ORIGINAL_ARTICLE
Vibration Analysis of Material Size-Dependent CNTs Using Energy Equivalent Model
This study presents a modified continuum model to investigate the vibration behavior of single and multi-carbon nanotubes (CNTs). Two parameters are exploited to consider size dependence; one derived from the energy equivalent model and the other from the modified couple stress theory. The energy equivalent model, derived from the basis of molecular mechanics, is exploited to describe size-dependent material properties such as Young and shear moduli for both zigzag and armchair CNT structures. A modified couple stress theory is proposed to capture the microstructure size effect by assisting material length scale. A modified kinematic Timoshenko nano-beam including shear deformation and rotary inertia effects is developed. The analytical solution is shown and verified with previously published works. Moreover, parametric studies are performed to illustrate the influence of the length scale parameter, translation indices of the chiral vector, and orientation of CNTs on the vibration behaviors. The effect of the number of tube layers on the fundamental frequency of CNTs is also presented. These findings are helpful in mechanical design of high-precision measurement nano-devices manufactured from CNTs.
https://jacm.scu.ac.ir/article_13086_1b839d2c3c70ab7e45b02e2baadad04a.pdf
2018-04-01
75
86
10.22055/jacm.2017.22579.1136
Energy Equivalent Model
Modified couple stress theory
Carbon nanotube
Vibration of Timoshenko Nano Beam
Analytical model
Mohamed A.
Eltaher
mohaeltaher@gmail.com
1
Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
LEAD_AUTHOR
Mohamed
Agwa
magwa@gmail.com
2
Mechanical Design & Production Dept., Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
AUTHOR
A
Kabeel
mkabeel@gmail.com
3
Mechanical Design & Production Dept., Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
AUTHOR
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59
ORIGINAL_ARTICLE
Thermal Analysis of Convective-Radiative Fin with Temperature-Dependent Thermal Conductivity Using Chebychev Spectral Collocation Method
In this paper, the Chebychev spectral collocation method is applied for the thermal analysis of convective-radiative straight fins with the temperature-dependent thermal conductivity. The developed heat transfer model was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conductivity (nonlinear) parameters on the thermal performance of the fin. The results of this study reveal that the rate of heat transfer from the fin increases as convective, radioactive, and magnetic parameters increase. This study finds good agreements between the obtained results using the Chebychev spectral collocation method and the results obtained using the Runge-Kutta method along with shooting, homotopy perturbation, and Adomian decomposition methods.
https://jacm.scu.ac.ir/article_13087_38bdf2d4e3e42c13f21ecbbd9d55854f.pdf
2018-04-01
87
94
10.22055/jacm.2017.22435.1130
Thermal analysis
Convective-radiative fin
Chebychev spectral collocation method
Temperature-dependent thermal conductivity
George
Oguntala
g.a.oguntala@bradford.ac.uk
1
Faculty of Engineering and Informatics University of Bradford, BD7 1DP West Yorkshire, UK
LEAD_AUTHOR
Raed
Abd-Alhameed
r.a.abd@bradford.ac.uk
2
School of Electrical Engineering Faculty of Engineering and Informatics, University of Bradford, UK
AUTHOR
[1] Aziz, A., Enamul-Huq, S.M., Perturbation solution for convecting fin with temperature dependent thermal conductivity, Journal of Heat Transfer, 97(2), 1973, pp. 300–301.
1
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[4] Chiu, C.H., Chen, C.K., A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer, 45(10),2002, pp. 2067-2075.
4
[5] Arslanturk, A., A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, International Communications in Heat and Mass Transfer, 32(6), 2005, pp. 831–841.
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[6] Ganji, D.D., The Application of He’s Homotopy Perturbation Method to Nonlinear Equations Arising in Heat Transfer, Physics Letter A,355(4-5), 2006, pp. 337–341.
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[7] He, J.H., Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineering, 178, 1999, pp. 257–262.
7
[8] Chowdhury, M.S.H., Hashim, I., Analytical Solutions to Heat Transfer Equations by Homotopy-Perturbation Method Revisited, Physical Letters A, 372(8), 2008, pp. 1240-1243.
8
[9] Rajabi, A., Homotopy Perturbation Method for Fin Efficiency of Convective Straight Fins with Temperature-dependent Thermal Conductivity, Physics Letters A, 364(1), 2007, pp.33-37.
9
[10] Inc, M., Application of Homotopy Analysis Method for Fin Efficiency of Convective Straight Fin with Temperature Dependent Thermal Conductivity, Mathematics and Computers Simulation, 79(2), 2008, pp. 189-200.
10
[11] Coskun, S.B., Atay, M.T., Analysis of Convective Straight and Radial Fins with Temperature-dependent Thermal Conductivity using Variational Iteration Method with Comparison with respect to Finite Element Analysis, Mathematical Problem in Engineering, 2007, Article ID 42072, 15p.
11
[12] Languri, E.M., Ganji, D.D., Jamshidi, N., Variational Iteration and Homotopy Perturbation Methods for Fin Efficiency of Convective Straight Fins with Temperature-dependent Thermal Conductivity, 5th WSEAS International Conference on Fluid Mechanics (Fluids 08), Acapulco, Mexico January 25-27, 2008.
12
[13] Sobamowo, M.G., Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual, Applied Thermal Engineering, 99, 2016, pp. 1316–1330.
13
[14] Atay, M.T., Coskun, S.B., Comparative Analysis of Power-Law Fin-Type Problems Using Variational Iteration Method and Finite Element Method, Mathematical Problems in Engineering, 2008, Article ID 635231, 9p.
14
[15] Domairry, G., Fazeli, M., Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity, Communication in Nonlinear Science and Numerical Simulation, 14(2), 2009, pp. 489-499.
15
[16] Hosseini, K., Daneshian, B., Amanifard, N., Ansari, R., Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity, International Journal of Nonlinear Science, 14(2), 2012, pp. 201-210.
16
[17] Joneidi, A.A., Ganji, D.D., Babaelahi, M., Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity, International Communication in Heat and Mass Transfer, 36, 2009, pp. 757-762.
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22
[23] Ganji, D.D., Dogonchi, A.S., Analytical investigation of convective heat transfer of a longitudinal fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation, International Journal of Physical Sciences, 9(21), 2013, pp. 466-474.
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32
[33] Huang, Z.J., Zhu, Z.J., Chebyshev spectral collocation method for solution of Burgers’ equation and laminar natural convection in two-dimensional cavities, Bachelor Thesis, University of Science and Technology of China, Hefei, 2009.
33
[34] Eldabe, N.T., Ouaf, M.E.M., Chebyshev ﬁnite difference method for heat and mass transfer in a hydromagnetic ﬂow of a micropolar ﬂuid past a stretching surface with Ohmic heating and viscous dissipation, Applied Mathematics and Computation, 177, 2006, pp. 561–571.
34
[35] Khater, A.H., Temsah, R.S., Hassan, M.M., A Chebyshev spectral collocation method for solving Burgers'-type equations, Journal of Computational and Applied Mathematics, 222, 2008, pp. 333–350.
35
[36] Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., Spectral Methods in Fluid Dynamics, Springer, New York, 1988.
36
[37] Doha, E.H., Bhrawy, A.H., Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials, Applied Numerical Mathematics, 58, 2008, pp. 1224–1244.
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[39] Doha, E.H., Bhrawy, A.H., Hafez, R.M., A Jacobi–Jacobi dual-Petrov–Galerkin method for third- and fifth-order differential equations, Mathematical and Computer Modelling, 53, 2011, pp. 1820–1832.
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[40] Doha, E.H., Bhrawy, A.H., Ezzeldeen, S.S., Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations, Applied Mathematical Modelling, 35(12), 2011, pp. 5662-5672.
40
ORIGINAL_ARTICLE
Study of Parameters Affecting Separation Bubble Size in High Speed Flows using k-ω Turbulence Model
Shock waves generated at different parts of vehicle interact with the boundary layer over the surface at high Mach flows. The adverse pressure gradient across strong shock wave causes the flow to separate and peak loads are generated at separation and reattachment points. The size of separation bubble in the shock boundary layer interaction flows depends on various parameters. Reynolds-averaged Navier-Stokes equations using the standard two-equation k-ω turbulence model is used in simulations for hypersonic flows over compression corner. Different deflection angles, including q ranging from 15o to 38o, are simulated at Mach 9.22 to study its effect on separated flow. This is followed by a variation in the Reynolds number based on the boundary layer thickness, Red from 1x105 to 4x105. Simulations at different constant wall conditions Tw of cool, adiabatic, and hot are also performed. Finally, the effect of free stream Mach numbers M∞, ranging from 5 to 9, on interaction region is studied. It is observed that an increase in parameters, q, Red, and Tw results in an increase in the separation bubble length, Ls, and an increase in M∞ results in the decrease in Ls.
https://jacm.scu.ac.ir/article_13088_b6b38a79b1c2587cf9542beaddee2f67.pdf
2018-04-01
95
104
10.22055/jacm.2017.22761.1140
High speed flows
shock/boundary-layer interaction
hypersonic flows
Shock-waves
Boundary-layer
compression corner
Computational fluid dynamics
Amjad Ali
Pasha
aapasha@kau.edu.sa
1
Department of Aeronautical Engineering, King Abdul Aziz University, Saudi Arabia.
LEAD_AUTHOR
[1] Babinsky, H., Harvey, J. K., Shock Wave-Boundary Layer Interactions, Cambridge University Press, 2011.
1
[2] Bose, D., Brown, J. L., Prabhu, D. K., Gnoffo, P., Johnston, C. O., Hollis, B., Uncertainty Assessment of Hypersonic Aerothermodynamics Prediction Capability, Journal of Spacecraft and Rockets, 50(1), 2013, pp. 12-18.
2
[3] DeBonis, J. R., Oberkampf, W. L., Wolf, R. T., Orkwis, P. D., Turner, M. G., Babinsky, H., and Benek, J. A., Assessment of Computational Fluid Dynamics and Experimental Data for Shock Boundary-Layer Interactions, AIAA Journal, 50(4), 2012, pp. 891-903.
3
[4] Sinha, K., Mahesh, K., Candler, G. V., Modeling Shock-Unsteadiness in Shock/Turbulence Interaction, Physics of Fluids, 15(8), 2003, pp. 2290-2297.
4
[5] Verma, S. B., Stark, R., Haid, O., Relation Between Shock Unsteadiness and the Origin of Side-Loads Inside a Thrust Optimized Parabolic Rocket Nozzle, Aerospace Science and Technology, 10(6), 2006, pp. 474-483.
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[6] Dussauge, J. P., Dupont, P., Debieve, J. F., Unsteadiness in Shock Wave Boundary layer Interactions with Separation, Progress in Aerospace Sciences, 10(2), 2006, pp. 85-91.
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[7] Estruch, D., Lawson, N. J., MacManus, D. G., Garry, K. P., Stollery, J. L., Measurement of Shock Wave Unsteadiness using a High-Speed Schlieren System and Digital Image Processing, Review of Scientific Instruments, 79(12), 2008, pp. 126108.
7
[8] Clemens, N. T., Narayanaswamy, V., Low-Frequency Unsteadiness of Shock Wave/Turbulent Boundary Layer Interactions, Annual Review of Fluid Mechanics, 46, 2014, pp. 469-492.
8
[9] Bertin, J. J., Hypersonic Aerothermodynamics, AIAA Education Series, AIAA, Washington, DC, 1994.
9
[10] Anderson, J. D., Hypersonic and High Temperature Gas Dynamics, AIAA, 2006.
10
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42
ORIGINAL_ARTICLE
Bending Response of Nanobeams Resting on Elastic Foundation
In the present study, the finite element method is developed for the static analysis of nano-beams under the Winkler foundation and the uniform load. The small scale effect along with Eringen's nonlocal elasticity theory is taken into account. The governing equations are derived based on the minimum potential energy principle. Galerkin weighted residual method is used to obtain the finite element equations. The validity and novelty of the results for bending are tested and comparative results are presented. Deflections according to different Winkler foundation parameters and small scale parameters are tabulated and plotted. As it can be seen clearly from figures and tables, for simply-supported boundary conditions, the effect of small scale parameter is very high when the Winkler foundation parameter is smaller. On the other hand, for clamped-clamped boundary conditions, the effect of small scale parameter is higher when the Winkler foundation parameter is high. Although the effect of the small scale parameter is adverse on deflection for simply-supported and clamped-clamped boundary conditions.
https://jacm.scu.ac.ir/article_13100_ed38f1850b2c640739f9b91952cfc134.pdf
2018-04-01
105
114
10.22055/jacm.2017.22594.1137
nonlocal elasticity theory
Static analysis
Weighted residual method
Winkler foundation
Euler-Bernoulli beam theory
Cigdem
Demir
c_demir86@yahoo.com
1
Department of Civil Engineering, Mechanical Division, Akdeniz University Antalya, TURKIYE
AUTHOR
Kadir
Mercan
mercankadir32@gmail.com
2
Department of Civil Engineering, Mechanical Division, Akdeniz University Antalya, TURKIYE
AUTHOR
Hayi Metin
Numanoglu
metin_numanoglu@akdeniz.edu.tr
3
Department of Civil Engineering, Mechanical Division, Akdeniz University Antalya, TURKIYE
AUTHOR
Omer
Civalek
ocivalek@akdeniz.edu.tr
4
Department of Civil Engineering, Mechanical Division, Akdeniz University Antalya, TURKIYE
LEAD_AUTHOR
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[6] Wang, C.M., Zhang, Z., Challamel, N., Duan, W.H., Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model, Journal of Physics D-Applied Physics, 46(34), 2013, 345501.
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7
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8
[9] Akgöz, B., Civalek, Ö., Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity, Composite Structures, 134, 2015, pp. 294-301.
9
[10] Akgoz, B., Civalek, O., Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory, Acta Astronautica, 119, 2016, pp. 1-12.
10
[11] Demir, Ç., Civalek, Ö., Nonlocal deflection of microtubules under point load, International Journal of Engineering and Applied Sciences, 7(3), 2015, pp. 33-39.
11
[12] Wang, Q., Liew, K.M., Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures, Physics Letters A, 363(3), 2007, pp. 236-242.
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[13] Reddy, J.N., Pang, S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103(2), 2008, 023511.
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14
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[16] De Rosa, M.A., Franciosi, C., A simple approach to detect the nonlocal effects in the static analysis of Euler-Bernoulli and Timoshenko beams, Mechanics Research Communications, 48, 2013, pp. 66-69.
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[17] Janghorban, M., Two different types of differential quadrature methods for static analysis of microbeams based on nonlocal thermal elasticity theory in thermal environment, Archive of Applied Mechanics, 82(5), 2012, pp. 669-675.
17
[18] Demir, C., Civalek, Ö., Tek katmanlı grafen tabakaların eğilme ve titreşimi, Mühendislik Bilimleri ve Tasarım Dergisi, 4(3), 2016, pp. 173-183.
18
[19] Farajpour, A., Shahidi, A.R., Mohammadi, M., Mahzoon, M., Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, 94(5), 2012, pp. 1605-1615.
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[20] Liu, C., Ke, L.-L., Yang, J., Kitipornchai, S., Wang, Y.-S., Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates, Theoretical and Applied Mechanics Letters, 6(6), 2016, pp. 253-267.
20
[21] 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.
21
[22] Asemi, S.R., Mohammadi, M., Farajpour, A., A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, 11(9), 2014, pp. 1541-1564.
22
[23] Malekzadeh, P., Farajpour, A., Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium, Acta Mechanica, 223(11), 2012, pp. 2311-2330.
23
[24] Gurses, M., Akgoz, B., Civalek, O., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation, Applied Mathematics and Computation, 219(6), 2012, pp. 3226-3240.
24
[25] Dinev, D., Analytical solution of beam on elastic foundation by singularity functions, Engineering Mechanics, 19(6), 2012, pp. 381-392.
25
[26] Demir, C., Akgoz, B., Erdinc, M.C., Mercan, K., Civalek, O., Free vibration analysis of graphene sheets on elastic matrix, Journal of the Faculty of Engineering and Architecture of Gazi, 32(2), 2017, pp. 551-562.
26
[27] Murmu, T., Pradhan, S.C., Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory, Computational Materials Science, 46(4), 2009, pp. 854-859.
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[28] Murmu, T., Pradhan, S.C., Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E, 41(7), 2009, pp. 1232-1239.
28
[29] Pradhan, S.C., Reddy, G.K., Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM, Computational Materials Science, 50(3), 2011, pp. 1052-1056.
29
[30] Yoon, J., Ru, C.Q., Mioduchowski, A., Vibration of an embedded multiwall carbon nanotube, Composite Science and Technology, 63(11), 2003, pp. 1533-1542.
30
[31] Mercan, K., Numanoglu, H., Akgöz, B., Demir, C., Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix, Archives of Applied Mechanics, 87(11), 2017, pp. 1797–1814.
31
[32] Mercan, K., Civalek, O., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ, Composite Part B: Engineering, 114, 2017, pp. 35-45.
32
[33] Mercan, K., Civalek, Ö., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix, Composite Structures, 143, 2016, pp. 300-309.
33
[34] Mercan, K., A Comparative Buckling Analysis of Silicon Carbide Nanotube and Boron Nitride Nanotube, International Journal of Engineering & Applied Sciences, 8(4), 2016, pp. 99-107.
34
[35] Demir, Ç., Nonlocal Vibration Analysis for Micro/Nano Beam on Winkler Foundation via DTM, International Journal of Engineering & Applied Sciences, 8(4), 2016, pp. 108-118.
35
[36] Demir, Ç., Civalek, Ö., Nonlocal finite element formulation for vibration, International Journal of Engineering & Applied Sciences, 8, 2016, pp. 109-117.
36
[37] Pradhan, S.C., Nonlocal finite element analysis and small scale effects of CNTs with Timoshenko beam theory, Finite Elements in Analysis and Design, 50, 2012, pp. 8-20.
37
[38] Demir, Ç., Civalek, Ö., A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix, Composite Structures, 168, 2017, pp. 872-884.
38
[39] Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E., Meletis, E.I., Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology, 26(11), 2012, pp. 3555-3563.
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42
[43] Civalek, Ö., Demir, C., A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method, Applied Mathematics and Computation, 289, 2016,pp. 335-352.
43
[44] Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F., Static analysis of nanobeams using nonlocal FEM, Journal of Mechanical Science and Technology, 27(7), 2013, pp. 2035-2041.
44
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45
ORIGINAL_ARTICLE
Buckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams
The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather than the classical power law distribution which permits gradually variation of stresses at the surface boundary and eliminates delamination. The Voigt model is proposed to homogenize micromechanical properties and to derive the effective material properties. The Euler-Bernoulli beam theory is selected to describe Kinematic relations. A finite element model is exploited to form stiffness and buckling matrices and solve the problem of eignivalue numerically. Numerical results present the effect of material graduations and elasticity ratios on the buckling behavior of FG beams. The proposed model is helpful in stability of mechanical systems manufactured from FGMs.
https://jacm.scu.ac.ir/article_13109_e8124cfb659bf6bf4151c6c70aa9bde7.pdf
2018-04-01
115
124
10.22055/jacm.2017.23040.1147
Static Stability
Buckling
Functional graded materials
Symmetric Power-Law
Sigmoid Function
Finite element
Khalid H.
Almitani
kalmettani@kau.edu.sa
1
Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Tel: +96653908744, Jeddah, Saudi Arabia
LEAD_AUTHOR
[1] Eltaher, M. A., Alshorbagy, A. E., Mahmoud, F. F, Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams, Composite Structures, 99, 2013, 193-201.
1
[2] Wang, C. M., Wang, C. Y., Reddy, J.N., Exact solutions for buckling of structural members, 2005, CRC press.
2
[3] Reddy, J. N., Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 47(1-3), 2000, pp. 663-684.
3
[4] Rastgo, A., Shafie, H., Allahverdizadeh, A., Instability of curved beams made of functionally graded material under thermal loading, International Journal of Mechanics and Materials in Design, 2(1), 2005, pp. 117-128.
4
[5] Alshorbagy, A. E., Eltaher, M. A., Mahmoud, F. F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35(1), 2011, pp. 412-425.
5
[6] Kocaturk, T., Akbas, S. D., Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading, Structural Engineering and Mechanics, 41(6), 2012, pp. 775-789.
6
[7] Eltaher, M. A., Emam, S. A., Mahmoud, F. F., Static and stability analysis of nonlocal functionally graded nanobeams, Composite Structures, 96, 2013, pp. 82-88.
7
[8] Li, S. R., Batra, R. C., Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler–Bernoulli beams, Composite Structures, 95, 2013, pp. 5-9.
8
[9] Fu, Y., Chen, Y., Zhang, P., Thermal buckling analysis of functionally graded beam with longitudinal crack, Meccanica, 48(5), 2013, pp. 1227-1237.
9
[10] Akbaş, Ş. D., Kocatürk, T., Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature, Journal of Thermal Stresses, 36(12), 2013, pp. 1233-1254.
10
[11] Kocaturk, T., Akbas, S. D., Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties, Steel and Composite Structures, 15(5), 2013, pp. 481-505.
11
[12] Eltaher, M. A., Hamed, M. A., Sadoun, A. M., Mansour, A., Mechanical analysis of higher order gradient nanobeams, Applied Mathematics and Computation, 229, 2014, pp. 260-272.
12
[13] Ebrahimi, F., Salari, E., Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams, Smart Materials and Structures, 24(12), 2015, p. 125007.
13
[14] Fu, Y., Zhong, J., Shao, X., Chen, Y., Thermal postbuckling analysis of functionally graded tubes based on a refined beam model, International Journal of Mechanical Sciences, 96, 2015, pp. 58-64.
14
[15] Ghiasian, S. E., Kiani, Y., Eslami, M. R., Nonlinear thermal dynamic buckling of FGM beams, European Journal of Mechanics-A/Solids, 54, 2015, pp. 232-242.
15
[16] Amara, K., Bouazza, M., Fouad, B., Postbuckling Analysis of Functionally Graded Beams Using Nonlinear Model, Periodica Polytechnica. Engineering. Mechanical Engineering, 60(2), 2016, p. 121.
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[17] Rezaiee-Pajand, M., Masoodi, A. R., Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections, Journal of Vibration and Control, 2016, doi: 1077546316668932.
17
[18] Kiani, K., Postbuckling scrutiny of highly deformable nanobeams: A novel exact nonlocal-surface energy-based model, Journal of Physics and Chemistry of Solids, 110, 2017, pp. 327-343.
18
[19] Maleki, V. A., Mohammadi, N., Buckling analysis of cracked functionally graded material column with piezoelectric patches, Smart Materials and Structures, 26(3), 2017, p. 035031.
19
[20] Ben-Oumrane, S., Abedlouahed, T., Ismail, M., Mohamed, B. B., Mustapha, M., El Abbas, A. B., A theoretical analysis of flexional bending of Al/Al 2 O 3 S-FGM thick beams, Computational Materials Science, 44(4), 2009, pp. 1344-1350.
20
[21] Chi, S. H., Chung, Y. L., Cracking in sigmoid functionally graded coating, International Journal of Structural Stability and Dynamics, 18, 2002, pp. 41-53.
21
[22] Mahi, A., Bedia, E. A., Tounsi, A., Mechab, I., An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions, Composite Structures, 92(8), 2010, pp. 1877-1887.
22
[23] Fereidoon, A., Mohyeddin, A., Bending analysis of thin functionally graded plates using generalized differential quadrature method, Archive of Applied Mechanics, 81(11), 2011, pp. 1523-1539.
23
[24] Duc, N. D., Cong, P. H., Nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material plate with metal-ceramic-metal layers on elastic foundation, Journal of Vibration and Control, 21(4), 2015, pp. 637-646.
24
[25] Lee, C. Y., Kim, J. H., Thermal post-buckling and snap-through instabilities of FGM panels in hypersonic flows, Aerospace Science and Technology, 30(1), 2013, pp. 175-182.
25
[26] Jung, W. Y., Han, S. C., Analysis of sigmoid functionally graded material (S-FGM) nanoscale plates using the nonlocal elasticity theory, Mathematical Problems in Engineering, 2013, Article ID 476131, 10p.
26
[27] Akbaş, Ş. D., On post-buckling behavior of edge cracked functionally graded beams under axial loads, International Journal of Structural Stability and Dynamics, 15(4), 2015, p. 1450065.
27
[28] Akbaş, Ş. D., Post-buckling analysis of axially functionally graded three-dimensional beams, International Journal of Applied Mechanics, 7(3), 2015, p. 1550047.
28
[29] Ebrahimi, F., Salari, E., Analytical modeling of dynamic behavior of piezo-thermo-electrically affected sigmoid and power-law graded nanoscale beams, Applied Physics A, 122(9), 2016, p. 793.
29
[30] Hamed, M. A., Eltaher, M. A., Sadoun, A. M., Almitani, K. H., Free vibration of symmetric and sigmoid functionally graded nanobeams, Applied Physics A, 122(9), 2016, p. 829.
30
[31] Swaminathan, K., Sangeetha, D. M., Thermal analysis of FGM plates–A critical review of various modeling techniques and solution methods, Composite Structures, 160, 2017, pp. 43-60.
31
[32] Yahia, S. A., Atmane, H. A., Houari, M. S. A., Tounsi, A., Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories, Structural Engineering and Mechanics, 53(6), 2015, pp. 1143-1165.
32
[33] Atmane, H. A., Tounsi, A., Bernard, F., Mahmoud, S. R., A computational shear displacement model for vibrational analysis of functionally graded beams with porosities, Steel and Composite Structures, 19(2), 2015, pp. 369-384.
33
[34] Attia, A., Tounsi, A., Bedia, E. A., Mahmoud, S. R., Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories, Steel and Composite Structures, 18(1), 2015, pp. 187-212.
34
[35] Beldjelili, Y., Tounsi, A., Mahmoud, S. R., Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems, 18(4), 2016, pp. 755-786.
35
[36] Bouderba, B., Houari, M. S. A., Tounsi, A., Mahmoud, S. R., Thermal stability of functionally graded sandwich plates using a simple shear deformation theory, Structural Engineering and Mechanics, 58(3), 2016, pp. 397-422.
36
[37] Bousahla, A. A., Benyoucef, S., Tounsi, A., Mahmoud, S. R., On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, 60(2), 2016, pp. 313-335.
37
[38] Boukhari, A., Atmane, H. A., Tounsi, A., Adda, B., Mahmoud, S. R., An efficient shear deformation theory for wave propagation of functionally graded material plates, Structural Engineering and Mechanics, 57(5), 2016, pp. 837-859.
38
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ORIGINAL_ARTICLE
Finite Element Solutions of Cantilever and Fixed Actuator Beams Using Augmented Lagrangian Methods
In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electric field to allow a smooth transi-tion of the electric field between center of a beam and edges of the beam. The numerical results obtained by the procedure are tabulated and compared with some existing results for beams in MEMS switches in literature. This procedure produces stable and accurate numerical results for simulation of these MEMS beams and can be a useful and efficient alternative for design and determining onset of pull-in for such devices.
https://jacm.scu.ac.ir/article_13110_04e7f84e34e96ab0e4562fe83534f551.pdf
2018-04-01
125
132
10.22055/jacm.2017.22700.1139
Microelectromechanical switch
pull-in
Microbeam
finite element solutions
Augmented Lagrangian methods
Dongming
Wei
dongming.wei@nu.edu.kz
1
Department of Mathematics, School of Science and Technology, Nazarbayev University, Astana, 010000, Kazakhstan
AUTHOR
Xuefeng
Li
li@loyno.edu
2
Department of Mathematics and Computer Science, Loyola University, New Orleans, LA 70118, USA
LEAD_AUTHOR
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