ORIGINAL_ARTICLE
Transient Natural Convection in an Enclosure with Variable Thermal Expansion Coefficient and Nanofluid Properties
Transient natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity, and the thermal expansion coefficient of Al2O3-water nanofluid. The study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ ϕ ≤ 7%), the enclosure aspect ratio (AR =1), and temperature differences between the cold and hot walls (∆T= 30). Transient parameters such as development time and time-average Nusselt number along the cold wall are also presented as a non-dimensional form. Increasing the Rayleigh number shortens the non-dimensional time of the initializing stage. By increasing the volume fraction of nanoparticles, the flow development time shows different behaviors for various Rayleigh numbers. The non-dimensional development time decreases by enhancing the concentration of nanoparticles.
http://jacm.scu.ac.ir/article_13099_bc7fbf2899e409686ed46e9a9988a56c.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
133
139
10.22055/jacm.2017.22206.1128
Nanofluid
natural convection
variable property
transient natural convection
Esmaeil
Ghahremani
eghahremani86@gmail.com
true
1
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
LEAD_AUTHOR
[1] Ghahremani, E., Ghaffari, R., Ghadjari, H., Mokhtari, J., Effect of variable thermal expansion coefficient and nanofluid properties on steady natural convection in an enclosure, Journal of Applied and Computational Mechanics, 3(4), 2017, pp. 240-250.
1
[2] Xuan, Y., Roetzel, W., Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer,43, 2000, pp. 3701–3707.
2
[3] Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer,46, 2003, pp. 3639–3653.
3
[4] Gosselin, L., da Silva, A. K., Combined heat transfer and power dissipation optimization of nanofluid flows”, Applied Physics Letters, 85, 2004, pp. 4160–4162.
4
[5] Brinkman, H. C., The viscosity of concentrated suspensions and solutions, Journal of Chemical Physics, 20, 1952, pp. 571–581.
5
[6] Polidori, G., Fohanno, S., Nguyen, C. T., A note on heat transfer modeling of Newtonian nanofluids in laminar free convection, International Journal of Thermal Sciences,46, 2007, pp. 739–744.
6
[7] Ho, C. J., Chen, M. W., Li, Z. W., Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer, 51, 2008, pp. 4506–4516.
7
[8] Maiga, S. E. B., Nguyen, C. T., Galanis, N., Roy, G., Heat transfer behaviors of nanofluids in a uniformly heated tube, Superlattices and Microstructures,35, 2004, pp. 543–557.
8
[9] Aminossadati, S. M., Ghasemi, B., Natural convection of water–CuO nanofluid in a cavity with two pairs of heat source–sink, International Communications in Heat and Mass Transfer,38, 2011, pp. 672–678.
9
[10] Koo, J., Kleinstreuer, C., A new thermal conductivity model for nanofluids, Journal of Nanoparticle Research,6(6), 2004, pp. 577–588.
10
[11] Koo, J., Kleinstreuer, C., Laminar nanofluid flow in micro heat-sinks, International Journal of Heat and Mass Transfer,48(13), 2005, pp. 2652–2661.
11
[12] Abu-Nada., E., Chamkha, A. J., Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–water nanofluid, International Journal of Thermal Sciences, 49(12), 2010, pp. 2339-2352.
12
[13] Sheikholeslami, M., Ellahi, R., Hassan, M., Soleimani, S., A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder, International Journal of Numerical Methods for Heat & Fluid Flow, 24(8), 2014, pp. 1906-1927.
13
[14] Leal, M. A., Machado, H. A., Cotta, R. M., Integral transform solutions of transient natural convection in enclosures with variable fluid properties, International Journal of Heat and Mass Transfer, 43(21), 2000, pp. 3977-3990.
14
[15] Yu, Z. -T., Wang, W., Xu, X., Fan, L. -W., Hu, Y. -C., Cen, K. -F., A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity, International Communications in Heat and Mass Transfer, 38, 2011, pp. 585–589.
15
[16] Yu, Z. -T., Xu, X., Hu, Y. -C., Fan, L. -W., Cen, K. -F., A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a horizontal concentric annulus, International Journal of Heat and Mass Transfer, 55, 2012, pp. 1141–1148.
16
[17] Rahman, M. M., Oztop, H. F., Mekhilef, S., Saidur, R., Al-Salem, K., Unsteady natural convection in Al2O3–water nanoliquid filled in isosceles triangular enclosure with sinusoidal thermal boundary condition on bottom wall, Superlattices and Microstructures, 67, 2014, pp. 181–196.
17
[18] Alsabery, A. I., Saleh, H., Hashim, I., Siddheshwar, P.G., Nanoliquid-Saturated Porous Oblique Cavity using Thermal Non-Equilibrium Model, International Journal of Mechanical Sciences, 114, 2016, pp. 233-245.
18
[19] Nguyen, M. T., Aly, A. M., Lee, S.-W., Unsteady natural convection heat transfer in a nanofluid-filled square cavity with various heat source conditions, Advances in Mechanical Engineering, 8(5), 2016, pp. 1–18.
19
[20] Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor and Francis Group, New York, 1980.
20
[21] Versteeg, H. K., Malalasekera, W., An Introduction to Computational Fluid Dynamic: The Finite Volume Method, John Wiley & Sons Inc., New York, 1995.
21
ORIGINAL_ARTICLE
Buckling Analysis of Embedded Nanosize FG Beams Based on a Refined Hyperbolic Shear Deformation Theory
In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FG nanobeams embedded in the elastic foundation are obtained. To predict the buckling behavior of embedded FG nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, power-law index, nonlocal parameter, and slenderness ratio on the critical buckling loads of size dependent FG nanobeams.
http://jacm.scu.ac.ir/article_13152_ea7f900222f2f8ab4a01ec11850c1f02.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
140
146
10.22055/jacm.2017.22996.1146
FG nanobeam
Elastic foundation
Buckling
nonlocal elasticity theory
Shear deformation beam theory
Aicha
Bessaim
aicha.bessaim@gmail.com
true
1
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
AUTHOR
Mohammed Sid
Ahmed Houari
houarimsa@yahoo.fr
true
2
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie | Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
LEAD_AUTHOR
Bousahla
Abdelmoumen Anis
bousahla.anis@gmail.com
true
3
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria | Centre Universitaire de Relizane, Algérie
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria | Centre Universitaire de Relizane, Algérie
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria | Centre Universitaire de Relizane, Algérie
AUTHOR
Abdelhakim
Kaci
abdelhakim.kaci@gmail.com
true
4
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
AUTHOR
Abdelouahed
Tounsi
tou_abdel@yahoo.com
true
5
Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie | Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
AUTHOR
El Abbes
Adda Bedia
adda.bedia@gmail.com
true
6
Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria
Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria
Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria
AUTHOR
[1] Bedjilili, Y., Tounsi, A., Berrabah, H.M., Mechab, I., Adda Bedia, E.A., Benaissa, S., Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation, Applied Mathematics and Mechanics, 30(6), 2009, 717-726.
1
[2] Ghugal, Y.M., Shimpi, R.P., A review of refined shear deformation theories for isotropic and anisotropic laminated beams, Journal of Reinforced Plastics and Composites, 20(3), 2001, 255-272.
2
[3] Sayyad, A.S., Ghugal, Y.M., A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates, International Journal of Applied Mechanics, 9(1), 2017, 1750007.
3
[4] Peddieson, J., Buchanan, G.R., Mc Nitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, 305–312.
4
[5] Ebrahimi, F., Barati, M.R., Electromechanical buckling behavior of smart piezoelectrically actuated higher order size-dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials, 7, 2016, 69–90.
5
[6] Eringen, A.C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10(1), 1972, 1-16.
6
[7] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54(9), 1983, 4703-4710.
7
[8] Yang, F.A.C.M., Chong, A.C.M., Lam, D.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2002, 2731-2743.
8
[9] Zemri, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A., A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics, 54(4), 2015, 693-710.
9
[10] Ebrahimi, F., Barati, M.R., Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(3), 2017, 937-952.
10
[11] Aydogdu, M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41, 2009, 1651–1655.
11
[12] Rahmani ,O., Jandaghian ,A.A., Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory, Applied Physics A, 119(3), 2015, 1019–1032.
12
[13] Tounsi, A, Semmah, A., Bousahla, A.A., Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory, Journal of Nanomechanics and Micromechanics, 3, 2013, 37–42.
13
[14] Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O., Mahmoud, S.R., Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 2015, 425-442.
14
[15] Pisano, A.A., Sofi, A., Fuschi, P., Finite element solutions for nonhomogeneous nonlocal elastic problems, Mechanics Research Communications, 36, 2009, 755–761.
15
[16] Pisano, A.A., Sofi, A., Fuschi, P., Nonlocal integral elasticity: 2D finite element based solutions, International Journal of Solids and Structures, 46, 2009, 3836–3849.
16
[17] Janghorban, M., Zare, A., Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method, Physica E: Low-dimensional Systems and Nanostructures, 43, 2011, 1602–1604.
17
[18] Eltaher, M.A., Emam, S.A., Mahmoud, F.F., Free vibration analysis of functionally graded size-dependent nanobeams, Applied Mathematics and Computation, 218, 2012, 7406-7420.
18
[19] Lim, C.W., Zhang, G., Reddy, J.N., A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 2015, 298–313.
19
[20] Ebrahimi, F, Barati, M.R, Dabbagh, A., A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science, 107, 2016, 169–182.
20
[21] Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A., Tounsi, A., A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems, 19(2), 2017, 115-126.
21
[22] Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics, 62(6), 2017, 695-702.
22
ORIGINAL_ARTICLE
Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a viscoelastic matrix was modeled as a three-parameter foundation. Furthermore, the differential quadrature method was applied by which the critical load was obtained. Finally, since there was no research available for the dynamic buckling of a nanoplate, the static buckling was taken into consideration to compare the results and explain some significant and novel findings. One of these results showed that for greater values of the nanoscale parameter, the small scale had further influences on the dynamic buckling.
http://jacm.scu.ac.ir/article_13235_97bcdc2fe5d861b8a98c5ad3f8e064b9.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
147
160
10.22055/jacm.2017.22661.1138
Dynamic buckling
Graphene sheet
Viscoelastic matrix
differential quadrature method
Mohammad
Malikan
mohammad.malikan@yahoo.com
true
1
Department of Mechanical engineering, faculty of engineering, Islamic Azad University, Mashhad branch, Iran
Department of Mechanical engineering, faculty of engineering, Islamic Azad University, Mashhad branch, Iran
Department of Mechanical engineering, faculty of engineering, Islamic Azad University, Mashhad branch, Iran
LEAD_AUTHOR
Mohammad Naser
Sadraee Far
sadrayifar_m@yahoo.com
true
2
Department of mechanical engineering, Islamic Azad university, Mashhad
Department of mechanical engineering, Islamic Azad university, Mashhad
Department of mechanical engineering, Islamic Azad university, Mashhad
AUTHOR
[1] Shijie, C., Hong, H., Hee Kiat, Ch., Numerical analysis of dynamic buckling of rectangular plates subjected to intermediate-velocity impact, International Journal of Impact Engineering, 25(2), 2001, 147-167.
1
[2] Hosseini-Ara, R., Mirdamadi, H.R., Khademyzadeh, H., Salimi, H., Thermal effect on dynamic stability of single-walled Carbon Nanotubes in low and high temperatures based on Nonlocal shell theory, Advanced Materials Research, 622-623, 2013, 959-964.
2
[3] Haftchenari, H., Darvizeh, M., Darvizeh, A., Ansari, R., Sharma, C.B., Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM), Composite Structures, 78(2), 2007, 292–298.
3
[4] Tamura, Y.S., Babcock, C.D., Dynamic stability of cylindrical shells under step loading, Journal of Applied Mechanics, 42(1), 1975, 190-194
4
[5] Jabareen, M., Sheinman, I., Dynamic buckling of a beam on a nonlinear elastic foundation under step loading, Journal of Mechanics of Materials and Structures, 4, 2009, 7-8.
5
[6] Ramezannezhad Azarboni, H., Darvizeh, M., Darvizeh, A., Ansari, R., Nonlinear dynamic buckling of imperfect rectangular plates with different boundary conditions subjected to various pulse functions using the Galerkin method, Thin-Walled Structures, 94, 2015, 577–584.
6
[7] Wang, X., Yang, W.D., Yang, S., Dynamic stability of carbon nanotubes reinforced composites, Applied Mathematical Modelling, 38(11-12), 2014, 2934-2945.
7
[8] Petry, D., Fahlbusch, G., Dynamic buckling of thin isotropic plates subjected to in-plane impact, Thin-Walled Structures, 38(3), 2000, 267–283.
8
[9] Kubiak, T., Criteria of dynamic buckling estimation of thin-walled structures, Thin-Walled Structures, 45(10-11), 2007, 888–892.
9
[10] Reddy, J.N., Srinivasa, A.R., Non-linear theories of beams and plates accounting for moderate rotations and material length scales, International Journal of Non-Linear Mechanics, 66, 2014, 43-53.
10
[11] Ghorbanpour Arani, A., Shiravand, A., Rahi, M., Kolahchi, R., Nonlocal vibration of coupled DLGS systems embedded on Visco-Pasternak foundation, Physica B, 407, 2012, 4123–4131.
11
[12] Eringen, A.C., Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002.
12
[13] Eringen, A.C., Linear theory of non-local elasticity and dispersion of plane waves, International Journal of Engineering Science, 10(5), 1972, 425-435.
13
[14] Duan, W.H., Wang, C.M., Zhang, Y.Y., Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of Applied Physics, 101(2), 2007, 24305-24311.
14
[15] Duan, W.H., Wang, C.M., Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology, 18(38), 2007, 385704.
15
[16] https://www.slideshare.net/zead28/concept-ofcomplexfrequency.
16
[17] Franco, S., Electric Circuits Fundamentals, Oxford University Press, Inc., 1995.
17
[18] Bellman, R., Kashef, B.G., Casti, J., Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equation, Journal of Computational Physics, 10(1), 1972, 40–52.
18
[19] Shu, C., Differential Quadrature and Its Application in Engineering, Springer, Berlin, 2000.
19
[20] Bellman, R., Casti, J., Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34(2), 1971, 235–238.
20
[21] Chen, W., Differential Quadrature Method and its Applications in Engineering, Shanghai Jiao Tong University, 1996.
21
[22] Golmakani, M.E., Rezatalab, J., Non uniform biaxial buckling of orthotropic Nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, 119, 2015, 238-250.
22
[23] Murmu, T., Pradhan, S.C., Buckling analysis of a single-walled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E, 41(7), 2009, 1232–9.
23
[24] 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(6), 2017, 2145-2161.
24
[25] Ansari, R., Sahmani, S., Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Applied Mathematical Modelling, 37(12-13), 2013, 7338–7351.
25
[26] Malikan, M., Jabbarzadeh, M., Sh. Dastjerdi, Non-linear Static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum, Microsystem Technologies, 23(7), 2017, 2973-2991.
26
[27] Malikan, M., Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory, Applied Mathematical Modelling, 48, 2017, 196–207.
27
[28] Malikan, M., Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory, Journal of Applied and Computational Mechanics, 3(3), 2017, 218–228.
28
[29] Malikan, M., Buckling analysis of micro sandwich plate with nano coating using modified couple stress theory, Journal of Applied and Computational Mechanics, 4(1), 2018, 1-15.
29
[30] Civalek, Ö., Korkmaz, A., Demir, Ç., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges, Advances in Engineering Software, 41(4), 2010, 557-560.
30
[31] Dastjerdi, S., Jabbarzadeh, M., Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics, Composites Part B: Engineering, 87, 2016, 161-175.
31
[32] Karličić, D., Adhikari, S., Murmu, T., Cajić, M., Exact closed-form solution for non-local vibration and biaxial buckling of bonded multi- nanoplate system, Composites Part B, 66, 2014, 328-339.
32
ORIGINAL_ARTICLE
Moving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod
In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable time steps to protect the positivity condition of the solution. The results of this computational technique are compared with the corresponding uniform mesh non-standard finite difference scheme. The simulations show that the presented method is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh non-standard finite difference fails.
http://jacm.scu.ac.ir/article_13202_1b9af05f7f7f9589e48852976ff2e4be.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
161
166
10.22055/jacm.2017.22854.1141
Non-standard finite difference
positivity
moving mesh
heat conduction equation
Morteza
Bisheh-Niasar
mbisheh@kashanu.ac.ir
true
1
Department of Applied Mathematics, Faculty of Mathematical Science, University of
Kashan, Kashan, Iran.
Department of Applied Mathematics, Faculty of Mathematical Science, University of
Kashan, Kashan, Iran.
Department of Applied Mathematics, Faculty of Mathematical Science, University of
Kashan, Kashan, Iran.
LEAD_AUTHOR
Maryam
Arab Ameri
arabameri@math.usb.ac.ir
true
2
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
AUTHOR
[1] Jordan, P.M., A nonstandard finite difference scheme for a nonlinear heat transfer in a thin finite rod, Journal of Difference Equations and Applications, 9(11), 2003, 1015-102.
1
[2] Dai ,W., Su, S., A non-standard finite difference scheme for solving one dimensional nonlinear heat transfer, Journal of Difference Equations and Applications,10(11), 2004, 1025-1032.
2
[3] Mohammadi, A., Malek, A., Stable non-standard implicit finite difference schemes for non-linear heat transfer in a thin finite rod, Journal of Difference Equations and Applications, 15(7), 2009, 719-728.
3
[4] Qin, W., Wang, L., Ding, X., A non-standard finite difference method for a hepatitis B virus infection model with spatial diffusion, Journal of Difference Equations and Applications, 20(12), 2014, 1641-1651.
4
[5] Elsheikh, S., Ouifki, R., Patidar, K.C., A non-standard finite difference method to solve a model of HIV-Malaria co-infection, Journal of Difference Equations and Applications, 20(3), 2014, 354-378.
5
[6] Mickens, R.E., Nonstandard finite difference schemes for differential equations, Journal of Difference Equations and Applications, 8(9), 2002, 823-847.
6
[7] Ehrhardt, M., Mickens, R.E., A nonstandard finite difference scheme for convection diffusion equations having constant coefficients, Applied Mathematics and Computation, 219(12), 2013, 6591-6604.
7
[8] Mickens, R.E., Nonstandard finite difference schemes for reaction-diffusion equations, Numerical Methods for Partial Differential Equation, 15(2), 1999, 201-2014.
8
[9] Mickens, R.E., Gumel, A.B., Construction and analysis of a nonstandard finite difference scheme for the Burgers-Fisher equation, Journal of Sound and Vibration, 257(4), 2002, 791-797.
9
[10] Sanz-Serna, J.M., Christie, I., A Simple Adaptive Technique for Nonlinear Wave Problems, Journal of Computational Physics, 67(2), 1986, 348-360.
10
[11] Mickens, R.E., Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
11
ORIGINAL_ARTICLE
Inherent Irreversibility of Exothermic Chemical Reactive Third-Grade Poiseuille Flow of a Variable Viscosity with Convective Cooling
In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.
http://jacm.scu.ac.ir/article_13194_1b328c31e4aa09a8339ba5500e57793f.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
167
174
10.22055/jacm.2017.22933.1144
Exothermic reaction
third-grade fluid
Poiseuille flow
Variable viscosity
Convective cooling
S.O.
Salawu
kunlesalawu2@gmail.com
true
1
Department of Mathematics, Landmark University, Omu-aran, Nigeria
Department of Mathematics, Landmark University, Omu-aran, Nigeria
Department of Mathematics, Landmark University, Omu-aran, Nigeria
LEAD_AUTHOR
S.I.
Oke
segunoke2016@gmail.com
true
2
Department of Mathematical Sciences, University of Zululand, Zululand, South Africa
Department of Mathematical Sciences, University of Zululand, Zululand, South Africa
Department of Mathematical Sciences, University of Zululand, Zululand, South Africa
AUTHOR
[1] Siddiqui, A.M., Mahmood, R., Ghori, Q.K., Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), 2006, 1-8.
1
[2] Ellahi, R., Afzal, A., Effects of variable viscosity in a third grade fluid with porous medium: an analytic solution, Communications in Nonlinear Science and Numerical Simulation, 14(5), 2009, 2056-2072.
2
[3] Makinde, O.D., Thermal stability of a reactive third grade fluid in a cylindrical pipe: an exploitation of Hermite–Padé approximation technique, Applied Mathematics and Computation, 189, 2007, 690-697.
3
[4] Rajagopal, K.R., On Boundary Conditions for Fluids of the Differential Type: Navier–Stokes Equations and Related Non-Linear Problems, Plenum Press, New York, 273,1995.
4
[5] Fosdick, R.L., Rajagopal, K.R., Thermodynamics and stability of fluids of third grade, Proceedings of the Royal Society of London, Series A, 1980, 339-351.
5
[6] Kamal, M.R., Ryan, M.E., Reactive polymer processing: techniques and trends, Advanced Polymer Technology, 4, 1984, 323-348.
6
[7] Datta, R., Henry, M., Lactic acid: recent advances in products, processes and technologies a review, Journal of Chemical Technology and Biotechnology, 81, 2006, 1119-1129.
7
[8] Bapat, S.S., Aichele, C.P., High, K.A., Development of a sustainable process for the production of polymer grade lactic acid, Sustainable Chemical Processes, 2, 2014, 1-8.
8
[9] Halley, P.J., George, G.A., Chemo-rheology of Polymers: From Fundamental Principles to Reactive Processing, Cambridge University Press, UK, 2009.
9
[10] Chinyoka, T., Two-dimensional flow of chemically reactive viscoelastic fluids with orwithout the influence of thermal convection, Communications in Nonlinear Science and Numerical Simulation, 16, 2011, 1387-1395.
10
[11] Makinde, O.D., On thermal stability of a reactive third-grade fluid in a channel with convective cooling at the walls, Applied Mathematics and Computation, 213, 2009, 170-176.
11
[12] Makinde, O.D., Thermal ignition in a reactive viscous flow through a channel filled with a porous medium, Journal of Heat Transfer, 128, 2006, 601-604.
12
[13] Beg, O.A., Motsa, S.S., Islam, M.N., Lockwood, M., Pseudospectral and variational iteration simulation of exothermically reacting Rivlin-Ericksen viscoelastic flow and heat transfer in a rocket propulsion duct, Computational Thermal Sciences, 6, 2014, 91-102.
13
[14] Chinyoka, T., Makinde, O.D., Analysis of transient Generalized Couette flow of a reactive variable viscosity third-grade liquid with asymmetric convective cooling, Mathematical and Computer Modelling, 54, 2011, 160-174.
14
[15] Makinde, O.D., Ogulu, A., The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, 195(12), 2008, 1575-1584.
15
[16] Gitima, P., Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field, International Journal for Basic Sciences and Social Sciences, 1(3), 2012, 69-77.
16
[17] Hazarika, G.C., Utpal, S.G.Ch., Effects of variable viscosity and thermal conductivity on MHD flow past a vertical plate, Matematicas Ensenanza Universitaria, 2, 2012, 45-54.
17
[18] Salawu, S.O., Dada, M.S., Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium, Journal of the Nigerian Mathematical Society, 35, 2016, 93-106.
18
[19] Bejan, A., Entropy Generation through Heat and Fluid Flow, Wiley, New York, 1982.
19
[20] 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, 222-229.
20
[21] Pakdemirli, M., Yilbas, B.S., Entropy generation for pipe low of a third grade fluid with Vogel model viscosity, International Journal of Non-Linear Mechanics, 41(3), 2006, 432-437.
21
[22] Hooman, K., Hooman, F., Mohebpour, S.R., Entropy generation for forced convection in a porous channel with isoflux or isothermal walls, International Journal of Exergy, 5(1), 2008, 78-96.
22
[23] Chauhan, D.S., Kumar, V., Entropy analysis for third-grade fluid flow with temperature-dependent viscosity in annulus partially filled with porous medium, Theoretical and Applied Mechanics, 40(3), 2013, 441-464.
23
[24] Das, S., Jana, R.N., Entropy generation due to MHD flow in a porous channel with Navier slip, Ain Shams Engineering Journal, 5, 2014, 575-584.
24
[25] Srinivas, J., Ramana Murthy, J.V., Second law analysis of the flow of two immiscible micropolar fluids between two porous beds, Journal of Engineering Thermophysics, 25(1), 2016, 126-142.
25
[26] Odejide, S.A., Aregbesola, Y.A.S., Applications of method of weighted residuals to problems with semi-finite domain, Romanian Journal of Physics, 56(1-2), 2011, 14-24.
26
[27] McGrattan, E.R., Application of weighted residual methods to dynamic economics models, Federal Reserve Bank of Minneapolis Research Department Staff Report, 232, 1998.
27
ORIGINAL_ARTICLE
Exact Radial Free Vibration Frequencies of Power-Law Graded Spheres
This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric study is fulfilled to study the effects of both the aspect ratio and the inhomogeneity parameters on the natural frequencies. The outcomes are presented in both graphical and tabular forms. It was seen that the fundamental frequency is mostly affected by the inhomogeneity parameters rather than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected by the thickness of the sphere. It is also revealed that there is a linear relationship between the fundamental frequency and others in higher modes of the same sphere under all boundary conditions.
http://jacm.scu.ac.ir/article_13243_4eaf2ad4b85da776b36411af6335d886.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
175
186
10.22055/jacm.2017.22987.1145
Free vibration
Functionally graded
Exact solution
Hollow sphere
Thick-walled
Vebil
Yıldırım
vebil@cu.edu.tr
true
1
Cukurova University, Department of Mechanical Engineering, Turkey
Cukurova University, Department of Mechanical Engineering, Turkey
Cukurova University, Department of Mechanical Engineering, Turkey
LEAD_AUTHOR
[1] Horace Lamb, M.A., On the Vibrations of an Elastic Sphere, Proceedings of the London Mathematical Society, 13(1), 1881, 189–212.
1
[2] Horace Lamb, M.A., On the Vibrations of a Spherical Shell, Proceedings of the London Mathematical Society, 14(1), 1882, 50-56.
2
[3] Sato, Y., Usami T., Basic Study on the oscillation of Homogeneous Elastic Sphere-Part I. Frequency of the Free Oscillations, Geophysics Magazine, 31(1), 1962, 15-24.
3
[4] Sato, Y., Usami, T., Basic Study on the oscillation of Homogeneous Elastics Sphere-Part II. Distribution of Displacement, Geophysics Magazine, 31(1), 1962, 25-47.
4
[5] Eason, G., On the Vibration of Anisotropic Cylinders and Spheres, Applied Scientific Research, 12, 1963, 81–85.
5
[6] Seide, P., Radial Vibrations of Spherical Shells, Journal of Applied Mechanics, 37(2), 1970, 528-530.
6
[7] Gosh, K., Agrawal, M.K., Radial Vibrations of Spheres, Journal of Sound and Vibration, 171(3), 1994, 315–322.
7
[8] Sharma, J.N., Sharma, N., Free Vibration Analysis of Homogeneous Thermoelastic Solid Sphere, Journal of Applied Mechanics, 77(2), 2010, 021004.
8
[9] Scafbuch, P.J., Rizzo, F.J., Thomson, R.B., Eigen Frequencies of an Elastic Sphere with Fixed Boundary Conditions, Journal of Applied Mechanics, 59(2), 1992, 458–459.
9
[10] Shah, H., Ramkrishana, C.V., Datta, S.K., Three Dimensional and Shell Theory Analysis of Elastic Waves in a Hollow Sphere-Part I. Analytical Foundation, Journal of Applied Mechanics, 36(3), 1969, 431-439.
10
[11] Shah, H., Ramkrishana, C.V., Datta, S.K., Three Dimensional and Shell Theory Analysis of Elastic Waves in a Hollow Sphere-Part II. Numerical Results, Journal of Applied Mechanics, 36(3), 1969, 440-444.
11
[12] Cohen, H., Shah, A.H., Free Vibrations of a Spherically Isotropic Hollow Sphere, Acustica, 26, 1972, 329–333.
12
[13] Grigorenko, Y.M., Kilina, T.N., Analysis of the Frequencies and Modes of Natural Vibration of Laminated Hollow Spheres in Three-Dimensional and Two-Dimensional Formulations, Soviet Applied Mechanics, 25, 1989, 1165-1171.
13
[14] Jiang, H., Young, P.G., Dickinson, S.M., Natural Frequencies of Vibration of Layered Hollow Spheres Using Three-Dimensional Elasticity Equations, Journal of Sound and Vibration, 195(1), 1996, 155-162.
14
[15] Chen, W.Q., Ding, H.J., Xu, R.Q., Three-Dimensional Free Vibration Analysis of a Fluid-Filled Piezoceramic Hollow Sphere, Computers and Structures, 79(6), 2001, 653-663.
15
[16] Chen, W.Q., Cai, J.B., Ye, G.R., Ding, H.J., On Eigen Frequencies of an Anisotropic Sphere, Journal of Applied Mechanics, 67(2), 2000, 422-424.
16
[17] Chen, W. Q., Ding, H.J., Free Vibration of Multi-Layered Spherically Isotropic Hollow Spheres, International Journal of Mechanical Sciences, 43(3), 2001, 667-680.
17
[18] Chen, W.Q., Ding, H.J., Natural Frequencies of a Fluid-Filled Anisotropic Spherical Shell, Journal of the Acoustical Society of America, 105, 1999, 174-182.
18
[19] Hoppmann II, W.H., Baker, W.E., Extensional Vibrations of Elastic orthotropic Spherical Shells, Journal of Applied Mechanics, 28, 1961, 229-237.
19
[20] Shul'ga, N.A., Grigorenko, A.Y., E’mova, T.L., Free Non-Axisymmetric oscillations of a Thick-Walled, Nonhomogeneous, Transversely Isotropic, Hollow Sphere, Soviet Applied Mechanics, 24, 1988, 439-444.
20
[21] Heyliger, P.R., Jilani, A., The Free Vibrations of Inhomogeneous Elastic Cylinders and Spheres, International Journal of Solids and Structures, 29(22), 1992, 2689-2708.
21
[22] Ding, H.J., Chen, W.Q., Nonaxisymmetric Free Vibrations of a Spherically Isotropic Spherical Shell Embedded in an Elastic Medium, International Journal of Solids and Structures, 33, 1996, 2575-2590.
22
[23] Ding, H.J., Chen, W.Q., Natural Frequencies of an Elastic Spherically Isotropic Hollow Sphere Submerged in a Compressible Fluid Medium, Journal of Sound and Vibration, 192(1), 1996, 173-198.
23
[24] Heyliger, P.R., Wu, Y.C., Electrostatic Fields in Layered Piezoelectric Spheres, International Journal of Engineering Science, 37, 1999, 143–161.
24
[25] Stavsky, Y., Greenberg, J.B., Radial Vibrations of orthotropic Laminated Hollow Spheres, Journal of the Acoustical Society of America, 113, 2003, 847–851.
25
[26] Ding, H.J., Wang, H.M., Discussions on “Radial vibrations of orthotropic laminated hollow spheres, [J. Acoust. Soc.Am. 113, 847–851 (2003)]”, Journal of the Acoustical Society of America, 115, 2004, 1414.
26
[27] Chiroiu, V., Munteanu, L., On the Free Vibrations of a Piezoceramic Hollow Sphere, Mechanics Research Communications, 34, 2007, 123–129.
27
[28] Keles, İ., Novel Approach to Forced Vibration Behavior of Anisotropic Thick-Walled Spheres, AIAA Journal, 54(4), 2016, 1438-1442.
28
[29] Sharma, J.N., Sharma, N., Vibration Analysis of Homogeneous Transradially Isotropic Generalized Thermoelastic Spheres, Journal of Vibration and Acoustics, 133(4), 2011, 041001.
29
[30] Sharma, N., Modeling and Analysis of Free Vibrations in Thermoelastic Hollow Spheres, Multidiscipline Modeling in Materials and Structures, 11(2), 2015, 134-159.
30
[31] Abbas, I., Natural Frequencies of a Poroelastic Hollow Cylinder, Acta Mechanica, 186(1–4), 2006, 229–237.
31
[32] Abbas, I., Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere, Mechanics Based Design of Structures and Machines, 43(3), 2015, 265-276.
32
[33] Nelson, R.B., Natural Vibrations of Laminated orthotropic Spheres, International Journal of Solids and Structures, 9(3), 1973, 305-311.
33
[34] Chen, W.Q., Wang, X., Ding, H.J., Free Vibration of a Fluid-Filled Hollow Sphere of a Functionally Graded Material with Spherical Isotropy, Journal of the Acoustical Society of America, 106, 1999, 2588-2594.
34
[35] Chen, W.Q., Wang, L.Z., Lu, Y., Free Vibrations of Functionally Graded Piezoceramic Hollow Spheres with Radial Polarization, Journal of Sound and Vibration, 251(1), 2002, 103-114.
35
[36] Ding, H.J., Wang, H.M., Chen, W.Q., Dynamic Responses of a Functionally Graded Pyroelectric Hollow Sphere for Spherically Symmetric Problems, International Journal of Mechanical Sciences, 45, 2003, 1029–1051.
36
[37] Kanoria, M., Ghosh, M.K., Study of Dynamic Response in a Functionally Graded Spherically Isotropic Hollow Sphere with Temperature Dependent Elastic Parameters, Journal of Thermal Stresses, 33, 2010, 459–484.
37
[38] Keleş, İ., Tütüncü, N., Exact Analysis of Axisymmetric Dynamic Response of Functionally Graded Cylinders (or Disks) and Spheres, Journal of Applied Mechanics, 78(6), 2011, 061014-1.
38
[39] Sharma, P.K., Mishra, K.C., Analysis of Thermoelastic Response in Functionally Graded Hollow Sphere without Load, Journal of Thermal Stresses, 40(2), 2017, 185-197.
39
[40] Yıldırım, V., Heat-Induced, Pressure-Induced and Centrifugal-Force-Induced Exact Axisymmetric Thermo-Mechanical Analyses in a Thick-Walled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material, International Journal of Engineering Applied Sciences, 9(3), 2017, 66-87.
40
[41] Kamdi, D., Lamba, N.K., Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field, Journal of Applied and Computational Mechanics, 2(2), 2016, 118-127.
41
[42] Talebi, S., Uosofvand, H., Ariaei, A., Vibration Analysis of a Rotating Closed Section Composite Timoshenko Beam by Using Differential Transform Method, Journal of Applied and Computational Mechanics, 1(4), 2015, 181-186.
42
[43] Mercan, K., Ersoy, H., Civalek, O., Free Vibration of Annular Plates by Discrete Singular Convolution and Differential Quadrature Methods, Journal of Applied and Computational Mechanics, 2(3), 2016, 28-133.
43
[44] Joubari, M.M., Ganji, D.D., Jouybari, H.J., Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method, Journal of Applied and Computational Mechanics, 1(1), 2015, 44-51.
44
[45] Sedighi H.M., Daneshmand F., Nonlinear Transversely Vibrating Beams by the Homotopy Perturbation Method with an Auxiliary Term, Journal of Applied and Computational Mechanics, 1(1), 2015, 1-9.
45
[46] Karimi, M., Shokrani, M.H., Shahidi, A.R., Size-Dependent Free Vibration Analysis of Rectangular Nanoplates with the Consideration of Surface Effects Using Finite Difference Method, Journal of Applied and Computational Mechanics, 1(3), 2015, 122-133.
46
[47] Watson, J.N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, London, 1922.
47
[48] Kim, J.O., Lee, J.G., Chun, H.Y., Radial Vibration Characteristics of Spherical Piezoelectric Transducers, Ultrasonics, 43, 2005, 531–537.
48
ORIGINAL_ARTICLE
Bending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theory
A trigonometric plate theory is assessed for the static bending analysis of plates resting on Winkler elastic foundation. The theory considers the effects of transverse shear and normal strains. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the traction free conditions at the top and bottom surfaces of the plate without using shear correction factors. The governing equations of equilibrium and the associated boundary conditions of the theory are obtained using the principle of virtual work. A closed-form solution is obtained using double trigonometric series. The numerical results are obtained for flexure of simply supported plates subjected to various static loadings. The displacements and stresses are obtained for three different values of foundation modulus. The numerical results are also generated using higher order shear deformation theory of Reddy, first order shear deformation theory of Mindlin, and classical plate theory for the comparison of the present results.
http://jacm.scu.ac.ir/article_13234_41ee272c21e0931940c8393ec05e7f83.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
187
201
10.22055/jacm.2017.23057.1148
Shear deformation
normal strain
Shear stress
shear correction factor
Winkler elastic foundation
Atteshamuddin
Sayyad
attu_sayyad@yahoo.co.in
true
1
SRES College of Engineering, Kopargaon, Maharashtra, India.
SRES College of Engineering, Kopargaon, Maharashtra, India.
SRES College of Engineering, Kopargaon, Maharashtra, India.
LEAD_AUTHOR
Yuwaraj M.
Ghugal
ghugal@rediffmail.com
true
2
Head of Department of Applied Mechanics, Govt. College of EngineeringKarad, Shivaji University, Maharashtra-415124, India
Head of Department of Applied Mechanics, Govt. College of EngineeringKarad, Shivaji University, Maharashtra-415124, India
Head of Department of Applied Mechanics, Govt. College of EngineeringKarad, Shivaji University, Maharashtra-415124, India
AUTHOR
[1] Kirchhoff, G.R., Uber das gleichgewicht und die bewegung einer elastischen Scheibe, Journal for Pure and Applied Mathematics, 40, 1850, 51-88.
1
[2] Mindlin, R.D., Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics, 18, 1951, 31-38.
2
[3] Reddy, J.N., A simple higher order theory for laminated composite plates, Journal of Applied Mechanics, 51, 1984, 745-752.
3
[4] Matsunaga, H., Vibration and stability of thick plates on elastic foundations, Journal of Engineering Mechanics, 126(1), 2000, 27–34.
4
[5] Huang, M.H., Thambiratnam, D.P., Analysis of plate resting on elastic supports and elastic foundation by finite strip method, Computers and Structures,79(29-30), 2001, 2547-2557.
5
[6] Chen, W.Q., Bian, Z.G., A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied Mathematical Modelling,28(10), 2004, 877–890.
6
[7] Atmane, H.A., Tounsi, A., Mechab, I., Bedia, E.A.A., Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design, 6(2), 2010, 113-121.
7
[8] Thai, H.T., Park, M., Choi, D.H., A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation, International Journal of Mechanical Science, 73, 2013, 40–52.
8
[9] Zenkour, A.M., Bending of orthotropic plates resting on Pasternak's foundations by mixed shear deformation theory, Acta Mechanica Sinica,27(6), 2011, 956–962.
9
[10] Zenkour, A.M., Allam, M.N.M., Shaker, M.O., Radwan, A.H., On the simple and mixed first-order theories for plates resting on elastic foundations, Acta Mechanica,220(1-4), 2011, 33–46.
10
[11] Sayyad, A.S., Flexure of thick orthotropic plates by exponential shear deformation theory, Latin American Journal of Solids and Structures,10, 2013, 473-490.
11
[12] Akbas, S.D., Vibration and static analysis of functionally graded porous plates,Journal of Applied and Computational Mechanics, 3(3), 2017, 199-207.
12
[13] Akbas, S.D., Stability of a non-homogenous porous plate by using generalized differantial quadrature method, International Journal of Engineering & Applied Sciences, 9(2), 2017, 147-155.
13
[14] Akbas, S.D., Static analysis of a nano plate by using generalized differential quadrature method,International Journal of Engineering & Applied Sciences, 8(2), 2016, 30-39.
14
[15] Civalek, O., Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory, Journal of Composite Materials, 42(26), 2008, 2853-2867.
15
[16] Gurses, M., Civalek, O., Korkmaz, A.K., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory, International Journal for Numerical Methods in Engineering, 79, 2009, 290–313.
16
[17] Sayyad, A.S., Ghugal, Y.M., On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite Structures, 129, 2015, 177–201.
17
[18] Sayyad, A.S., Ghugal, Y.M., Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures, 171, 2017, 486–504.
18
[19] Ghugal, Y.M., Sayyad, A.S., A static flexure of thick isotropic plates using trigonometric shear deformation theory, Journal of Solid Mechanics, 2(1), pp. 79-90, 2010.
19
[20] Ghugal, Y.M., Sayyad, A.S., Free vibration of thick isotropic plates using trigonometric shear deformation theory, Journal of Solid Mechanics, 3(2), 2011, 172-182.
20
[21] Ghugal, Y.M., Sayyad, A.S., Static flexure of thick orthotropic plates using trigonometric shear deformation theory, Journal of Structural Engineering, 39(5), 2013, 512-521.
21
[22] Ghugal, Y.M., Sayyad, A.S., Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin American Journal of Solids and Structures, 8, 2011, 229-243.
22
[23] Timoshenko, S.P., Goodier, J.M., Theory of Elasticity, McGraw-Hill, Singapore, 1970.
23
ORIGINAL_ARTICLE
Semi-Analytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation
Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are first obtained, where external electric voltage, viscoelastic foundation, piezoelectric effect, and nonlocal effect are considered simultaneously. Subsequently, Galerkin strip distributed transfer function method is developed to solve the governing equations for the semi-analytical solutions of natural frequencies. Numerical results from the model are also presented to show the effects of nonlocal parameter, external electric voltages, boundary conditions, viscoelastic foundation, and geometric dimensions on vibration responses of the plate. The results demonstrate the efficiency of the proposed methods for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation.
http://jacm.scu.ac.ir/article_13203_8c61226444364818bc945b3647976948.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
202
215
10.22055/jacm.2017.23096.1149
Nonlocal piezoelectric plates
Vibration characteristics
viscoelastic foundation
Galerkin strip distributed transfer function method
D.P.
Zhang
d.p.zhang@hotmail.com
true
1
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
AUTHOR
Yongjun
Lei
leiyj108@nudt.edu.cn
true
2
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
LEAD_AUTHOR
Z.B.
Shen
z.b.shen@hotmail.com
true
3
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
AUTHOR
[1] Liu, C., Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S., Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures, 106, 2013, 167-170.
1
[2] Ke, L.L., Wang, Y.S., Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory, Smart Materials and Structures, 21, 2012, 025018.
2
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[15] Asemi, S.R., Farajpour, A., Asemi, H.R., Mohammadi, M., Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E, 63, 2014, 169-179.
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[16] Kolahchi, R., Hosseini, H., Esmailpour, M., Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories, Composite Structures, 157, 2016, 174-186.
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[17] Kolahchi, R., Zarei, M.S., Hajmohammad, M.H., Oskouei, A.N., Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods, Thin-Walled Structures, 113, 2017, 162-169.
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[18] Arefi, M., Zenkour, A.M., Size-dependent free vibration and dynamic analyses of piezo-electromagnetic sandwich nanoplates resting on viscoelastic foundation, Physica B, 521, 2017, 188-197.
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[19] Bouafia, K., Kaci, A., Houari, M., Benzair, A., Tounsi, A., A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems, 19(2), 2017, 115-126.
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[20] Bounouara, F., Benrahou, K.H., Belkorissat, I., Tounsi, A., A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation, Steel and Composite Structures, 20(2), 2016, 227-249.
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[21] Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics, 62(6), 2017, 695-702.
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[22] Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A., Mahmoud, S.R., Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 2015, 425-442.
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[23] Besseghier, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory, Smart Structures and Systems, 19(6), 2017, 601-614.
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[24] Ahouel, M., Houari, M.S.A., Bedia, E.A.A., Tounsi, A., Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept, Steel and Composite Structures, 20(5), 2016, 963-981.
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30
ORIGINAL_ARTICLE
The Complementary Functions Method (CFM) Solution to the Elastic Analysis of Polar Orthotropic Rotating Discs
This study primarily deals with introducing an efficient numerical technique called the Complementary Functions Method (CFM) for the solutions of the initial value problem for the linear elastic analysis of anisotropic rotating uniform discs. To bring the performance of the method to light, first, closed form formulas are derived for such discs. The governing equation of the problem at stake is solved analytically with the help of the Euler-Cauchy technique under three types of boundary conditions namely free-free, fixed-free, and fixed-guided constraints. Secondly, the CFM is applied to the same problem. It was found that both numerical and analytical results coincide with each other up to a desired numerical accuracy. Third, after verifying the results with the literature, a parametric study with CFM on the elastic behavior of discs made up of five different materials which physically exist is performed. And finally, by using hypothetically chosen anisotropy degrees from 0.3 through 5, the effects of the anisotropy on the elastic response of such structures are investigated analytically. Useful graphs are provided for readers.
http://jacm.scu.ac.ir/article_13293_64e5af46bf182153111bbf596f22db7c.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
216
230
10.22055/jacm.2017.23188.1150
Initial value problem (IVP)
Exact elasticity solution
Polar orthotropic
Rotating disc
Vebil
Yıldırım
vebil@cu.edu.tr
true
1
Department of Mechanical Engineering, Çukurova University, Adana, 01330, Turkey
Department of Mechanical Engineering, Çukurova University, Adana, 01330, Turkey
Department of Mechanical Engineering, Çukurova University, Adana, 01330, Turkey
LEAD_AUTHOR
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1
[2] Akano, T.T., Fakinlede, O.A., Olayiwola, P.S., Deformation Characteristics of Composite Structures, Journal of Applied and Computational Mechanics, 2(3), 2016, 174-191.
2
[3] Katsikadelis, J.T., Tsiatas G.C., Saint-Venant Torsion of Non-Homogeneous Anisotropic Bars, Journal of Applied and Computational Mechanics, 2(1), 2016, 42-53.
3
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36
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37
[38] Zheng, Y., Bahaloo, H., Mousanezhad, D., Vaziri, A., Nayeb-Hashemi, H., Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk with Nonuniform Thickness and Variable Angular Velocity, Journal of Engineering Materials and Technology, 39, 2017, 031010-1-9.
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[45] Kacar, İ., Yıldırım, V., Free Vibration/Buckling Analyses of Non-Cylindrical Initially Compressed Helical Composite Springs, Mechanics Based Design of Structures and Machines, 44 (4), 2016, 340-353.
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46
ORIGINAL_ARTICLE
Verification and Validation of Common Derivative Terms Approximation in Meshfree Numerical Scheme
In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations for functions and derivatives are of the second accuracy order, and the scale of the support domain has some influences on numerical errors but not on accuracy orders. With a discrete scale h=0.01, the relative errors of the numerical simulation for the selected functions and their derivatives are within 0.65%.
http://jacm.scu.ac.ir/article_13292_2fbc5a7086ed163a0cc15b7e895c10da.pdf
2018-07-01T11:23:20
2019-01-17T11:23:20
231
244
10.22055/jacm.2017.23557.1163
Meshfree method
Smoothed particle hydrodynamics
Physics evoked cloud method
Approximation of spatial derivative
Verification and validation
Zhibo
Ma
mazhibo@iapcm.ac.cn
true
1
Institute of Applied Physics and Computational Mathematics, China
Institute of Applied Physics and Computational Mathematics, China
Institute of Applied Physics and Computational Mathematics, China
AUTHOR
Yazhou
Zhao
asiabuaasa@163.com
true
2
Division of Water Resources and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
Division of Water Resources and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
Division of Water Resources and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
LEAD_AUTHOR
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[14] Rafiee, A., Thiagarajan, K.P., An SPH projection method for simulating fluid-hypoelastic structure interaction, Computer Methods in Applied Mechanics and Engineering, 198(33-36), 2009, 2785-2795.
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[19] The American Society of Mechanical Engineers. V&V 20-2009, Standard for verification and validation in computational fluid dynamics and heat transfer, New York, 2009, 1-87.
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[25] Ma, Z., Physics Evoked Cloud Method: A Versatile Systematic Method for Numerical Simulations, Chinese Journal of Computational Physics, 34(3), 2017, 261-272.
25