2018
4
1
0
74
Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory
2
2
The present study investigates the buckling of a thick sandwich plate under the biaxial nonuniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (SFSDT) is employed and the governing differential equations are obtained using the Hamilton’s principle by considering the VonKarman’s nonlinear strains. An analytical approach is applied to obtain exact results with different boundary conditions. Due to the fact that there is no research on the stability of micro/nano sandwich plates based on SFSDT including the couple stress effect, the obtained results are compared with the FSDT studies which use the Eringen nonlocal elasticity.
1

1
15


Mohammad
Malikan
Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Mashhad, Iran
Department of Mechanical Engineering, Faculty
Iran
mohammad.malikan@yahoo.com
Thick sandwich plate
Modified couple stress theory
SFSDT
[[1] Ovid’ko, I.A., Mechanical properties of graphene, Review on Advanced Materials Science, 34, 2013, pp. 111.##[2] Walker, L.S., Marotto, V.R., Rafiee, M.A., Koretkar, N., Corral, E.L., Toughening in graphene ceramic composites, ACS Nano, 5, 2011, pp. 318290.##[3] Kvetkova, L., Duszova, A., Hvizdos, P., Dusza, J., Kun, P., Balazsi, C., Fracture toughness and toughening mechanisms in graphene platelet reinforced Si 3 N 4 composites, Scripta Materialia, 66, 2012, pp. 793796.##[4] Liang, J., Huang, Y., Zhang, L., Wang, Y., Ma, Y., Guo, T., Chen, Y., Molecular‐level dispersion of graphene into poly (vinyl alcohol) and effective reinforcement of their nanocomposites, Advanced Functional Materials, 19, 2009, pp. 22972302.##[5] Rafiee, M.A., Rafiee, J., Srivastana, I., Wang, Z., Song, H., Yu, ZZ., Koratkar, N., Fracture and fatigue in graphene Nano composites, Small, 6, 2010, pp. 17983.##[6] Plantema, F.J., Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates, and Shells, Jon Wiley and Sons, New York, 1966.##[7] Kraus, G., Interactions of Elastomers and Reinforcing Fillers, Rubber Chemistry and Technology, 38, 1965, pp. 10701114.##[8] Malekzadeh, P., Setoodeh, A.R., Beni, A.A., Small scale effect on the thermal buckling of orthotropic arbitrary straightsided quadrilateral nanoplates embedded in an elastic medium, Composite Structures, 93, 2011, pp. 2083–2089.##[9] Zenkour, A.M., Sobhy, M., Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E, 53, 2013, pp. 251–259.##[10] Murmu, T., Sienz, J., Adhikari, S., Arnold, C., Nonlocal buckling of doublenanoplatesystems under biaxial compression, Composites: Part B, 44, 2013, pp. 84–94.##[11] Wang, YZ., Cui, HT., Li, FM., Kishimoto, K., Thermal buckling of a nanoplate with smallscale effects, Acta Mechanica, 224, 2013, pp. 1299–1307.##[12] Malekzadeh, P., Alibeygi, A., Thermal Buckling Analysis of Orthotropic Nanoplates on Nonlinear Elastic Foundation, Encyclopedia of Thermal Stresses, 2014, pp. 48624872.##[13] Mohammadi, M., Farajpour, A., Moradi, A., Ghayour, M., Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites: Part B, 56, 2014, pp. 629–637.##[14] Radic, N., Jeremic, D., Trifkovic, S., Milutinovic, M., Buckling analysis of doubleorthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory, Composites: Part B, 61, 2014, pp. 162–171.##[15] Karlicic, D., Adhikari, S., Murmu, T., Exact closedform solution for nonlocal vibration and biaxial buckling of bonded multinanoplate system, Composites: Part B, 66, 2014, pp. 328339.##[16] Anjomshoa, A., Shahidi, A.R., Hassani, B., Jomehzadeh, E., Finite Element Buckling Analysis of MultiLayered Graphene Sheets on Elastic Substrate Based on Nonlocal Elasticity Theory, Applied Mathematical Modelling, 38, 2014, pp. 122.##[17] Radebe, I.S., Adali, S., Buckling and sensitivity analysis of nonlocal orthotropic nanoplates with uncertain material properties, Composites: Part B, 56, 2014, pp. 840–846.##[18] Nguyen, T.K., Vo, T. P., Nguyen, B.D., Lee, J., An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi3D shear deformation theory, Composite Structures, 156, 2015, pp. 238252.##[19] Golmakani, M.E., Rezatalab, J., Non uniform biaxial buckling of orthotropic Nano plates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, 119, 2015, pp. 238250.##[20] Jamali, M., Shojaee, T., Mohammadi, B., Uniaxial buckling analysis comparison of nanoplate and nanocomposite plate with central square cut out using domain decomposition method, Journal of Applied and Computational Mechanics, 2, 2016, pp. 230242.##[21] Radic, N., Jeremić, D., Thermal buckling of doublelayered graphene sheets embedded in an elastic medium with various boundary conditions using a nonlocal new firstorder shear deformation theory, Composites: Part B, 97, 2016, pp. 201215.##[22] Zarei, M. Sh., Hajmohammad, M. H., Nouri, A., Dynamic buckling of embedded laminated nanocomposite plates based on sinusoidal shear deformation theory, Journal of Applied and Computational Mechanics, 2, 2016, pp. 254261.##[23] Malikan, M., Jabbarzadeh, M., Dastjerdi, Sh., Nonlinear Static stability of bilayer carbon nanosheets resting on an elastic matrix under various types of inplane shearing loads in thermoelasticity using nonlocal continuum, Microsystem Technologies, 23(7), 2017, pp. 29732991.##[24] Mindlin, R.D., Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates, Journal of Applied Mechanics, 73, 1951, pp. 31–38.##[25] Thai, HT., Choi, DH., A simple firstorder shear deformation theory for laminated composite plates, Composite Structures, 106, 2013, pp. 754763.##[26] Mindlin, R.D., Tiersten, H.F., Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11, 1962, pp. 415–48.##[27] Toupin, R.A., Elastic materials with couple stresses, Archive for Rational Mechanics and Analysis, 11, 1962, pp. 385414.##[28] Koiter, W. T., Couple stresses in the theory of elasticity, I and II. Proc K Ned Akad Wet (B), 67, 1964, pp. 1744.##[29] Cosserat, E., Cosserat, F., Theory of deformable bodies, Scientific Library, 6. Paris: A. Herman and Sons, Sorbonne, 6, 1909.##[30] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2002, pp. 2731–43.##[31] Akgöz, B., Civalek, O., Free vibration analysis for singlelayered graphene sheets in an elastic matrix via modified couple stress theory, Materials and Design, 42, 2012, pp. 164–171.##[32] Malikan, M., Electromechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory, Applied Mathematical Modeling, 48, 2017, pp. 196–207.##[33] Malikan, M., Analytical prediction for buckling of nanoplate subjected to nonuniform compression based on fourvariable plate theory, Journal of Applied and Computational Mechanics, 3(3), 2017, pp. 218228.##[34] Thai, HT., Thuc, P. Vo, Nguyen, TK., Lee, J., Sizedependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory, Composite Structures, 123, 2015, pp. 337–349.##[35] Dey, T., Ramachandra, L.S., Buckling and postbuckling response of sandwich panels under nonuniform mechanical edge loadings, Composites: Part B, 60, 2014, pp. 537–545.##[36] Leissa, A.W., Kang, JaeHoon, Exact solutions for vibration and buckling of an SSCSSC rectangular plate loaded by linearly varying inplane stresses, International Journal of Mechanical Sciences, 44, 2002, pp. 1925–1945.##[37] Hwang, I., Seh Lee, J., Buckling of Orthotropic Plates under Various Inplane Loads, KSCE Journal of Civil Engineering, 10, 2006, pp. 349–356.##[38] Golmakani, M.E., Sadraee Far, M.N., Buckling analysis of biaxially compressed double‑layered graphene sheets with various boundary conditions based on nonlocal elasticity theory, Microsystem Technologies, 23, 2017, pp. 21452161.##[39] Ansari, R., Sahmani, S., Prediction of biaxial buckling behavior of singlelayered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Applied Mathematical Modeling, 37, 2013, pp. 7338–7351.##]
Ritz Method Application to Bending, Buckling and Vibration Analyses of Timoshenko Beams via Nonlocal Elasticity
2
2
Bending, buckling and vibration behaviors of nonlocal Timoshenko beams are investigated in this research using a variational approach. At first, the governing equations of the nonlocal Timoshenko beams are obtained, and then the weak form of these equations is outlined in this paper. The Ritz technique is selected to investigate the behavior of nonlocal beams with arbitrary boundary conditions along them. To find the equilibrium equations of bending, buckling, and vibration of these structures, an analytical procedure is followed. In order to verify the proposed formulation, the results for the nonlocal Timoshenko beams with four classical boundary conditions are computed and compared wherever possible. Since the Ritz technique can efficiently model the nanosized structures with arbitrary boundary conditions, two types of beams with general boundary conditions are selected, and new results are obtained.
1

16
26


Seyyed Amir Mahdi
Ghannadpour
Aerospace department, Faculty of New Technology and Engineering, Shahid Beheshti University, Tehran, Iran
Aerospace department, Faculty of New Technology
Iran
a_ghannadpour@sbu.ac.ir
Ritz method
Weak Form
Bending
Buckling
Vibration
Nonlocal Timoshenko beam
[[1] Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S., Buckling analysis of micro and nanorods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 39, 2006, pp. 39043909.##[2] Wang, C.M., Kitipornchai, S., Lim, C.W., Eisenberger, M., Beam bending solutions based on nonlocal Timoshenko beam theory, Journal of Engineering Mechanics, 134, 2008, pp. 475481.##[3] Ghannadpour, S.A.M., Mohammadi, B., Buckling analysis of micro and nanorods/tubes based on nonlocal Timoshenko beam theory using Chebyshev polynomials, Advanced Materials Research, 123125, 2010, pp. 619622.##[4] Ghannadpour, S.A.M., Mohammadi, B., Vibration of Nonlocal Euler Beams Using Chebyshev Polynomials, Key Engineering Materials, 471, 2011, pp. 10161021.##[5] Salamat, D., Sedighi, H.M., The effect of small scale on the vibrational behavior of singlewalled carbon nanotubes with a moving nanoparticle, Journal of Applied and Computational Mechanics, 3(3), 2017, pp. 208217.##[6] Shen, HS., Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments, Composite Structures, 93, 2011, pp. 11431152.##[7] Duan, W.H., Wang, C.M., Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology, 18, 2007, pp. 385704.##[8] Wang, Q., Wang, C.M., The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology, 18, 2007, pp. 075702.##[9] Eringen, A.C., Suhubi, E.S., Nonlinear theory of simple microelastic solidsI, International Journal of Engineering Science, 2, 1964, pp. 189203.##[10] Chen, Y., Lee, J.D., Eskandarian, A., Atomistic viewpoint of the applicability of microcontinuum theories, International Journal of Solids and Structures, 41, 2004, pp. 20852097.##[11] Toupin, R.A., Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis, 11, 1962, pp. 385414.##[12] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 1983, pp. 4703.##[13] Hu, Y., Liew, K.M., Wang, Q., He, X.Q., Yakobson, B.I., Nonlocal shell model for flexural wave propagation in doublewalled carbon nanotubes, Journal of the Mechanics and Physics of Solids, 56, 2008, pp. 3475 3485.##[14] Peddieson, J., Buchanan, G.R., McNitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, pp. 305312.##[15] Polizzotto, C., Nonlocal elasticiy and related variational principles, International Journal of Solids and Structures, 38, 2001, pp. 73597380.##[16] Challamel, N., Wang, C.M., The small length scale effect for a nonlocal cantilever beam: a paradox solved, Nanotechnology, 19, 2008, pp. 345703.##[17] Wang, C.M., Zhang, Y.Y., He, X.Q., Vibration of nonlocal Timoshenko beams, Nanotechnology, 18, 2007, pp. 105401.##[18] Wang, Q., Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics, 98, 2005, pp. 124301.##[19] Murmu, T., Pradhan, S.C., Thermal Effects on the Stability of Embedded Carbon Nanotubes, Computational Materials Science, 47, 2010, pp. 721726.##[20] Pradhan, S.C., Phadikar, J.K., Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory, Structural Engineering and Mechanics, 33, 2009, pp. 193213.##[21] Pradhan, S.C., Phadikar, J.K., Small Scale Effect on Vibration of Embedded Multilayered Graphene Sheets Based on Nonlocal Continuum Models, Physics Letters A, 373, 2009, pp. 10621069.##[22] Pradhan, S.C., Phadikar, J.K., Nonlocal Elasticity Theory for Vibration of Nanoplates, Journal of Sound and Vibration, 325, 2009, pp. 206223.##[23] Pradhan, S.C., Murmu, T., Small Scale Effect on the Buckling of SingleLayered Graphene Sheets under Biaxial Compression via Nonlocal Continuum Mechanics, Computational Materials Science, 47, 2009, pp. 268274.##[24] Murmu, T., Pradhan, S.C., Vibration Analysis of Nanoplates under Uniaxial Prestressed Conditions via Nonlocal Elasticity, Journal of Applied Physics, 106, 2009, pp. 104301.##[25] Aghababaei, R., Reddy, J.N., Nonlocal thirdorder shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration, 326, 2009, pp. 277289.##[26] Phadikar, J.K., Pradhan, S.C., Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates, Computational Materials Science, 49(3), 2010, pp. 492499.##[27] Ghannadpour, S.A.M., Mohammadi, B., Fazilati, J., Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method, Composite Structures, 96, 2013, pp. 584589##[28] Reddy, J.N., Energy principles and variational methods in applied mechanics, John Wiley, 2002.##]
QuasiStatic Transient Thermal Stresses in an Elliptical Plate due to Sectional Heat Supply on the Curved Surfaces over the Upper Face
2
2
This paper is an attempt to determine quasistatic thermal stresses in a thin elliptical plate which is subjected to transient temperature on the top face with zero temperature on the lower face and the homogeneous boundary condition of the third kind on the fixed elliptical curved surface. The solution to conductivity equation is elucidated by employing a classical method. The solution of stress components is achieved by using Goodier’s and Airy’s potential function involving the Mathieu and modified functions and their derivatives. The obtained numerical results are accurate enough for practical purposes, better understanding of the underlying elliptic object, and better estimates of the thermal effect on the thermoelastic problem. The conclusions emphasize the importance of better understanding of the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect on the thermoelastic problem.
1

27
39


Lalsingh
Khalsa
Department of Mathematics, M.G. College, Armori, Gadchiroli, India
Department of Mathematics, M.G. College,
Iran
lalsinghkhalsa@yahoo.com


Ishaque
Khan
Department of Mathematics, M.G. College, Armori, Gadchiroli, India
Department of Mathematics, M.G. College,
Iran
iakhan_get@rediffmail.com


Vinod
Varghese
Department of Mathematics, S.S.R. Bharti Science College, Arni, India
Department of Mathematics, S.S.R. Bharti
Iran
vino7997@gmail.com
Elliptical plate
Temperature distribution
Thermal stresses
Mathieu function
[[1] Gupta, R.K., A finite transform involving Mathieu functions and its application, Proc. Net. Inst. Sc., India, Part A, 30(6), 1964, pp. 779795.##[2] El Dhaba, A.R., Ghaleb, A.F., AbouDina, M.S., A problem of plane, uncoupled linear thermoelasticity for an infinite, elliptical cylinder by a boundary integral method, Journal of Thermal Stresses, 26(2), 2003, pp. 93121.##[3] Sato, K., Heat conduction in an infinite elliptical cylinder during heating or cooling, Proceedings of the 55th Japan National Congress on Theoretical and Applied Mechanics, 55, 2006, pp. 157158.##[4] Helsing, J., Integral equation methods for elliptic problems with boundary conditions of mixed type, Journal of Computational Physics, 228(23), 2009, pp. 88928907.##[5] Dang, Q.A., Mai, X.T., Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics, Boletim da Sociedade Paranaense de Matemática, 31(1), 2013, pp. 65–78.##[6] Al Duhaim, H.R., Zaman, F.D., Nuruddeen, R.I., Thermal stress in a halfspace with mixed boundary conditions due to time dependent heat source, IOSR Journal of Mathematics, 11(6), 2015, pp. 1925.##[7] Parnell, W.J., Nguyen, V.H., Assier, R., Naili, S., Abrahams, I.D., Transient thermal mixed boundary value problems in the halfspace, SIAM Journal on Applied Mathematics, 76(3), 2016, pp. 845–866.##[8] Nuruddeen, R.I., Zaman, F.D., Temperature distribution in a circular cylinder with general mixed boundary conditions, Journal of Multidisciplinary Engineering Science and Technology, 3(1), 2016, pp. 36533658.##[9] Bhad, P.P., Varghese, V., Khalsa, L.H., Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments, Journal of Thermal Stresses, 40(1), 2016, pp. 96107.##[10] Bhad, P.P., Varghese, V., Khalsa, L.H., Thermoelasticinduced vibrations on an elliptical disk with internal heat sources, Journal of Thermal Stresses, 40(4), 2016, pp. 502516.##[11] Ventsel, E., Krauthammer, T., Thin Plates and Shells: Theory, Analysis, and Applications, Marcel Dekker, New York, 2001.##[12] McLachlan, N.W., Theory and Application of Mathieu function, Clarendon Press, Oxford, 1947.##[13] Bhad, P.P., Varghese, V., Thermoelastic analysis on a circular plate subjected to annular heat supply, Global Journal for Research Analysis, 3(4), 2014, pp. 141145.##]
Buckling and Vibration Analysis of Tapered Circular Nano Plate
2
2
In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to inplane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture sizedependent effects. The RaleighRitz method and differential transform method were utilized to obtain the frequency equations for simply supported and clamped boundary conditions. To verify the accuracy of the Ritz method, the differential transform method (DTM) was also used to drive the sizedependent natural frequencies of circular nanoplates. Both methods reported good results. The validity of solutions was performed by comparing the present results with those of the literature for both classical plate and nanoplate. The effects of nonlocal parameter, mode number, and taper parameter on the natural frequency were investigated. The results showed that increasing the taper parameter causes increasing of buckling load and natural frequencies, and its effects on the clamped boundary condition is more than the simply support.
1

40
54


Mehdi
Zarei
Tarbiat Modares University
Tarbiat Modares University
Iran
mehdi.zarei@modares.ac.ir


Gholamreza
Faghani
Department of Mechanical Engineering, Khatam Al Anbia Air Defense University,
Tehran, Iran
Department of Mechanical Engineering, Khatam
Iran
g.r.faghani@stud.nit.ac.ir


Mehran
Ghalami
Tarbiat Modares University
Tarbiat Modares University
Iran
m.ghalami.c@gmail.com


Gholam Hossien
Rahimi
Tarbiat Modares University
Tarbiat Modares University
Iran
rahimi_gh@modares.ac.ir
nonlocal theory
axisymmetric vibration analysis
variable thickness plate
Ritz method
Differential Transform Method
[[1] Sari, M.S., AlKouz, W.G., Vibration analysis of nonuniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory, International Journal of Mechanical Sciences, 114, 2016, pp. 1–11.##[2] SakhaeePour, A., Ahmadian, M.T., Vafai, A., Applications of singlelayered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications, 145, 2008, pp. 168–172.##[3] Arash, B., Wang, Q., A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Computational Materials Science, 51, 2012, pp. 303313.##[4] Murmu, T., Pradhan, S.C., Vibration analysis of nanosinglelayered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, Journal of Applied Physics, 105, 2009, pp. 64319.##[5] Arash, B., Wang, Q., A Review on the Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes, Modeling of Carbon Nanotubes, Graphene and their Composites, Springer International Publishing, 2014, pp. 57–82.##[6] Mindlin, R.D., Eshel, N.N., On first straingradient theories in linear elasticity, International Journal of Solids and Structures, 4, 1968, pp. 109124.##[7] Mindlin, R.D., Second gradient of strain and surfacetension in linear elasticity, International Journal of Solids and Structures, 1, 1965, pp. 417–438.##[8] Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P., Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51, 2003, pp. 1477–1508.##[9] Ramezani, S., A micro scale geometrically nonlinear Timoshenko beam model based on strain gradient elasticity theory, International Journal of NonLinear Mechanics, 47, 2012, pp. 863–873.##[10] Alibeigloo, A., Free vibration analysis of nanoplate using threedimensional theory of elasticity, Acta Mechanica, 222, 2011, pp. 149159.##[11] Şimşek, M., Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science, 48, 2010, pp. 1721–1732.##[12] Sahmani, S., Ansari, R., Gholami, R., Darvizeh, A., Dynamic stability analysis of functionally graded higherorder shear deformable microshells based on the modified couple stress elasticity theory, Composites Part B, 51, 2013, pp. 4453.##[13] Toupin, R.A., Theories of elasticity with couplestress, Archive for Rational Mechanics and Analysis, 17(2), 1964, pp. 85–112.##[14] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2002, pp. 2731–2743.##[15] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 1983, pp. 4703–4710.##[16] Peddieson, J., Buchanan, G.R., McNitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, pp. 305–312.##[17] Lu, P., Lee, H.P., Lu, C., Zhang, P.Q., Application of nonlocal beam models for carbon nanotubes, International Journal of Solids and Structures, 44, 2007, pp. 5289–5300.##[18] Rahmani, O., Pedram, O., Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77, 2014, pp. 55–70.##[19] Şimşek, M., Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, International Journal of Engineering Science, 105, 2016, pp. 12–27.##[20] HosseiniHashemi, S., Bedroud, M., Nazemnezhad, R., An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity, Composite Structures, 103, 2013, pp. 108–118.##[21] Belkorissat, I., Houari, MSA., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., On vibration properties of functionally graded nanoplate using a new nonlocal refined four variable model, Steel and Composite Structures, 18, 2015, pp. 1063–1081.##[22] Şimşek, M., Yurtcu, H.H., Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures, 97, 2013, pp. 378–386.##[23] Murmu, T., Pradhan, S.C., Buckling analysis of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E: LowDimensional Systems and Nanostructures, 41, 2009, pp. 1232–1239.##[24] Aksencer, T., Aydogdu, M., Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E: LowDimensional Systems and Nanostructures, 43, 2011, pp. 954959.##[25] Narendar, S., Buckling analysis of micro/nanoscale plates based on twovariable refined plate theory incorporating nonlocal scale effects, Composite Structures, 93, 2011, pp. 3093–3103.##[26] Farajpour, A., Mohammadi, M., Shahidi, A.R., Mahzoon, M., Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: LowDimensional Systems and Nanostructures, 43, 2011, pp. 1820–1825.##[27] Tornabene, F., Fantuzzi, N., Bacciocchi, M., The local GDQ method for the natural frequencies of doublycurved shells with variable thickness: A general formulation, Composites Part B, 92, 2016, pp. 265–289.##[28] Farajpour, A., Shahidi, A.R., Mohammadi, M., Mahzoon, M., Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics, Composite Structures, 94, 2012, pp. 1605–1615.##[29] Farajpour, A., Danesh, M., Mohammadi, M., Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: LowDimensional Systems and Nanostructures, 44, 2011, pp. 719–727.##[30] Danesh, M., Farajpour, A., Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, 39, 2012, pp. 23–27.##[31] Şimşek, M., Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science, 61, 2012, pp. 257–265.##[32] Efraim, E., Eisenberger, M., Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration, 299, 2007, pp. 720–738.##[33] Zhou, J.K., Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China, 1986.##[34] Arikoglu, A., Ozkol, I., Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method, Composite Structures, 92, 2010, pp. 3031–3039.##[35] Mohammadi, M., Farajpour, A., Goodarzi, M., Shehni nezhad pour, H., Numerical study of the effect of shear inplane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, 82, 2014, pp. 510–520.##[36] Pradhan, S.C., Phadikar, J.K., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A, 373, 2009, pp. 1062–1069.##[37] Behfar, K., Naghdabadi, R., Nanoscale vibrational analysis of a multilayered graphene sheet embedded in an elastic medium, Composites Science and Technology, 65, 2005, pp. 1159–1164.##[38] Mirzabeigy, A., Semianalytical approach for free vibration analysis of variable crosssection beams resting on elastic foundation and under axial force, International Journal of Engineering  Transactions C, 27, 2013, pp. 385394.##[39] Mohammadi, M., Goodarzi, M., Ghayour, M., Farajpour, A., Influence of inplane preload on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B, 51, 2013, pp. 121–129.##[40] Karimi, M., Shahidi, A.R., Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermomechanical and shear loadings, Applied Physics A, 123(5), 2017, pp. 304.##[41] Karimi, M., Haddad, H.A., Shahidi, A.R., Combining surface effects and nonlocal two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates, Micro and Nano Letters, 10, 2015, pp. 276–281.##[42] Karimi, M., Shahidi, A.R., ZiaeiRad, S, Surface layer and nonlocal parameter effects on the inphase and outofphase natural frequencies of a doublelayer piezoelectric nanoplate under thermoelectromechanical loadings, Microsystem Technologies, 23(10), 2017, pp. 4903–4915.##[43] Karimi, M., Mirdamadi, H.R, Shahidi, A.R., Positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in–plane loadings based on nonlocal elasticity theory, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 2017, pp. 1391–1404.##[44] Shokrani, M.H., Karimi, M., Tehrani, M.S., Mirdamadi, H.R., Buckling analysis of doubleorthotropic nanoplates embedded in elastic media based on nonlocal twovariable refined plate theory using the GDQ method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, 2016, pp. 2589–2606.##[45] Karimi, M., Mirdamadi, H.R., Shahidi, A.R., Shear vibration and buckling of doublelayer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects, Microsystem Technologies, 23, 2017, pp. 765–797.##[46] Liu, C., Ke, L.L., Yang, J., Kitipornchai, S., Wang, Y.S., Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory, Mechanics of Advanced Materials and Structures, 2016, doi: 10.1080/15376494.2016.1149648.##[47] Asemi, S.R., Farajpour, A., Asemi, H.R., Mohammadi, M., Influence of initial stress on the vibration of doublepiezoelectricnanoplate systems with various boundary conditions using DQM, Physica E, 63, 2014, pp. 169179.##[48] Liu, C., Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S., Buckling and postbuckling analyses of sizedependent piezoelectric nanoplates, Theoretical and Applied Mechanics Letters, 6(6), 2016, pp. 253267.##[49] Mohammadi, M, Moradi, A., Ghayour, M., Farajpour, A., Exact solution for thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, 11(3), 2014, pp. 437458.##[50] Ke, L.L., Liu, C., Wang, Y.S., Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions, Physica E: Lowdimensional Systems and Nanostructures, 66, 20415, pp. 93106.##[51] Malekzadeh, P., Farajpour, A., Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium, Acta Mechanica, 223, 2012, pp. 2311–2330.##[52] Bedroud, M., HosseiniHashemi, S., Nazemnezhad, R., Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica, 224, 2013, pp. 2663–2676.##[53] Anjomshoa, A., Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nanoplates based on nonlocal elasticity theory, Meccanica, 48, 2013, pp. 13371353.##[54] Singh, B., Saxena, V., Axisymmetric vibration of a circular plate with double linear variable thickness, Journal of Sound and Vibration, 179, 1995, pp. 879–897.##[55] Liew, K.M., He, X.Q., Kitipornchai, S., Predicting nanovibration of multilayered graphene sheets embedded in an elastic matrix, Acta Materialia, 54, 2006, pp. 4229–4236.##[56] Mohammadi, M., Ghayour, M., Farajpour, A., Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B, 45, 2013, pp. 32–42.##[1] Sari, M.S., AlKouz, W.G., Vibration analysis of nonuniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory, International Journal of Mechanical Sciences, 114, 2016, pp. 1–11.##[2] SakhaeePour, A., Ahmadian, M.T., Vafai, A., Applications of singlelayered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications, 145, 2008, pp. 168–172.##[3] Arash, B., Wang, Q., A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Computational Materials Science, 51, 2012, pp. 303313.##[4] Murmu, T., Pradhan, S.C., Vibration analysis of nanosinglelayered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, Journal of Applied Physics, 105, 2009, pp. 64319.##[5] Arash, B., Wang, Q., A Review on the Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes, Modeling of Carbon Nanotubes, Graphene and their Composites, Springer International Publishing, 2014, pp. 57–82.##[6] Mindlin, R.D., Eshel, N.N., On first straingradient theories in linear elasticity, International Journal of Solids and Structures, 4, 1968, pp. 109124.##[7] Mindlin, R.D., Second gradient of strain and surfacetension in linear elasticity, International Journal of Solids and Structures, 1, 1965, pp. 417–438.##[8] Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P., Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51, 2003, pp. 1477–1508.##[9] Ramezani, S., A micro scale geometrically nonlinear Timoshenko beam model based on strain gradient elasticity theory, International Journal of NonLinear Mechanics, 47, 2012, pp. 863–873.##[10] Alibeigloo, A., Free vibration analysis of nanoplate using threedimensional theory of elasticity, Acta Mechanica, 222, 2011, pp. 149159.##[11] Şimşek, M., Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science, 48, 2010, pp. 1721–1732.##[12] Sahmani, S., Ansari, R., Gholami, R., Darvizeh, A., Dynamic stability analysis of functionally graded higherorder shear deformable microshells based on the modified couple stress elasticity theory, Composites Part B, 51, 2013, pp. 4453.##[13] Toupin, R.A., Theories of elasticity with couplestress, Archive for Rational Mechanics and Analysis, 17(2), 1964, pp. 85–112.##[14] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2002, pp. 2731–2743.##[15] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 1983, pp. 4703–4710.##[16] Peddieson, J., Buchanan, G.R., McNitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, pp. 305–312.##[17] Lu, P., Lee, H.P., Lu, C., Zhang, P.Q., Application of nonlocal beam models for carbon nanotubes, International Journal of Solids and Structures, 44, 2007, pp. 5289–5300.##[18] Rahmani, O., Pedram, O., Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77, 2014, pp. 55–70.##[19] Şimşek, M., Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, International Journal of Engineering Science, 105, 2016, pp. 12–27.##[20] HosseiniHashemi, S., Bedroud, M., Nazemnezhad, R., An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity, Composite Structures, 103, 2013, pp. 108–118.##[21] Belkorissat, I., Houari, MSA., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., On vibration properties of functionally graded nanoplate using a new nonlocal refined four variable model, Steel and Composite Structures, 18, 2015, pp. 1063–1081.##[22] Şimşek, M., Yurtcu, H.H., Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures, 97, 2013, pp. 378–386.##[23] Murmu, T., Pradhan, S.C., Buckling analysis of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E: LowDimensional Systems and Nanostructures, 41, 2009, pp. 1232–1239.##[24] Aksencer, T., Aydogdu, M., Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E: LowDimensional Systems and Nanostructures, 43, 2011, pp. 954959.##[25] Narendar, S., Buckling analysis of micro/nanoscale plates based on twovariable refined plate theory incorporating nonlocal scale effects, Composite Structures, 93, 2011, pp. 3093–3103.##[26] Farajpour, A., Mohammadi, M., Shahidi, A.R., Mahzoon, M., Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: LowDimensional Systems and Nanostructures, 43, 2011, pp. 1820–1825.##[27] Tornabene, F., Fantuzzi, N., Bacciocchi, M., The local GDQ method for the natural frequencies of doublycurved shells with variable thickness: A general formulation, Composites Part B, 92, 2016, pp. 265–289.##[28] Farajpour, A., Shahidi, A.R., Mohammadi, M., Mahzoon, M., Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics, Composite Structures, 94, 2012, pp. 1605–1615.##[29] Farajpour, A., Danesh, M., Mohammadi, M., Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: LowDimensional Systems and Nanostructures, 44, 2011, pp. 719–727.##[30] Danesh, M., Farajpour, A., Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, 39, 2012, pp. 23–27.##[31] Şimşek, M., Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science, 61, 2012, pp. 257–265.##[32] Efraim, E., Eisenberger, M., Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration, 299, 2007, pp. 720–738.##[33] Zhou, J.K., Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China, 1986.##[34] Arikoglu, A., Ozkol, I., Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method, Composite Structures, 92, 2010, pp. 3031–3039.##[35] Mohammadi, M., Farajpour, A., Goodarzi, M., Shehni nezhad pour, H., Numerical study of the effect of shear inplane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, 82, 2014, pp. 510–520.##[36] Pradhan, S.C., Phadikar, J.K., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A, 373, 2009, pp. 1062–1069.##[37] Behfar, K., Naghdabadi, R., Nanoscale vibrational analysis of a multilayered graphene sheet embedded in an elastic medium, Composites Science and Technology, 65, 2005, pp. 1159–1164.##[38] Mirzabeigy, A., Semianalytical approach for free vibration analysis of variable crosssection beams resting on elastic foundation and under axial force, International Journal of Engineering  Transactions C, 27, 2013, pp. 385394.##[39] Mohammadi, M., Goodarzi, M., Ghayour, M., Farajpour, A., Influence of inplane preload on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B, 51, 2013, pp. 121–129.##[40] Karimi, M., Shahidi, A.R., Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermomechanical and shear loadings, Applied Physics A, 123(5), 2017, pp. 304.##[41] Karimi, M., Haddad, H.A., Shahidi, A.R., Combining surface effects and nonlocal two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates, Micro and Nano Letters, 10, 2015, pp. 276–281.##[42] Karimi, M., Shahidi, A.R., ZiaeiRad, S, Surface layer and nonlocal parameter effects on the inphase and outofphase natural frequencies of a doublelayer piezoelectric nanoplate under thermoelectromechanical loadings, Microsystem Technologies, 23(10), 2017, pp. 4903–4915.##[43] Karimi, M., Mirdamadi, H.R, Shahidi, A.R., Positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in–plane loadings based on nonlocal elasticity theory, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 2017, pp. 1391–1404.##[44] Shokrani, M.H., Karimi, M., Tehrani, M.S., Mirdamadi, H.R., Buckling analysis of doubleorthotropic nanoplates embedded in elastic media based on nonlocal twovariable refined plate theory using the GDQ method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, 2016, pp. 2589–2606.##[45] Karimi, M., Mirdamadi, H.R., Shahidi, A.R., Shear vibration and buckling of doublelayer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects, Microsystem Technologies, 23, 2017, pp. 765–797.##[46] Liu, C., Ke, L.L., Yang, J., Kitipornchai, S., Wang, Y.S., Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory, Mechanics of Advanced Materials and Structures, 2016, doi: 10.1080/15376494.2016.1149648.##[47] Asemi, S.R., Farajpour, A., Asemi, H.R., Mohammadi, M., Influence of initial stress on the vibration of doublepiezoelectricnanoplate systems with various boundary conditions using DQM, Physica E, 63, 2014, pp. 169179.##[48] Liu, C., Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S., Buckling and postbuckling analyses of sizedependent piezoelectric nanoplates, Theoretical and Applied Mechanics Letters, 6(6), 2016, pp. 253267.##[49] Mohammadi, M, Moradi, A., Ghayour, M., Farajpour, A., Exact solution for thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, 11(3), 2014, pp. 437458.##[50] Ke, L.L., Liu, C., Wang, Y.S., Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions, Physica E: Lowdimensional Systems and Nanostructures, 66, 20415, pp. 93106.##[51] Malekzadeh, P., Farajpour, A., Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium, Acta Mechanica, 223, 2012, pp. 2311–2330.##[52] Bedroud, M., HosseiniHashemi, S., Nazemnezhad, R., Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica, 224, 2013, pp. 2663–2676.##[53] Anjomshoa, A., Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nanoplates based on nonlocal elasticity theory, Meccanica, 48, 2013, pp. 13371353.##[54] Singh, B., Saxena, V., Axisymmetric vibration of a circular plate with double linear variable thickness, Journal of Sound and Vibration, 179, 1995, pp. 879–897.##[55] Liew, K.M., He, X.Q., Kitipornchai, S., Predicting nanovibration of multilayered graphene sheets embedded in an elastic matrix, Acta Materialia, 54, 2006, pp. 4229–4236.##[56] Mohammadi, M., Ghayour, M., Farajpour, A., Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B, 45, 2013, pp. 32–42.##]
Reducing Retrieval Time in Automated Storage and Retrieval System with a Gravitational Conveyor Based on MultiAgent Systems
2
2
The main objective of this study is to reduce the retrieval time of a list of products by choosing the best combination of storage and retrieval rules at any time. This is why we start by implementing some storage rules in an Automated Storage/Retrieval System (Automated Storage and Retrieval System: AS/RS) fitted with a gravity conveyor while some of these rules are dedicated to storage and others to retrieval. The system is seen as a MultiAgent System (MAS) where the produced agents are reactive agents that can interact to achieve a behavior (organizing the store). Our MAS is characterized by a decentralized control, which means that there is no preset plan. The produced agents exchange information such as their color, their distance from the output station, etc. Each product merely applies a set of behavioral rules. The aim is to choose the best product to be retrieved in the shortest possible time. The producttype agents have no cognitive ability, but still perform complex tasks.
1

55
68


Imén
Kouloughli
Manufacturing Engineering Laboratory of Tlemcen, University of Tlemcen, Algeria.
Manufacturing Engineering Laboratory of Tlemcen,
Iran
kouloughli_imen@hotmail.com


Pierre
Castagna
LUNAM University, QLIO Department, University of Nantes 44000, France.
LUNAM University, QLIO Department, University
Iran


Zaki
Sari
LUNAM University, QLIO Department, University of Nantes 44000, France.
LUNAM University, QLIO Department, University
Iran
AS/RS fitted with gravity conveyor
storage / retrieval
combination of rules
MAS
retrieval time
[[1] Material Handling Institute, Considerations for planning and installing an automated storage/retrieval systems, Material Handling Institute, 1977.##[2] Roodbergen, K.J., Vis, I.F. A survey of literature on automated storage and retrieval systems, European Journal of Operational Research, 194(2), 2009, pp. 343362.##[3] Azzouz, A., Sari, Z., Ghouali, N., La méthode de Branch & Bound appliquée à l’optimisation des dimensions d’un AS/RS à convoyeur gravitationnel, Conférence Internationale sur la production, CIP2001, June 2001, Alger pp. 911, 2001.##[4] Azzouz, A., Optimisation des dimensions d’un AS/RS à convoyeur gravitationnel pour un temps de cycle minimum, Doctoral Dissertation, Thèse de magister, Université de Tlemcen Algérie, 2001.##[5] Azzouz, A., Sari, Z., Ghouali, N., Une synthèse sur l’optimisation des dimensions d’un AS/RS à convoyeur gravitationnel, Conférence Internationale sur la conception et la production intégrée, October 2001, pp. 2426.##[6] Gaouar, N., Amélioration des performances d’un AS/RS à convoyeur gravitationnel, Doctoral Dissertation, Thèse de magister, Université de Tlemcen Algérie, 2001.##[7] Sari, Z., Saygin, C., Ghouali, N., Traveltime models for flowrack automated storage and retrieval systems, International Journal of Advanced Manufacturing Technology, 25(910), 2005, pp. 979987.##[8] Ouhoud, A., Guezzen, A., Sari, Z., Experimental Validation of Travel Time Models for Multi Aisle Automated Storage and Retrieval System in ClassBased Storage. Electrotehnica, Electronica, Automatica, 64(1), 2016, pp. 150.##[9] Mansour, W., Jelassi, K., Flexible Software solution for intelligent multiagent manufacturing systems. In Electrical Sciences and Technologies in Maghreb (CISTEM), 2014 International Conference on, November 2014, pp. 14.s##[10] Indriago, C., Cardin, O., Rakoto, N., Castagna, P., Chacòn, E., H 2 CM: A holonic architecture for flexible hybrid control systems, Computers in Industry, 77, 2016, pp. 1528.##[11] Anane, D., Pinson, S., Aknine, S., Les approches agents pour la coordination d’activités dans les chaînes logistiques, CAHIER DU LAMSADE 291, University ParisDauphine, 2009.##[12] Sayda, A.F., Multiagent Systems for Industrial Applications: Design, Development, and Challenges, Multi Agent Systems  Modeling, Control, Programming, Simulations and Applications, Dr. Faisal Alkhateeb (Ed.), InTech, 2013.##[13] Pannequin, R., Thomas, A., Proposition d'une plateforme d'expérimentation sur le contrôle par le produit des flux de production. In 6ème Conférence Francophone de Modélisation et Simulation, MOSIM'06, April, 2006.##[14] CLAIR, G., Gestion de production par système multiagent autoorganisateur, Rapport de Master, 2, 2008.##[15] Seddik, R., Elaboration d'un protocole de coordination dans un SMA pour la gestion de production dynamique: Vers une approhe décentralisée, Doctoral Dissertation, Université Ahmed Ben Bella d'Oran1 Es Senia, 2011.##[16] Taghezout, N., Conception et développement d'un système multiagent d'aide à la décision pour la gestion de production dynamique, Doctoral dissertation, Université de Toulouse, Université Toulouse IIIPaul Sabatier, 2011.##[17] Moyaux, T., Comment les syst mes multiagents pourraient aider la gestion de la production, de la distribution et des stocks, 2001.##[18] Kouloughli, I., Castagna, P., Sari, Z., Development of a MultiAgent System (MAS) to optimize the retrieval time within an automated storage/retrieval system, Electrotehnica, Electronica, Automatica, 64(3), 2016, pp. 115.##[19] Lu, W., Giannikas, V., McFarlane, D., Hyde, J., The role of distributed intelligence in warehouse management systems. In Service Orientation in Holonic and MultiAgent Manufacturing and Robotics, 2014, pp. 6377.##[20] Gazdar, M.K., Optimisation Heuristique Distribuee du Probleme de Stockage de Conteneurs dans un port, Ecole Nationale des sciences de I'informatique, Universite de Manouba, 2008.##[21] Thomas, A., Borangiu, T., Trentesaux, D., Holonic and multiagent technologies for service and computing oriented manufacturing, Journal of Intelligent Manufacturing, 28, 2017, pp. 1501–1502.##[22] Perera, L.C.M., Karunananda, A.S., Using A Multiagent System For Supply Chain Management, International Journal of Design & Nature and Ecodynamics, 11(2), 2016, pp. 107115.##[23] Naveh, Y., Ronen, A., U.S. Patent No. 9, 430, 299. Washington, DC: U.S. Patent and Trademark Office, 2016.##[24] Tisue, S., Wilensky, U., Netlogo: A simple environment for modeling complexity, International Conference on Complex Systems, 21, May 2004, pp. 1621.##]
Experimental Investigation on Radial Ball Bearing Parameters Using Taguchi Method
2
2
In this work, characteristics of various ball bearing parameters are studied under different loads and rotational speeds. By using Dimensional Analysis (DA), dimensionless parameters are computed which provides solution for a group of parameters. This analysis can be accomplished by using the Buckingham πtheorem. DA leads to reduction of the number of independent parameters involved in a problem. These independent parameters get expressed as dimensionless groups. These dimensionless groups are always ratios of important physical quantities involved in the problem of interest. In modeling and experimentation, its main function is to reduce the amount of independent variables, simplify the solution, and generalize the results. It becomes an effective method, especially if a complete mathematical model of the investigated process is not known. Moreover, in the present work the Buckingham πtheorem is applied to find the influencing parameter π5 by using the Taguchi method.
1

69
74


G.
Maheedhara Reddy
Mechanical Engineering, Assistant professor, NBKR institute of science and Technology, Nellore, India
Mechanical Engineering, Assistant professor,
Iran
mahee.8029@gmail.com


V.
Diwakar Reddy
MECHANICAL ENGINEERING,PROFESSOR,S V UNIVERSITY
MECHANICAL ENGINEERING,PROFESSOR,S V UNIVERSITY
Iran
vdrsvuce@gmail.com


B.
Satheesh Kumar
MECHANICAL ENGINEERING,ASSOCIATE PROFESSOR,NBKRIST,NELLORE
MECHANICAL ENGINEERING,ASSOCIATE PROFESSOR,NBKRIST
Iran
satheeshkumar76svu@gmail.com


J.
Shyamsunder
Department of Mechanical Engineering, CMR College of Engineering and Technology
Kandlakoya, Hyderabad, 501401
India
Department of Mechanical Engineering, CMR
Iran
shyamv4u@gmail.com
Ball bearing
Dimensional analysis (DA)
Buckingham πtheorem
Taguchi method
ANOVA
[[1] Kunes, J., Similarity and modeling in science and Engineering, Cambridge International Science Publishing, 2012.##[2] Pinkus, O., The Reynolds Centennial: A Brief History of the Theory of Hydrodynamic Lubrication, Journal of Tribology, 109, 1987, pp. 220.##[3] Cameron, A., Wood, L., The Full Journal Bearing, Proceedings of Institution of Mechanical Engineers, London, 161, 1949, pp. 59.##[4] Wilcock, D.F., Pinkus, O., Effect of Turbulence and Viscosity Variation on Dynamic Coefficients of Fluid Film Journal Bearings, Journal of Tribology, 107, 1985, pp. 256262.##[5] Petrusevich, A.I., Fundamental conclusions from the contacthydrodynamic theory of lubrication, Izvestiya Akademii Nauk SSR, 2, 1951, pp. 209.##[6] Ocvirk, F.W., Short Bearing Approximation for Full Journal Bearings, NACA, TN  2808, 1952.##[7] Oliver, D.R., Load Enhancement Effects due to Polymer Thickening in a Short Model Journal Bearing, Journal of NonNewtonian Fluid Mechanics, 30, 1988, pp.185196.##[8] Sommerfeld, A., Gaussian algorithm for solving finite difference equations of Reynolds equation, Zeitschrift für angewandte Mathematik und Physik, 50, 1904, pp. 77155.##[9] Wilcock, D.F., Pinkus, O., Effect of Turbulence and Viscosity Variation on Dynamic Coefficients of Fluid Film Journal Bearings, Journal of Tribology, 107, 1985, pp. 256262.##[10] Raimondi, A.A., Boyd, J., A Solution for the Finite Journal Bearing and Its Application to Analysis and DesignIII, ASLE Transactions, 1(1), 1958, pp. 159174.##[11] Goneka, P.K., Booker, J.F., Spherical Bearings: Static and Dynamic Analysis via Finite Element Method, Journal of Lubrication Technology, 102, 1980, pp. 308319.##[12] Ng, C.W., Pan, C.H.T., A Linearised Turbulent Lubrication Theory, Journal of Basic Engineering, 87(3), 1965, pp. 625688.##[13] Lund, J.W., The Stability of an Elastic Rotor in Journal Bearing with Flexible Damped Supports, Journal of Applied Mechanics, 32(4), 1965, pp. 91192.##[14] Abed Alr Zaq, S., Alshqirate, M.T., Mahmoud, H., Dimensional analysis and empirical correlations for heat transfer and pressure drop in condensation and evaporation processes of flow inside micro pipes, Journal of the Brazil Society of Mechanical Science & Engineering, 34(1), 2012, pp. 8996.##[15] Storey, B.A., Fluid dynamics and heat transfer  An introduction to the fundamentals, Olin College, 2015.##]