homogeneousheterogeneous autocatalytic chemical reaction in the dynamics of micropolar fluid, relaxation of heat transfer is inevitable; hence CattaneoChristov heat flux model is investigated in this report. In this study, radiative heat flux through an optically thick medium is treated as nonlinear due to the fact that thermal radiation at low heat energy is distinctly different from that of high heat energy, hence classical approach of using Taylor series for simplification is ignored and implicit differentiation is used leading to temperature parameter. Uniqueness of the present analysis is the consideration of cubic autocatalytic chemical reaction between the homogeneous bulk fluid and two species of catalyst at the wall. Application of similarity analysis enabled us to recast the flow equations into a set of coupled nonlinear ODEs. The resulting equations along with the appropriate conditions are solved computationally. Graphical illustrations of the effect of pertinent parameters on momentum, heat and mass boundary layers are presented and discussed. The concentration of the homogeneous bulk fluid with microstructures and catalyst at the surface decreases and increases with diffusion ratio, respectively. Buoyancy has a decreasing effect on temperature distribution.
1

77
89


G.
Sarojamma
Department of Applied Mathematics, Sri Padmavati Mahila University, Tirupati51752, India
Department of Applied Mathematics, Sri Padmavati
Iran
gsarojamma@gmail.com


R.
Vijaya Lakshmi
Department of Applied Mathematics, Sri Padmavati Mahila University, Tirupati51752, India
Department of Applied Mathematics, Sri Padmavati
Iran
vijayalakshmirayanki@gmail.com


P.V.
Satya Narayana
Department of Mathematics, SAS, VIT, Vellore63, India
Department of Mathematics, SAS, VIT, Vellore63,
Iran
pvsatya8@yahoo.co.in


I.L.
Animasaun
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
Department of Mathematical Sciences, Federal
Iran
anizakph2007@gmail.com
Boundary layer flow
Nonlinear thermal radiation
Auto catalysis
CattaneoChristov heat flux
[[1] Fourier, J.B.J., Theorieanalytique De La Chaleur, Paris: Chez Firmin Didot, 1822.##[2] Cattaneo, C., Sulla conduzionedelcalore, Atti Del SeminarioMaermaticoe Fisico dell Universita di Modena e Reggio Emilia, 3, 1948, 83101.##[3] Christov, C.I., On frame indifferent formulation of the MaxwellCattaneo model of finitespeed heat conduction. Mechanics Research Communications, 36, 2009, 481486.##[4] Hayat, T., Farooq, M., Alsaedi, A., AlSolamy, F., Impact of CattaneoChristov heat flux in the flow over a stretching sheet with variable thickness. AIP Advances, 5, 2015, 0871591.##[5] Li, J., Zheng, L., Liu, L., MHD viscoelastic flow and heat transfer over a vertical stretching sheet with CattaneoChristov heat flux effects. Journal of Molecular Liquids, 221, 2016, 1925.##[6] Muhammad, N., Nadeem, S., Mustafa, T., Squeezed flow of a nanofluid with CattaneoChristov heat and mass fluxes. Results in Physics, 7, 2017, 862869.##[7] Gnaneswara Reddy, M., Rama Subba Reddy, G., Micropolar fluid flow over a nonlinear stretching convectively heated vertical surface in the presence of CattaneoChristov heat flux and viscous dissipation. Frontiers in Heat and Mass Transfer, 8, 2017, 19.##[8] Khan, S.M., Hammad, M., Sunny, D.A., Chemical reaction, thermal relaxation time and internal material parameter effects on MHD viscoelastic fluid with internal structure using the CattaneoChristov heat flux equation. European Physical Journal Plus, 132, 2017, 111.##[9] Ramadevi, B., Ramana Reddy, J.V., Sugunamma, V., Sandeep, N., Combined influence of viscous dissipation and nonuniform heat source/sink on MHD nonNewtonian fluid flow with CattaneoChristov heat flux. Alexandria Engineering Journal, 57(2), 2018, 10091018##[10] Khan, M.I., Waqas, M., Hayat, T., Khan, M.I., Alsaedi. A., Chemically reactive flow of upperconvected Maxwell fluid with CattaneoChristov heat flux model. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 2017, 45714578.##[11] Zhang, Y., Zhang, M., Bai, Y., Unsteady flow and heat transfer of powerlaw nanofluid thin film over a stretching sheet with variable magnetic field and powerlaw velocity slip effect. Journal of the Taiwan Institute of Chemical Engineers,70, 2017, 104110.##[12] Zhang, Y., Zhang, M., Bai, Y., Flow and heat transfer of an OldroydB nanofluid thin film over an unsteady stretching sheet. Journal of Molecular Liquids, 220, 2016, 665670.##[13] Ramzan, M., Bilal, M., Chung, J.D., Influence of homogeneousheterogeneous reactions on MHD 3D Maxwell fluid flow with CattaneoChristov heat flux and convective boundary condition. Journal of Molecular Liquids, 230, 2017, 415422.##[14] Ramzan, M., Bilal, M., Chung, J.D., MHD stagnation point CattaneoChristov heat flux in Williamson fluid flow with homogeneousheterogeneous reactions and convective boundary condition—A numerical approach. Journal of Molecular Liquids, 225, 2017, 856862.##[15] Ramzan, M., Bilal, M., Chung, J.D., Effects of MHD homogeneousheterogeneous reactions on third grade fluid with CattaneoChristov heat flux. Journal of Molecular Liquids, 223, 2016, 12841290.##[16] Lu, D., Li, Z., Ramzan, M., Shafee, A., Jae Dong Chung, Unsteady squeezing carbon nanotubes based nanoliquid flow with CattaneoChristov heat flux and homogeneousheterogeneous reactions. Applied Nanoscience, 9, 2019, 169178.##[17] Lu, D., Ramzan, M., Ahmad S., Chung, J.D., Farooq, U., A numerical treatment of MHD radiative flow of Micropolar nanofluid with homogeneousheterogeneous reactions past a nonlinear stretched surface. Scientific Reports, 8, 2018, 117.##[18] Lu, D., Ramzan, M., Ahmad, S., Chung, J.D., Farooq, U., Upshot of binary chemical reaction and activation energy on carbon nanotubes with CattaneoChristov heat flux and buoyancy effects. Physics of Fluids, 29, 2018, 123103.##[19] Lu, D., Ramzan, M., Ullah, N., Chung, J.D., Farooq, U., A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy. Scientific Reports, 7, 2017, 17008.##[20] Ramzan, M., Ullah, N., Chung, J.D., Lu, D., Farooq, U., Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction. Scientific Reports, 7, 2017, 12901.##[21] Zhang, Y., Yuan, B., Bai, Y., Cao, Y., Shen, Y., Unsteady CattaneoChristov double diffusion of OldroydB fluid thin film with relaxationretardation viscous dissipation and relaxation chemical reaction. Powder Technology, 338, 2018, 975982.##[22] Chaudhary, M.A., Merkin, J.H., A simple isothermal model for homogeneousheterogeneous reactions in boundarylayer flow. I equal diffusivities. Fluid Dynamics Research, 16, 1995, 311333.##[23] Koriko, O.K., Omowaye, A.J., Sandeep, N., Animasaun, I.L., Analysis of boundary layer formed on an upper horizontal surface of a paraboloid of revolution within nanofluid flow in the presence of thermophoresis and Brownian motion of 29 nm CuO. International Journal of Mechanical Sciences, 124125, 2017, 2236.##[24] Koriko, K., Animasaun, I.L., New similarity solution of micropolar fluid flow problem over an uhspr in the presence of quartic kind of autocatalytic chemical reaction. Frontiers in Heat and Mass Transfer, 8, 2017, 113.##[25] Makinde, O.D., Animasaun, I.L., Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution. International Journal of Thermal Sciences, 109, 2016, 159171.##[26] Ramzan, M., Chung, J.D., Ullah, N., Radiative Magnetohydrodynamic nanofluid flow due to gyrotactic microorganisms with chemical reaction and nonlinear thermal radiation. International Journal of Mechanical Sciences, 130, 2017, 3140.##[27] Hayat, T., Zubair, M., Waqas, M., Alsaedi, A., Ayub, M., On doubly stratified chemically reactive flow of Powell–Eyring liquid subject to nonFourier heat flux theory. Results in Physics, 7, 2017, 99106.##[28] Hayat, T., Kiran, A., Imtiaz, M., Alsaedi, A., Unsteady flow of carbon nanotubes with chemical reaction and CattaneoChristov heat flux model. Results in Physics, 7, 2017, 823831.##[29] Satya Narayan, P.V., Tarakaramu, N., Makinde, O.D., Venkateswarlu, B., Sarojamma, G., MHD Stagnation Point Flow of Viscoelastic Nanofluid Past a Convectively Heated Stretching Surface. Defect Diffusion Forum, 387, 2018, 106120.##[30] Sarojamma, G., Vijaya Lakshmi, R., Satya Narayana, P.V., Makinde, O.D., Nonlinear radiative flow of a micropolar nano fluid through a vertical channel with porous collapsible walls. Defect Diffusion Forum, 387, 2018, 498509.##[31] Vajravelu, K., Li, R., Dewasurendra, M., Benarroch, J., Ossi, N., Zhang, Y., Sammarco, M., Prasad, K.V., Analysis of MHD boundary layer flow of an UpperConvected Maxwell fluid with homogeneousheterogeneous chemical reactions. Communications in Numerical Analysis, 2, 2017, 202216.##[32] Ramzan, M., Bilal, M., Chung, J.D., Effects of MHD homogeneousheterogeneous reactions on third grade fluid flow with CattaneoChristov heat flux. Journal of Molecular Liquids, 223, 2016, 12841290.##[33] Hashim, Khan, M., On CattaneoChristov heat flux model for Carreau fluid flow over a slandering sheet. Results in Physics, 7, 2017, 310319.##[34] Sarkar, A., Kundu, P.K., Exploring the CattaneoChristov heat flux phenomenon on a Maxwelltype nanofluid coexisting with homogeneous/heterogeneous reactions. European Physical Journal Plus, 132, 2017, 534.##[35] Grubka L.J, Bobba K.M. Heat transfer characteristics of a continuous stretching surface with variable temperature. Journal of Heat Transfer, 107, 1985, 248250.##[36] Ishak, I., Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica, 45, 2010, 367373.##[37] Keimanesh, R., Aghanajafi, C., The effect of temperature dependent viscosity and thermal conductivity on micropolar fluid over a stretching sheet. Tehnickivjesnik, 24, 2017, 371378.##[38] Animasaun, I.L., Raju, C.S.K., Sandeep, N., Unequal diffusivities case of homogeneousheterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic field and nonlinear thermal radiation. Alexandria Engineering Journal, 55, 2016, 15951606.##[39] Shah, N.A., Animasaun, I.L., R O Ibraheem, Babatund, H.A., Sandeep, N., Pop, I., Scrutinization of the effects of Grashof number on the flow of different fluids driven by convection over various surfaces. Journal of Molecular Liquids, 249, 2018, 980990.##[40] Li, J., Zheng, L., Liu, L., MHD viscoelastic flow and heat transfer over a vertical stretching sheet with CattaneoChristov heat flux effects. Journal of Molecular Liquids, 221, 2016, 1925.##[41] Khan, S.M., Hammad, M., Sunny, D.A., Chemical reaction, thermal relaxation time and internal material parameter effects on MHD viscoelastic fluid with internal structure using the CattaneoChristov heat flux equation. European Physical Journal Plus, 132, 2017, 338.##]
Stress Redistribution Analysis of Piezomagnetic Rotating ThickWalled Cylinder with Temperatureand MoistureDependent Material Properties
2
2
In this article, the problem of timedependent stress redistribution of a piezomagnetic rotating thickwalled cylinder under an axisymmetric hygrothermomagnetoelectromechanical loading is analyzed analytically for the condition of plane strain. Using the constitutive equations, a differential equation is found in which there are creep strains. Primarily, eliminating creep strains, an analytical solution for the primitive electric and magnetic potential in addition to stresses is obtained. Then, creep strains are kept and creep stress rates are found by utilizing Norton’s law and PrandtlReuss equations for steadystate hygrothermal boundary condition. Lastly, the history of stresses and radial displacement as well as magnetic and potential fields during the time is obtained using an iterative method. In the numerical examples, the effect of angular velocity, hygrothermal loading and thermal and moisture concentration dependency of elastic constants is investigated comprehensively.
1

90
104


Mahdi
Saadatfar
Department of Mechanical Engineering, University of Qom, Qom, P.O. Box 3716146611, Iran
Department of Mechanical Engineering, University
Iran
m.saadatfar@gmail.com
Hollow cylinder
Piezomagnetic
Hygrothermal condition
Timedependent analysis
[[1] Smittakorn, W., Heyliger, P.R., A discretelayer model of laminated hygrothermopiezoelectric plates, Mechanics of Composite Materials and Structures, 7, 2000, 79104.##[2] Raja, S., Sinha, P.K., Prathap, G., Dwarakanthan, D., Thermally induced vibration control of composite plates and shells with piezoelectric active damping, Smart Materials and Structures,13, 2004, 939950.##[3] Allam, M.N.M., Zenkour, A.M., Tantawy, R., Analysis of Functionally Graded Piezoelectric Cylinders in a Hygrothermal Environment, Advances in Applied Mathematics and Mechanics, 6, 2014, 233246.##[4] Saadatfar, M., AghaieKhafri, M., Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an elastic foundation, Smart Materials and Structures, 23, 2014, 113.##[5] Saadatfar, M., AghaieKhafri, M., Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation, Aerospace Science and Technology, 43, 2015, 3750.##[6] Saadatfar, M., AghaieKhafri, M., On the behavior of a rotating functionally graded hybrid cylindrical shell with imperfect bonding subjected to hygrothermal condition, Journal of Thermal Stresses, 38, 2015, 854881.##[7] Saadatfar, M., Effect of multiphysics conditions on the behavior of an exponentially graded smart cylindrical shell with imperfect bonding, Meccanica, 50, 2015, 2135–2152.##[8] Zenkour, A.M., Bending analysis of piezoelectric exponentially graded fiberreinforced composite cylinders in hygrothermal environments, International Journal of Mechanics and Materials in Design, 13, 2017, 515529.##[9] Vinyas, M., Kattimani, S., Hygrothermal Analysis of MagnetoElectroElastic Plate using 3D Finite Element Analysis, Composite Structures, 180, 2017, 617637.##[10] Hou, P.F., Leung, A.W.T., The transient responses of magnetoelectroelastic hollow cylinders. Smart Materials and Structures, 13, 2004, 762.##[11] Wang, H.M., Ding, H.J., Transient responses of a special nonhomogeneous magnetoelectroelastic hollow cylinder for a fully coupled axisymmetric plane strain problem, Acta Mechanica, 184, 2006, 137–157.##[12] Babaei, M.H., Chen, Z.T., Exact solutions for radially polarized and magnetized magneto electro elastic rotating cylinders, Smart Materials and Structures, 17, 2008, 025035.##[13] Ootao, Y., Ishihara, M., Exact Solution of Transient Thermal Stress Problem of a Multilayered MagnetoElectroThermoelastic Hollow Cylinder, Applied Mathematical Modelling, 5, 2011, 90103.##[14] Akbarzadeh, A.H., Chen, Z.T., Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading, Smart Materials and Structures, 21, 2012, 125013.##[15] Loghman, A., Ghorbanpour Arani, A., Amir, A.S., Vajedi, A., Magnetothermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessels and Piping, 87, 2011, 389395.##[16] Singh, T., Gupta, V.K., Effect of anisotropy on steady state creep in functionally graded cylinder, Composite Structures, 93, 2011, 747758.##[17] Sharma, S., Sahay, I., Kumar, R., Creep transition in non homogeneous thickwalled circular cylinder under internal and external pressure, Applied Mathematical Sciences, 122, 2012, 60756080.##[18] Loghman, A., Atabakhshian, V., Semianalytical solution for timedependent creep analysis of rotating cylinders made of anisotropic exponentially graded material (EGM), Journal of Solid Mechanics, 4, 2012, 313326.##[19] Jamian, S., Sato, H., Tsukamoto, H., Watanabe, Y., Creep analysis of functionally graded material thickwalled cylinder, Applied Mechanics and Materials, 315, 2013, 867871.##[20] Nejad, M.Z., Kashkoli, M.D., Timedependent thermocreep analysis of rotating FGM thickwalled cylindrical pressure vessels under heat flux, International Journal of Engineering Science, 82, 2014, 222–237.##[21] Singh, T., Gupta, V.K., Analysis of steady state creep in whisker reinforced functionally graded thick cylinder subjected to internal pressure by considering residual stress, Mechanics of Advanced Materials and Structures, 21, 2014, 384392.##[22] Nejad, M.Z., Hoseini, Z., Niknejad, A., Ghannad, M., Steadystate creep deformations and stresses in FGM rotating thick cylindrical pressure vessels, Journal of Mechanics, 31, 2015, 16.##[23] Kashkoli, M.D., Tahan, K.N., Nejad, M.Z., Timedependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under nonuniform internal pressure, International Journal of Applied Mechanics, 9, 2017, 750086.##[24] Kashkoli, M.D., Tahan, K.N., Nejad, M.Z., Timedependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory, Journal of Mechanics, 33, 2017, 461474.##[25] Sharma, S., Yadav, S., Sharma, R., Thermal creep analysis of functionally graded thickwalled cylinder subjected to torsion and internal and external pressure, Journal of Solid Mechanics, 9, 2017, 302318.##[26] Bakhshizadeh, A., Nejad, M.Z., Kashkoli, M.D., TimeDependent HygroThermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field, Journal of Solid Mechanics, 9, 2017, 663679.##[27] Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A.A., Loghman, A., TimeDependent ThermoElectroMechanical Creep Behavior of Radially Polarized FGPM Rotating Cylinder, Journal of Solid Mechanics, 3, 2011, 142157.##[28] Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R., Mozdianfard, M.R., Loghman, A., Semianalytical solution of timedependent electrothermomechanical creep for radially polarized piezoelectric cylinder, Computers and Structures, 89, 2011, 1494–1502.##[29] Saadatfar, M., AghaieKhafri, M., On the magnetothermoelastic behavior of a FGM cylindrical shell with pyroelectric layers featuring interlaminar bonding imperfections rested in an elastic foundation, Journal of Solid Mechanics, 7, 2015, 344363.##[30] Saadatfar, M., Razavi, A.S., Piezoelectric hollow cylinder with thermal gradient, Journal of Mechanical Science and Technology, 23, 2009, 4553.##[31] Chang, W.J., Transient hygrothermal responses in a solid cylinder by linear theory of coupled heat and moisture, Applied Mathematical Modelling, 18, 1994, 467473.##[32] Saadatfar, M., AghaieKhafri, M., Thermoelastic analysis of a rotating functionally graded cylindrical shell with functionally graded sensor and actuator layers on an elastic foundation placed in a constant magnetic field, Journal of Intelligent Materials Systems and Structures, 27, 2015, 512527.##[33] Saadatfar, M., Effect of Interlaminar Weak Bonding and Constant Magnetic Field on the Hygrothermal Stresses of a FG Hybrid Cylindrical Shell Using DQM, Journal of Stress Analysis, 3, 2018, 93110.##[34] Dai, H.L., Jiang, H.J., Yang, L., Timedependent behaviors of a FGPM hollow sphere under the coupling of multifields Solid State Sciences, Solid State Sciences, 14, 20112, 587597.##[35] Loghman, A., Abdollahian, M., Jafarzadeh Jazi, A., Ghorbanpour Arani, A., Semianalytical solution for electromagnetothermoelastic creep response of functionally graded piezoelectric rotating disk, International Journal of Thermal Sciences, 65, 2013, 254266.##]
The Development and Application of the RCW Method for the Solution of the Blasius Problem
2
2
In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (RahmanzadehCaiWhite) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common numerical methods, the answer is considered only as a Taylor series. It should be noted that in these algorithms which use Taylor expansion, the values of the truncation error are considerable. However, adding the Fourier series to the Taylor series leads to reduce the amount of the truncation error. Nevertheless, the results of this research show the RCW method has the ability to achieve the accuracy of analytical solution. Moreover, it is well illustrated that the accuracy of RCW method is higher than the RungeKutta one.
1

105
111


Mostafa
Rahmanzadeh
Department of Chemical Engineering, Sirjan University of Technology, Sirjan, Iran
Department of Chemical Engineering, Sirjan
Iran
rahmanzadeh.mostafa@gmail.com


Tahereh
Asadi
Department of Chemical Engineering, Sirjan University of Technology, Sirjan, Iran
Department of Chemical Engineering, Sirjan
Iran
t62.asasdi@yahoo.com


Meysam
Atashafrooz
Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran
Department of Mechanical Engineering, Sirjan
Iran
m.atashafrooz@sirjantech.ac.ir
Boundary layer
Blasius equation
Initial value problems
RCW method
[[1] Ahmadi, G., Selfsimilar solution of incompressible micropolar boundary layer flow over a semiinfinite plate, International Journal of Engineering Science, 14(7), 1976, 639646.##[2] Fang, T., A note on the unsteady boundary layers over a flat plate, International Journal of NonLinear Mechanics, 43(9), 2008, 10071011.##[3] Aziz, A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Communications in Nonlinear Science Numerical Simulation, 14(4), 2009, 10641068.##[4] Li, Y., Rao, Y., Wang, D., Zhang, P. and Wu, X., Heat transfer and pressure loss of turbulent flow in channels with miniature structured ribs on one wall, International Journal of Heat and Mass Transfer, 131, 2019, 584593.##[5] Ushida, A., Shuichi Ogawa, S., Narumi, T., Sato, T. and Hasegawa T., Pseudolaminarization effect of dilute and ultradilute polymer solutions on flows in narrow pipes, Experimental Thermal Fluid Science, 99, 2018, 233241.##[6] Najafi, E., Numerical quasilinearization scheme for the integral equation form of the Blasius equation, Computational Methods for Differential Equations, 6(2), 2018, 141156.##[7] Sewell, G., The numerical solution of ordinary and partial differential equations, John Wiley & Sons, New York, 2005.##[8] Parand, K., Dehghan, M. and Pirkhedri, A., Sinccollocation method for solving the Blasius equation, Physics Letters A, 373(44), 2009, 40604065.##[9] Iacono, R. and Boyd, J. P., Simple analytic approximations for the Blasius problem, Physica D: Nonlinear Phenomena, 310, 2015, 7278.##[10] Cortell, R., Numerical solutions of the classical Blasius flatplate problem, Applied Mathematics and Computation, 170(1), 2005, 706710.##[11] Chavaraddi, K. B. and Page, M. H., Solution of Blasius equation by adomian decomposition Mmethod and differential transform method, International Journal of Mathematics and its Applications, 55, 2018, 219–1226##[12] Jafarimoghaddam, A. and Aberoumand, S., Exact approximations for skin friction coefficient and convective heat transfer coefficient for a class of power law fluids flow over a semiinfinite plate: Results from similarity solutions, Engineering Science and Technology, An International Journal, 20(3), 2017, 11151121.##[13] Benlahsen, M., Guedda, M. and Kersner, R., The generalized Blasius equation revisited, Mathematical and Computer Modelling, 47(910), 2008, 10631076.##[14] Wang, L., A new algorithm for solving classical Blasius equation, Applied Mathematics and Computation, 157(1), 2004, 19.##[15] Munson, B. R., Okiishi, T. H., Huebsch, I. W. W., Rothmayer, A. P., Fundamentals of fluid mechanics, Wiley Singapore, 2013.##[16] White, F. M., Fluid mechanics, McGrawhill, 1986.##[17] Brugnano, L. and Magherini, C., Blended implementation of block implicit methods for ODEs, Applied Numerical Mathematics, 42(13), 2002, 2945.##[18] Ibáñez, J. J., Hernández, V., Ruiz, P. A. and Arias, E., A piecewiselinearized algorithm based on the Krylov subspace for solving stiff ODEs, Journal of Computational Applied Mathematics, 235(7), 2011, 17981804.##[19] Brugnano, L., Magherini, C. and Mugnai, F., Blended implicit methods for the numerical solution of DAE problems, Journal of Computational Applied Mathematics, 189(12), 2006, 3450.##[20] Fazio, R., A novel approach to the numerical solution of boundary value problems on infinite intervals, SIAM Journal on Numerical Analysis, 33(4), 1996, 14731483.##[21] Fang, T., Guo, F. and Chiafon, F. L., A note on the extended Blasius equation, Applied Mathematics Letters, 19(7), 2006, 613617.##[22] Catal, S., Some of semi analytical methods for Blasius problem, Applied Mathematics, 3(7), 2012, 724728.##[23] Rahmanzadeh, M., Cai, L., and White, R. E., A new method for solving initial value problems, Computers and Chemical Engineering, 58, 2013, 3339.##[24] Nelder, J. A. and Mead, R., A simplex method for function minimization, The Computer Journal, 7(4), 1965, 308313.##[25] Bock, H. G., Diehl, M. M., Leineweber, D. B., Schlöder, J. P., Nonlinear Model Predictive Control, Birkhiiuser Verlag Basel, Switzerland, 2000.##[26] Rahmanzadeh, M. and Barfeie, M., An explicit timestepping method based on error minimization for solving stiff system of ordinary differential equations, Malaysian Journal of Mathematical Sciences, 12(2), 2018, 267283.##[27] Ahmad, F. and AlBarakati, W. H., An approximate analytic solution of the Blasius problem, Communications in Nonlinear Science Numerical Simulation, 14(4), 2009, 10211024.##]
Upgrading the Seismic Capacity of PileSupported Wharfs Using SemiActive Liquid Column Gas Damper
2
2
One of the most important structures in the ports is the wharf. The most common one is the pilesupported wharf. This type of wharf is consisted of a number of piles and one deck which placed on the piles. In addition to the conventional loads that this structure should withstand, in seismic areas, pilesupported wharfs should have the necessary capacity and strength against seismic excitations. There are some approaches to increase the seismic capacity of the berth. One of these methods is to control the vibrations of the pilesupported wharf against earthquake loads using a damper. In this research, for the first time, a new semiactive damper called the semi active liquid column gas damper (SALCGD), was used to reduce the response of pile supported wharf under seismic loads. In the first step by applying different records of the earthquake, the most important parameter of this damper  the optimal opening ratio of the horizontal column was obtained for this particular structure. In the following, the performances of this damper and its comparison with the tuned liquid column gas damper (TLCGD) were discussed. This study showed that the use of this semiactive damper (SALCGD) reduces the displacement of the pilesupported wharf by 35% and reduces the acceleration of the structure by 50% on average. In contrast, the passive damper (TLCGD) reduces the displacement of about 20 percent and the acceleration of about 30 percent. Therefore, it was observed that the semiactivation of the damper (SALCGD) had a significant improvement in its performance in controlling the vibrations of pilesupported wharf.
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Reza
Dezvareh
Assistant Professor, Faculty of Civil Engineering, Babol Noshirvani University of Technology, Shariati Av., Babol, Mazandaran, 47148  71167, Iran
Assistant Professor, Faculty of Civil Engineering,
Iran
rdezvareh@nit.ac.ir
PileSupported wharf
SALCGD
Seismic capacity
Vibration control
[[1] Gerolymos, N., Giannakou, A., Anastasopoulos, I. and Gazetas, G., Evidence of beneficial role of inclined piles: observations and summary of numerical analyses. Bulletin of Earthquake Engineering, 6(4), 2008, 705722.##[2] Poulos, H.G., Raked piles—Virtues and drawbacks. Journal of Geotechnical and Geoenvironmental Engineering, 132(6), 2006, 795803.##[3] Oyenuga, D., Abrahamson, E., Krimotat, A., Kozak, A., Labasco, T. and Lobedan, F., A study of the pilewharf deck connection at the Port of Oakland. In Ports' 01: America's Ports: Gateway to the Global Economy, 2001, 110.##[4] Mageau, D. and Chin, K., Effectiveness of stone columns on slope deformations beneath wharves. In TCLEE 2009: Lifeline Earthquake Engineering in a Multihazard Environment, 2009, 112.##[5] Soong, T.T. and Dargush, G.F., Passive Energy Dissipation Systems in Structural Engineering Wiley. Chichester, UK, 1997.##[6] Tributsch, A. and Adam, C., Evaluation and analytical approximation of Tuned Mass Damper performance in an earthquake environment. Smart Structures and Systems, 10(2), 2012, 155179.##[7] De Domenico, D. and Ricciardi, G., Earthquakeresilient design of base isolated buildings with TMD at basement: Application to a case study. Soil Dynamics and Earthquake Engineering, 113, 2018, 503521.##[8] De Domenico, D. and Ricciardi, G., Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems. Earthquake Engineering & Structural Dynamics, 47(12), 2018, 25392560.##[9] Elias, S., Matsagar, V. and Datta, T.K., Along‐wind response control of chimneys with distributed multiple tuned mass dampers. Structural Control and Health Monitoring, 26(1), 2019, 2275.##[10] Nishimura, I., Kobori, T., Sakamoto, M., Koshika, N., Sasaki, K. and Ohrui, S., Active tuned mass damper. Smart Materials and Structures, 1(4), 1992, 306.##[11] Suleman, A., Oliveira, F., Botto, M. and Morais, P., Semiactive viscous damper for controlling civil engineering structures subjected to earthquakes. In CONTROLO, 2012.##[12] Di Matteo, A., Furtmüller, T., Adam, C. and Pirrotta, A., Optimal design of tuned liquid column dampers for seismic response control of baseisolated structures. Acta Mechanica, 229(2), 2018, 437454.##[13] Min, K.W., Kim, H.S., Lee, S.H., Kim, H. and Ahn, S.K., Performance evaluation of tuned liquid column dampers for response control of a 76story benchmark building. Engineering Structures, 27(7), 2005, 11011112.##[14] Di Matteo, A., Pirrotta, A. and Tumminelli, S., Combining TMD and TLCD: analytical and experimental studies. Journal of Wind Engineering and Industrial Aerodynamics, 167, 2017, 101113.##[15] Hitchcock, P.A., Kwok, K.C.S., Watkins, R.D. and Samali, B., Characteristics of liquid column vibration absorbers (LCVA)—I. Engineering Structures, 19(2), 1997, 126134.##[16] Hitchcock, P.A., Kwok, K.C.S., Watkins, R.D. and Samali, B., Characteristics of liquid column vibration absorbers (LCVA)—II. Engineering Structures, 19(2), 1997, 135144.##[17] Yalla, S.K., Kareem, A. and Kantor, J.C., Semiactive tuned liquid column dampers for vibration control of structures. Engineering Structures, 23(11), 2001, 14691479.##[18] Hemmati, A. and Oterkus, E., SemiActive Structural Control of Offshore Wind Turbines Considering Damage Development. Journal of Marine Science and Engineering, 6(3), 2018, 102.##[19] Hemmati, A., Oterkus, E. and Khorasanchi, M., Vibration suppression of offshore wind turbine foundations using tuned liquid column dampers and tuned mass dampers. Ocean Engineering, 172, 2019, 286295.##[20] Hochrainer, M.J. and Ziegler, F., Control of tall building vibrations by sealed tuned liquid column dampers. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures, 13(6), 2006, 9801002.##[21] Dezvareh, R., Bargi, K. and Mousavi, S.A., Control of wind/waveinduced vibrations of jackettype offshore wind turbines through tuned liquid column gas dampers. Structure and Infrastructure Engineering, 12(3), 2016, 312326.##[22] Bargi, K., Dezvareh, R. and Mousavi, S.A., Contribution of tuned liquid column gas dampers to the performance of offshore wind turbines under wind, wave, and seismic excitations. Earthquake Engineering and Engineering Vibration, 15(3), 2016, 551561.##[23] LindnerSilwester, T. and Schneider, W., The moving contact line with weak viscosity effects–an application and evaluation of Shikhmurzaev’s model. Acta Mechanica, 176(34), 2005, 245258.##[24] Cheng, F.Y., Jiang, H. and Lou, K., Smart structures: innovative systems for seismic response control. CRC Press, 2008.##[25] Mousavi, S.A., Bargi, K. and Zahrai, S.M., Optimum parameters of tuned liquid column–gas damper for mitigation of seismic‐induced vibrations of offshore jacket platforms. Structural Control and Health Monitoring, 20(3), 2013, 422444.##[26] Wu, J.C., Experimental calibration and head loss prediction of tuned liquid column damper. Tamkang Journal of Science and Engineering, 8(4), 2005, 319325.##[27] Uang, C.M. and Bertero, V.V., Use of energy as a design criterion in earthquakeresistant design, Berkeley, California: Earthquake Engineering Research Center, University of California, 88(18), 1998.##[28] Sorace, S. and Terenzi, G., Seismic protection of frame structures by fluid viscous damped braces. Journal of Structural Engineering, 134(1), 2008, 4555.##[29] De Domenico, D. and Ricciardi, G., Earthquake protection of structures with nonlinear viscous dampers optimized through an energybased stochastic approach. Engineering Structures, 179, 2019, 523539.##[30] Reggio, A. and Angelis, M.D., Optimal energy‐based seismic design of non‐conventional Tuned Mass Damper (TMD) implemented via inter‐story isolation. Earthquake Engineering & Structural Dynamics, 44(10), 2015, 16231642.##[31] Towhata, I., Alam, M.J., Honda, T. and Tamate, S., Model tests on behaviour of gravitytype quay walls subjected to strong shaking. Bulletin of the New Zealand Society for Earthquake Engineering, 42(1), 2009, 47.##[32] Overseas coastal area development institute of Japan, Ports and harbours bureau, Ministry of land, infrastructure, transport and tourism, National institute for land and infrastructure management and Port and airport research institute, Technical standards and commentaries for port and harbour facilities in Japan. Overseas Coastal Area Development Institute of Japan, 2009.##[33] MATLAB, User Guide, Simulink, MathWorks Inc., Version 8.1.0, 2013.##[34] DeVries, P.L. and Hasbun, J.E., A first course in computational physics. Jones & Bartlett Publishers, 2011.##[35] Chopra, A.K. and Chopra, A.K., Dynamics of structures: theory and applications to earthquake engineering, Upper Saddle River, NJ: Pearson/Prentice Hall, 2007.##[36] PEER, Strong Ground Motion Database,http://peer.berkeley.edu/smcat/, 2009.##[37] ASCE710, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers (ASCE), Reston, Virginia, 2010.##[38] Wang, J.F., Lin, C.C. and Lian, C.H., Two‐stage optimum design of tuned mass dampers with consideration of stroke. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures, 16(1), 2009, 5572.##]
Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy
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This paper develops a computational model for nonlinear bending analysis of functionally graded (FG) plates using a fournode quadrilateral element SQ4T within the context of the first order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations are based on Total Lagrangian approach in which the motion at the present state compared with the initial state is considered to be large. Small strainlarge displacement theory of von Kármán is used in nonlinear formulations of the quadrilateral element SQ4T with twice interpolation strategy (TIS). The solution of the nonlinear equilibrium equations is obtained by the iterative method of NewtonRaphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these structures.
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Hoang Lan
Ton That
Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Vietnam  Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur
Faculty of Civil Engineering, Ho Chi Minh
Iran
hoanglantonthat@gmail.com


Hieu
NguyenVan
Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur Street, District 3, Ho Chi Minh City, Vietnam
Faculty of Civil Engineering, Ho Chi Minh
Iran


Thanh
ChauDinh
Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Vietnam
Faculty of Civil Engineering, Ho Chi Minh
Iran
Functionally graded material
Nonlinear bending
Firstorder shear deformation theory (FSDT)
Twice interpolation strategy (TIS)
Von Kármán theory
[[1] G. Udupa, S. S. Rao, and K. V. Gangadharan, Functionally Graded Composite Materials: An Overview, Procedia Materials Science, 5, 2014, 12911299.##[2] V.H. Nguyen, T.K. Nguyen, H.T. Thai, and T. P. Vo, A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates, Composites Part B: Engineering, 66, 2014, 233246.##[3] T. Thai and D.H. Choi, A simple firstorder shear deformation theory for the bending and free vibration analysis of functionally graded plates, Composite Structures, 101, 2013, 332340.##[4] S. S. Vel and R. C. Batra, Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates, AIAA Journal, 40, 2002, 14211433.##[5] E. Carrera, S. Brischetto, and A. Robaldo, Variable Kinematic Model for the Analysis of Functionally Graded Material plates, AIAA Journal, 46, 2008, 194203.##[6] G. N. Praveen and J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramicmetal plates, International Journal of Solids and Structures, 35, 1998, 44574476.##[7] J. R. Xiao, R. C. Batra, D. F. Gilhooley, J. Gillespie Jr, and M. McCarthy, Analysis of thick plates by using a higherorder shear and normal deformable plate theory and MLPG method with radial basis functions, Computer Methods in Applied Mechanics and Engineering, 196, 2007, 979987.##[8] A. M. A. Neves, A. J. M. Ferreira, E. Carrera, M. Cinefra, C. M. C. Roque, R. M. N. Jorge, et al., Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi3D higherorder shear deformation theory and a meshless technique, Composites Part B: Engineering, 44, 2013, 657674.##[9] C. H. Thai, A. M. Zenkour, M. Abdel Wahab, and H. NguyenXuan, A simple fourunknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis, Composite Structures, 139, 2016, 7795.##[10] X. Zhao and K. M. Liew, Geometrically nonlinear analysis of functionally graded plates using the elementfree kpRitz method, Computer Methods in Applied Mechanics and Engineering, 198, 2009, 27962811.##[11] T. T. Yu, S. Yin, T. Q. Bui, and S. Hirose, A simple FSDTbased isogeometric analysis for geometrically nonlinear analysis of functionally graded plates, Finite Elements in Analysis and Design, 96, 2015, 110.##[12] T. Q. Bui, T. V. Do, L. H. T. Ton, D. H. Doan, S. Tanaka, D. T. Pham, et al., On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new thirdorder shear deformation plate theory, Composites Part B: Engineering, 92, 2016, 218241.##[13] V. N. Van Do and C.H. Lee, Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation meshfree method, Applied Mathematical Modelling, 57, 2018, 120.##[14] H. NguyenVan, N. NguyenHoai, T. ChauDinh, and T. NguyenThoi, Geometrically nonlinear analysis of composite plates and shells via a quadrilateral element with good coarsemesh accuracy, Composite Structures, 112, 2014, 327338.##[15] H. NguyenVan, N. NguyenHoai, T. ChauDinh, and T. TranCong, Large deflection analysis of plates and cylindrical shells by an efficient fournode flat element with mesh distortions, Acta Mechanica, 226, 2015, 26932713.##[16] L. T. ThatHoang, H. NguyenVan, T. ChauDinh, and C. HuynhVan, Enhancement to fournode quadrilateral plate elements by using cellbased smoothed strains and higherorder shear deformation theory for nonlinear analysis of composite structures, Journal of Sandwich Structures & Materials, 2018, doi: 10.1177/1099636218797982.##[17] D. Jha, T. Kant, and R. Singh, A critical review of recent research on functionally graded plates, Composite Structures, 96, 2013, 833–849.##[18] H. NguyenVan, H. L. TonThat, T. ChauDinh, and N. D. Dao, Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations, in International Conference on Advances in Computational Mechanics Singapore, 2018, 461475.##[19] H. L. TonThat, H. NguyenVan, and T. ChauDinh, An Improved FourNode Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy, International Journal of Computational Methods, 2019, doi: 10.1142/S0219876219500208.##[20] J. S. Moita, A. L. Araújo, V. F. Correia, C. M. Mota Soares, and J. Herskovits, Buckling and nonlinear response of functionally graded plates under thermomechanical loading, Composite Structures, 202, 2018, 719730.##[21] J. S.Moita, V. Franco Correia, C. M. Mota Soares, and J. Herskovits, Higherorder finite element models for the static linear and nonlinear behaviour of functionally graded material plateshell structures, Composite Structures, 212, 2019, 465475.##[22] N. Valizadeh, S. Natarajan, O. A. GonzalezEstrada, T. Rabczuk, T. Q. Bui, and S. P. A. Bordas, NURBSbased finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter, Composite Structures, 99, 2013, 309326.##[23] S. Shojaee and N. Valizadeh, NURBSbased isogeometric analysis for thin plate problems, Structural Engineering and Mechanics, 41, 2012, 617632.##[24] S. Shojaee, N. Valizadeh, E. Izadpanah, T. Bui, and T.V. Vu, Free vibration and buckling analysis of laminated composite plates using the NURBSbased isogeometric finite element method, Composite Structures, 94, 2012, 16771693.##[25] N. NguyenThanh, N. Valizadeh, M. N. Nguyen, H. NguyenXuan, X. Zhuang, P. Areias, et al., An extended isogeometric thin shell analysis based on Kirchhoff–Love theory, Computer Methods in Applied Mechanics and Engineering, 284, 2015, 265291.##[26] P. K. Karsh, T. Mukhopadhyay, and S. Dey, Stochastic dynamic analysis of twisted functionally graded plates, Composites Part B: Engineering, 147, 2018, 259278.##[27] P. K. Karsh, T. Mukhopadhyay, and S. Dey, Stochastic lowvelocity impact on functionally graded plates: Probabilistic and nonprobabilistic uncertainty quantification, Composites Part B: Engineering, 159, 2019, 461480.##[28] L. W. Zhang, K. M. Liew, and J. N. Reddy, Geometrically nonlinear analysis of arbitrarily straightsided quadrilateral FGM plates, Composite Structures, 154, 2016, 443452.##[29] T. N. Nguyen, C. H. Thai, H. NguyenXuan, and J. Lee, Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory, Composite Structures, 193, 2018, 268280.##[30] T. Quoc Bui, D. Quang Vo, Chuanzeng Zhang, and D. Dinh Nguyen, A consecutiveinterpolation quadrilateral element (CQ4): Formulation and applications, Finite Elements in Analysis and Design, 84, 2014, 1431.##[31] C. Zheng, S. C. Wu, X. H. Tang, and J. H. Zhang, A novel twiceinterpolation finite element method for solid mechanics problems, Acta Mechanica Sinica, 26, 2010, 265278.##[32] S. C. Wu, W. H. Zhang, X. Peng, and B. R. Miao, A twiceinterpolation finite element method (TFEM) for crack propagation problems, International Journal of Computational Methods, 9, 2012, 1250055.##]
Numerical Analysis of Transient Heat Transfer in Radial Porous Moving Fin with Temperature Dependent Thermal Properties
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In this article, a time dependent partial differential equation is used to model the nonlinear boundary value problem describing heat transfer through a radial porous moving fin with rectangular profile. The study is performed by applying a numerical solver in MATLAB (pdepe), which is a centered finite difference scheme. The thermal conductivity and fin surface emissivity are linearly dependent on temperature while the heat transfer coefficient is given by power law function of temperature. The effects of thermophysical parameters, such as the Peclet number, surface emissivity coefficient, power index of heat transfer coefficient, convectiveconductive parameter, radiativeconductive parameter and nondimensional ambient temperature on temperature are studied.
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Partner Luyanda
Ndlovu
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private, Bag 3, WITS 2050, Johannesburg, South Africa  Standard Bank of South Africa, 30 Baker Street, Rosebank, Johannesburg, 2196, South Africa
School of Computer Science and Applied Mathematics
Iran
luyandandlovu@icloud.com
Numerical analysis
heat transfer
Thermal conductivity
Moving fin
Fin tip temperature
[[1] Kraus, A.D., Aziz, A., Welty, J., Extended Surface Heat Transfer, Wiley, New York, 2001.##[2] Kern, Q.D., Kraus, A.D., Extended Surface Heat Transfer, McGrawHill, New York, 1972.##[3] Gorla, R.S.R., Bakier, A.Y., Thermal analysis of natural convection and radiation in porous fins, International Communications in Heat and Mass Transfer, 38, 2011, 638645.##[4] Moradi, A., Fallah, A.P.M., Hayat, T., Aldossary, O.M., On Solution of Natural Convection and Radiation Heat Transfer Problem in a Moving Porous Fin, Arabian Journal for Science and Engineering, 39, 2014, 1303–1312.##[5] Ndlovu, P.L., Moitsheki, R.J., Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with TemperatureDependent Properties, Mathematical Problems in Engineering, 2013, Article ID: 273052, 14p.##[6] Ndlovu, P.L., Moitsheki, R.J., Application of the twodimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins, Communications in Nonlinear Science and Numerical Simulation, 18, 2013, 26892698.##[7] Mosayebidorcheh, S., RahimiGorji, M., Ganji, D.D., Moayebidorcheh, T., Pourmehran, O., Biglarian, O., Transient thermal behavior of radial fins of rectangular, triangular and hyperbolic profiles with temperaturedependent properties using DTMFDM, Journal of Central South University, 24(3), 2017, 675682.##[8] Kanti Roy, P., Mallick, A., Mondal, H., Sibanda, P., A Modified Decomposition Solution of Triangular Moving Fin with Multiple Variable Thermal Properties, Arabian Journal for Science and Engineering, 43(30), 2017, 14851497.##[9] Turkyilmazoglu, M., Heat transfer from moving exponential fins exposed to heat generation, International Journal of Heat and Mass Transfer, 116, 2018, 346351.##[10] Singla, R.K., Das, R., Application of decomposition solution and inverse prediction of parameters in a moving fin, Energy Conversion and Management, 84, 2014, 268281.##[11] Dogonchi, A.S., Ganji, D.D., Convectionradiation heat transfer study of moving fin with temperaturedependent thermal conductivity, heat transfer coefficient and heat generation, Applied Thermal Engineering, 103, 2016, 705–712.##[12] Ndlovu, P.L., Moitsheki, R.J., Thermal analysis of natural convection and radiation heat transfer in moving porous fins, Frontiers in Heat and Mass Transfer, 12(7), 2019, 8p.##[13] Mosayebidorcheh, S., Farzinpoor, M., Ganji, D.D., Transient thermal analysis of longitudinal fins with internal heat generation considering temperaturedependent properties and different fin profiles, Energy Conversion and Management, 86, 2014, 365370.##[14] Ledari, S.T., Mirgolbabaee, H., Ganji, D.D., Heat transfer analysis of a fin with temperature dependent thermal conductivity and heat transfer coefficient, New Trends in Mathematical Sciences, 3(2), 2015, 5569.##[15] Moitsheki, R.J., Harley, C., Transient heat transfer in longitudinal fins of various profiles with temperaturedependent thermal conductivity and heat transfer coefficient, Pramana Journal of Physics, 77(3), 2011, 519532.##[16] Ndlovu, P.L., Moitsheki, R.J., Predicting the Temperature Distribution in Longitudinal Fins of Various Profiles with Power Law Thermal Properties Using the Variational Iteration Method, Defect and Diffusion Forum, 387, 2018, 403416.##[17] Sobamowo, M.G., Analysis of convective longitudinal fin with temperaturedependent thermal conductivity and internal heat generation, Alexandria Engineering Journal, 56, 2017, 111.##[18] Aziz, A., Lopez, J.R.J., Convectionradiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing, International Journal of Thermal Sciences, 50, 2011, 15231531.##[19] Jaluria, Y., Transport from continuously moving materials undergoing thermal processing, Annual Reviews of Heat Transfer, 4, 1992, 187245.##[20] Ünal, H.C., An analytical study of boiling heat transfer from a fin, International Journal of Heat and Mass Transfer, 31(7), 1988, 148396.##]
Analysis of Highorder Approximations by Spectral Interpolation Applied to One and Twodimensional Finite Element Method
2
2
The implementation of highorder (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation nodes are positioned in the zeros of orthogonal polynomials (Legendre, Lobatto, or Chebychev) or equally spaced nodal bases. A comparative study between the bases in the recovery of solutions to 1D and 2D elastostatic problems are performed. Examples are evaluated, and a significant improvement is observed when the SFEM, particularly the Lobatto approach, is used in comparison to the equidistant base interpolation.
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159


Luís Philipe Ribeiro
Almeida
Federal University of Alagoas, Laboratory of Scientific Computing and Visualization Technology Center, Campus A.C. Simões, MaceióAL, 57092970, Brazil
Federal University of Alagoas, Laboratory
Iran
luis.almeida@ctec.ufal.br


Hilton Marques
Souza Santana
Federal University of Sergipe, Department of Civil Engineering, Campus São Cristovão, AracajuSE, 49100000, Brazil
Federal University of Sergipe, Department
Iran
hiltonmarquess@gmail.com


Fabio Carlos
Da Rocha
Federal University of Sergipe, Department of Civil Engineering, Campus São Cristovão, AracajuSE, 49100000, Brazil
Federal University of Sergipe, Department
Iran
fcrocha@ufs.br
Spectral finite element method
Elastostatic problem
Orthogonal basis
[[1] Babuska, I., Szabo, B.A., Katz, I.N., The pversion of the finite element method. SIAM Journal on Numerical Analysis, 18(3), 1981, 515545.##[2] Rocha, F.C., Kzam, A.K.L., Análise das aproximações de alta ordem por meio da interpolação espectral aplicadas ao MEC potencial. In proceeding XXXIV Iberian LatinAmerican Congress in Computational Methods in Engineering, 2013.##[3] Zak, A., Krawczuk, M., Certain numerical issues of wave propagation modelling in rods by the Spectral Finite Element Method. Finite Elements in Analysis and Design, 47, 2011, 10361046.##[4] Kudela, P., et al. Wave propagation modelling in 1D structures using spectral finite elements. Journal of Sound and Vibration, 300(12), 2007, 88100.##[5] Karniadaki, G. E., Sherwin, S. J., Spectral/Hp Element Methods for CFD. Oxford: Oxford University Press, 1999.##[6] Nogueira, A.C. Jr., Bittencourt, M.L., Spectral/HP finite elements applied to linear and nonlinear structural elastic problems. Latin American Journal of Solids and Structures, 4, 2007, 6185.##[7] Willberg, C., Duczek, S., Vivar Perez, J.M., Schmicker, D., Gabbert, U., Comparison of different higher order finite element schemes for the simulation of lamb waves. Computer Methods in Applied Mechanics and Engineering, 241, 2012, 246261.##[8] Fornberg, B., and Julia, Z., The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Computers & Mathematics with Applications, 54(3), 2007, 379398.##[9] Brutman, L., Lebesgue functions for polynomial interpolation, a survey. Annals of Numerical Mathematics, 4, 1997, 111127.##[10] Vos, P.E.J., Sherwin, S.J., Kirby, R.M., From h to p efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low and highorder discretisations. Journal of Computational Physics,229(13), 2010, 51615181.##[11] Sherwin, S.J., Karniadakis, G.E., A triangular element method; applications to the imcompressible NavierStokes equations. Computer Methods in Applied Mechanics and Engineering, 123(1–4), 1995, 189229.##[12] Sherwin, S.J., Karniadakis, G.E., Tetrahedral hp finite elements: algorithms and flow simulations. Journal of Computational Physics, 124, 1996, 1445.##[13] Tai, C.Y., & Chan, Y. J. A hierarchic highorder Timoshenko beam finite element. Computers & Structures, 165, 2016, 4858.##[14] W. Dauksher, A.F. Emery, The solution of elastostatic and elastodynamic problems with Chebyshev spectral finite elements, Computer Methods in Applied Mechanics and Engineering, 188, 2000, 21733.##[15] Khaji, N., & Zakian, P. Uncertainty analysis of elastostatic problems incorporating a new hybrid stochasticspectral finite element method. Mechanics of Advanced Materials and Structures, 24(12), 2016, 10301042.##[16] Man, H., Song, C., Xiang, T., Gao, W., & TinLoi, F. Highorder plate bending analysis based on the scaled boundary finite element method. International Journal for Numerical Methods in Engineering, 95(4), 2013, 331360.##[17] Man, H., Song, C., Gao, W., & TinLoi, F. Semianalytical analysis for piezoelectric plate using the scaled boundary finiteelement method. Computers & Structures, 137, 2014, 4762.##[18] Lin, G., Zhang, P., Liu, J., & Li, J. Analysis of laminated composite and sandwich plates based on the scaled boundary finite element method. Composite Structures, 187, 2018, 579592.##[19] Zak, A., & Krawczuk, M. Static and dynamic analysis of isotropic shell structures by the spectral finite element method. Journal of Physics: Conference Series, 382, 2012, 012054.##[20] Wang, Q., Sprague, M.A., Legendre spectral finite element implementation of geometrically exact beam theory, in: Proceedings of the 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, National Harbor, USA, 2013.##[21] Proriol, J., Sur une famille de polynomes à deux variables orthogonaux dans um triangle. Comptes Rendus Mathematique Academie des Sciences, 245(26), 1957, 24592461.##[22] Fejer, L. Lagrangesche interpolation und die zugehorigen konjugierten punkte. Mathematische Annalen, 106, 1932, 155.##[23] Blyth, M. G., & Pozrikidis, C. A Lobatto interpolation grid over the triangle. IMA Journal of Applied Mathematics, 71(1), 2016, 153169.##[24] Pozrikidis, C., Introduction to Finite and Spectral Element Methods Using Matlab. Chapman & Hall/CRC, 2005.##[25] Franco, N. B., Cálculo numérico, São Paulo: Pearson Prentice Hall, 2007.##[26] Oñate, E., Structural Analysis with the Finite Element Method. Linear Statics. 1st ed. Barcelona: Springer, 2013.##[27] Ostachowicz, W., Kudela, P., Krawczuk, M., Zak, A., Guided Waves in Structures for SHM: The Timedomain Spectral Element Method. John Wiley & Sons Ltd: Chichester, UK, 2011.##[28] Blyth, M.G., Pozrikidis, C. A., Lobatto interpolation grid over the triangle. 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Modeling of Weld Bead Geometry Using Adaptive NeuroFuzzy Inference System (ANFIS) in Additive Manufacturing
2
2
Additive Manufacturing describes the technologies that can produce a physical model out of a computer model with a layerbylayer production process. Additive Manufacturing technologies, as compared to traditional manufacturing methods, have the high capability of manufacturing the complex components using minimum energy and minimum consumption. These technologies have brought about the possibility to make small pieces of raw materials in the shortest possible time without the need for a mold or tool. One of the technologies used to make pieces of the layerbylayer process is the Gas Metal Arc Welding (GMAW). One of the basic steps in this method of making parts is the prediction of bead geometry in each pass of welding. In this study, taking into account the effective parameters on the geometry of weld bead, an empirical study has been done in this field. For this purpose, three parameters of voltage, welding speed and wire feeding rate are considered as effective parameters on the welding geometry of the process. Width and height of the bead are also determined by the parameters of the geometry of the weld according to the type and application of the research as output parameters are considered. In this paper, an adaptive neurofuzzy inference system (ANFIS) is used to create an adaptive model between input process data and parameters of weld bead geometry. The least squares mean error is used to evaluate the model. The predicted results by the model have a good correlation with the experimental data.
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170


Abolfazl
Foorginejad
Department of Mechanical Engineering, Birjand Ubiversity of Technology, Birjand, Iran
Department of Mechanical Engineering, Birjand
Iran
foorginejad@birjandut.ac.ir


Majid
Azargoman
Department of Mechanical Engineering, Birjand University of Technology, Birjand, Iran
Department of Mechanical Engineering, Birjand
Iran
azargomanmajid@gmail.com


Nader
Mollayi
Department of Computer engineering and Information Technology, Birjand University of Technology, Birjand, Ira
Department of Computer engineering and Information
Iran
mollayi@birjandut.ac.ir


Morteza
Taheri
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Department of Mechanical Engineering, Tarbiat
Iran
morteza.taheri@modares.ac.ir
Weld bead geometry
Additive manufacturing
modeling
ANFIS
Gas Metal Arc Welding (GMAW)
[[1] Zhang, Y., Chen, Y., Li, P., Male, A. T., Weld depositionbased rapid prototyping: a preliminary study, Journal of Materials Processing Technology, 135 (2), 2003, 347357.##[2] Suryakumar, S., Karunakaran ,K., Bernard, A., Chandrasekhar, U., Raghavender, N., Sharma, D., Weld bead modeling and process optimization in hybrid layered manufacturing, ComputerAided Design, 43 (4), 2011, 331344.##[3] Wanjara, P., Brochu, M., Jahazi, M., Electron beam freeforming of stainless steel using solid wire feed, Materials & design, 28 (8), 2007, 22782286.##[4] Karunakaran, K., Suryakumar, S., Pushpa, V., Akula, S., Retrofitment of a CNC machine for hybrid layered manufacturing, The International Journal of Advanced Manufacturing Technology, 45 (7), 2009, 690703.##[5] Xiong, J., Zhang, G., Hu, J., Wu, L., Bead geometry prediction for robotic GMAWbased rapid manufacturing through a neural network and a secondorder regression analysis, Journal of Intelligent Manufacturing, 25 (1), 2014,157163.##[6] Merz, R., Prinz, F., Ramaswami, K., Terk, M., Weiss, L., Shape deposition manufacturing Engineering Design Research Center, Carnegie Mellon Univ, 1994, 18.##[7] Song, YA., Park, S., Experimental investigations into rapid prototyping of composites by novel hybrid deposition process, Journal of Materials Processing Technology, 171 (1), 1006, 3540.##[8] Kovacevic, R., Rapid prototyping technique based on 3D welding, In NSF design & manufacturing grantees conference, 1999, 1216.##[9] Cortes, C., Vapnik, V., Supportvector networks, Machine learning, 20 (3), 1995, 273297.##[10] Weiss, L., Prinz, F., Adams, D., Siewiorek, D., Thermal spray shape deposition. Journal of Thermal Spray Technology, 1 (3), 1992, 231237##[11] Kim, IS., Son, JS., Lee, SH., Yarlagadda, P. K., Optimal design of neural networks for control in robotic arc welding, Robotics and computerintegrated manufacturing, 20 (1), 2004, 5763.##[12] RamosJaime, D., LópezJuárez, I., Perez, P., Effect of process parameters on robotic GMAW bead area estimation, Procedia Technology, 7, 2013, 398405.##[13] Lee, Wc., Wei, CC., Chung, SC., Development of a hybrid rapid prototyping system using lowcost fused deposition modeling and fiveaxis machining, Journal of Materials Processing Technology, 214 (11), 2014, 23662374.##[14] Dewan, M. W., Huggett, D. J., Liao, T. W., Wahab, M. A., Okeil, A. M., Prediction of tensile strength of friction stir weld joints with adaptive neurofuzzy inference system (ANFIS) and neural network, Materials & Design, 92, 2016, 288299.##[15] Kovacevic, R., Zhang, Y. M., Neurofuzzy modelbased weld fusion state estimation. IEEE Control Systems Magazine, 17(2),1997, 3042.##[16] Zhang, Y. M., Kovacevic, R., Neurofuzzy modelbased predictive control of weld fusion zone geometry. IEEE Transactions on Fuzzy Systems, 6(3), 1998, 389401.##[17] Karuthapandi, S., Ramu, M., Thyla, P., Effects of the use of a flat wire electrode in gas metal arc welding and fuzzy logic model for the prediction of weldment shape profile, Journal of Mechanical Science and Technology, 31 (5), 2017, 24772486.##[18] Chandrasekhar, N., Vasudevan, M., Bhaduri, A., Jayakumar, T., Intelligent modeling for estimating weld bead width and depth of penetration from infrared thermal images of the weld pool, Journal of Intelligent Manufacturing, 26 (1), 2015, 5971.##[19] Vishnuvaradhan, S., Chandrasekhar, N., Vasudevan, M., Jayakumar, T., Intelligent modeling using adaptive neuro fuzzy inference system (ANFIS) for predicting weld bead shape parameters during ATIG welding of reduced activation ferriticmartensitic (RAFM) steel, Transactions of the Indian Institute of Metals, 66 (1), 2013, 5763.##[20] Liu, Y., Zhang, W., Zhang, Y., Dynamic neurofuzzybased human intelligence modeling and control in GTAW. IEEE Transactions on Automation Science and Engineering, 12(1), 2013, 324335.##[21] Liu, Y., Zhang, Y., Iterative local ANFISbased human welder intelligence modeling and control in pipe GTAW process: A datadriven approach. IEEE/ASME Transactions on Mechatronics, 20(3), 2014, 10791088.##[22] Liu, Y. K., Zhang, W. J., Zhang, Y. M., Nonlinear modeling for 3D weld pool characteristic parameters in GTAW. Weld J, 94(7), 2015, 231240.##[23] Ozcelik, S., Moore, K., Modeling, sensing and control of gas metal arc welding, Elsevier, 2003.##[24] Olabi, A., Alsinani, F., Alabdulkarim, A., Ruggiero, A., Tricarico, L., Benyounis, K., Optimizing the CO 2 laser welding process for dissimilar materials, Optics and Lasers in Engineering, 51 (7), 2013, 832839.##[25] Murugan, V. V., Gunaraj, V., Effects of process parameters on angular distortion of gas metal arc welded structural steel plates, Welding journal, 11, 2005, 165171.##[26] Li, K., Zhang, Y., Consumable doubleelectrode GMAWPart 1: The process, WELDING JOURNALNEW YORK, 87 (1), 2008, 11,##[27] Wang, LX., A course in fuzzy systems, PrenticeHall press, USA, 1999.##[28] Jang, JS. R., Sun, CT., Mizutani, E., Neurofuzzy and soft computing: a computational approach to learning and machine intelligence, Proceedings of the IEEE, 86(3), 1998, 600603.##[29] Ghomsheh, V. S,, Shoorehdeli, M. A., Teshnehlab, M., Training ANFIS structure with modified PSO algorithm. In 2007 Mediterranean Conference on Control & Automation , IEEE, 2007, 16.##[30] Zangeneh, A. Z., Mansouri, M., Teshnehlab, M., Sedigh, A. K., Training ANFIS system with DE algorithm. The Fourth International Workshop on Advanced Computational Intelligence. IEEE, 2011.##[31] Liu, P., Leng, W., Fang, W., Training anfis model with an improved quantumbehaved particle swarm optimization algorithm, Mathematical Problems in Engineering, 2013.##]
Entropy Generation of Variable Viscosity and Thermal Radiation on Magneto Nanofluid Flow with Dusty Fluid
2
2
The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into nonlinear ordinary differential equations which are then transformed into linear form using the spectral quasilinearization method (SQLM) for direct Taylor series expansions that can be applied to nonlinear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The validity of our model is established using relative entropy generation analysis. A convergence schematic was obtained graphically. Consequence of various parameters on flow features have been delivered via graphs. Some important findings reported in this study that entropy generation analysis have significant impact in controlling the rate of heat transfer in the boundary layer region. The paper acquires realistic numerical explanations for rapidly convergent solutions using the Spectral quasilinearization method. Convergence of the numerical solutions was monitored using the convergence graph. The initial guess values are automatically satisfied the boundary conditions. The resulting equations are then integrated using the Spectral quasilinearization methods. The influence of radiation, heat and mass parameters on the flow are made appropriately via graphs. The effects of varying certain physical parameters of interest are examined and presented.
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182


Hiranmoy
Mondal
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Private Bag X01 Scottsville, 3209, South Africa
School of Mathematics, Statistics and Computer
Iran
hiranmoymondal@yahoo.co.in


Shweta
Mishra
Amity Institute of Information Technology, Amity University, NewTown, Kolkata, West Bengal 700135, India
Amity Institute of Information Technology,
Iran
shweta9935@gmail.com


Prabir Kumar
Kundu
Deptartment of Mathematics, Jadavpur University, West Bengal, Kolkata 700032, India
Deptartment of Mathematics, Jadavpur University,
Iran
kunduprabir@yahoo.co.in


Precious
Sibanda
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Private Bag X01 Scottsville, 3209, South Africa
School of Mathematics, Statistics and Computer
Iran
sibandap@ukzn.ac.za
Spectral quasiliearization method
Viscous dissipation
Variable viscosity
Entropy generation
Thermal radiation
[[1] O.D. Makinde, A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, 50, 2011, 13261332.##[2] X.Q. Wang and A.S. Mujumdar, A review on nanofluids  part ii: Experiments and applications, Brazilian Journal of Chemical Engineering, 25, 2008, 631648.##[3] S. Kakac, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer, 52, 2009, 31873196.##[4] D. Pal, H. Mondal, SoretDufour effects on hydromagnetic nonDarcy convectiveradiative heat and mass transfer over a stretching sheet in porous medium with viscous dissipation and Ohmic heating, Journal of Applied Fluid Mechanics, 7(3), 2014, 513–523.##[5] D. Pal, H. Mondal, MHD nonDarcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with nonuniform heat source/sink, variable viscosity and Soret effects. Communications in Nonlinear Science and Numerical Simulation, 17, 2012, 672684.##[6] M.M. Rashidi, E. Momoniat, B. Rostami, Analytic approximate solutions for the MHD boundary layer viscoelastic fluid flow over continuously moving stretched surface by homotopy analysis method with two auxiliary parameters, Journal of Applied Mathematics, 2012, Article ID: 780415.##[7] M.M. Rashidi, E. Erfani, Analytical method for solving steady MHD and convective flow due to a rotating disk with viscous dissipation and ohmic heating, Engineering Computations, 29, 2012, 562–579.##[8] D. Pal, S. Chatterjee, Heat and mass transfer in mhd nondarcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with nonuniform heat source and thermal radiation, Communications in Nonlinear Science and Numerical Simulation, 15(7), 2010, 18431857.##[9] R. Kandasamy, K. Periasamy, K.S. Prabhu, Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection, International Journal of Heat and Mass Transfer, 48(7), 2005, 13881394.##[10] R. Kandasamy, I. Muhaimin, A.B. Khamis, Thermophoresis and variable viscosity effects on mhd mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction, Heat and Mass Transfer, 45(6), 2009, 703712.##[11] D. Pal, H. Mondal, Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with nonuniform heat source/sink and variable viscosity, International Communications in Heat and Mass Transfer, 39, 2012, 913917##[12] S. Manjunatha, B.J. Gireesha, Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid, Ain Shams Engineering Journal, 7, 2016, 505515.##[13] A. Pantokratoras, Further results on the variable viscosity on the flow and heat transfer to a continuous moving flat plate, International Journal of Engineering Science, 42, 2004, 18911896.##[14] S. Mukhopadhyay, G.C. Layek, Effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface, International Journal of Heat and Mass Transfer, 21, 2008, 216778.##[15] M.S. Abel, P.G. Siddheshwar, M.M. Nandeppanawar, Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and nonuniform heat source, International Journal of Heat and Mass Transfer, 50, 2007, 960966.##[16] A. Noghrehabadi, M.R. Saffarian, R. Pourrajab, M. Ghalambaz, Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip. Journal of Mechanical Science and Technology, 27(3), 2013, 92737.##[17] H. Sithole, H. Mondal, P. Sibanda, Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation, Results in Physics, 9, 2018, 10771085.##[18] N. Hidouri, M. Magherbi, H. Abbassi, A. Ben Brahim, Entropy generation in double diffusive in presence of Soret effect, Progress in Computational Fluid Dynamics, 5, 2007, 23746.##[19] L. Aracely, I. Guillermo, P. Joel, M. Joel, L. Orlando, Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convectiveradiative boundary conditions, International Journal of Heat and Mass Transfer, 107, 2017, 98294.##[20] Kh.A. Maleque, Effects of binary chemical reaction and activation energy on mhd boundary layer heat and mass transfer flow with viscous dissipation and heat generation/ absorption, ISRN Thermodynamics, 2013, Article ID 284637.##[21] D. Pal, H. Mondal, Influence of chemical reaction and thermal radiation on mixed convection heat and mass transfer over a stretching sheet in Darcian porous medium with Soret and Dufour effects, Energy Conversion and Management, 62, 2012, 102108##[22] M. Dhlamini, K. Peri, K. Kameswaran, P. Sibanda, S. Motsa, H. Mondal, Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions, Journal of Computational Design and Engineering, 6(2), 2019, 149158.##[23] F.G. Awad, S. Motsa, M. Khumalo, Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy, PloS One, 9(9), 2014, 107622.##[24] H. Sithole, H. Mondal, S. Goqo, P. Sibanda, S. Motsa, Numerical simulation of couple stress nanofluid flow in magnetoporous medium with thermal radiation and a chemical reaction, Applied Mathematics and Computation, 339, 2018, 820836.##]