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http://dx.doi.org/10.12989/sem.2016.59.3.475

A unified formulation for static behavior of nonlocal curved beams  

Tufekci, Ekrem (Istanbul Technical University, Faculty of Mechanical Engineering)
Aya, Serhan A. (Istanbul Technical University, Faculty of Mechanical Engineering)
Oldac, Olcay (Istanbul Technical University, Faculty of Mechanical Engineering)
Publication Information
Structural Engineering and Mechanics / v.59, no.3, 2016 , pp. 475-502 More about this Journal
Abstract
Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nano-sized machines depends on proper understanding of mechanical behavior of these nano-sized beam elements. Small length scales such as lattice spacing between atoms, surface properties, grain size etc. are need to be considered when applying any classical continuum model. In this study, Eringen's nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The displacements, slopes and the stress resultants are obtained analytically. A detailed parametric study is conducted to examine the effect of the nonlocal parameter, mechanical loadings, opening angle, boundary conditions, and slenderness ratio on the static behavior of the nanobeam.
Keywords
curved nanobeams; nonlocal elasticity; in-plane statics; exact solution; initial value method;
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Times Cited By KSCI : 7  (Citation Analysis)
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1 Abramowitz, M. and Stegun, I.A. (1972), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Printing, Dover, New York, NY, USA.
2 Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205.   DOI
3 Alotta, G., Failla, G. and Zingales, M. (2014), "Finite element method for a nonlocal Timoshenko beam model", Finite Elem. Anal. Des., 89, 77-92.   DOI
4 Arash, B., Wang, Q. and Duan, W.H. (2011), "Detection of gas atoms via vibration of graphenes", Phys. Lett. A, 375(24), 2411-2415.   DOI
5 Behera, L. and Chakraverty, S. (2014), "Free vibration of nonhomogeneous Timoshenko nanobeams", Meccanica, 49(1), 51-67.   DOI
6 Berrabah, H.M., Tounsi, A., Semmah, A. and Bedia, E.A.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365.   DOI
7 Bradshaw, R.D., Fisher, F.T. and Brinson, L.C. (2003), "Fiber waviness in nanotube-reinforced polymer composites-II: modeling via numerical approximation of the dilute strain concentration tensor", Compos. Sci. Technol., 63(11), 1705-1722.   DOI
8 Craighead, H.G. (2000), "Nanoelectromechanical systems", Science, 290(5496), 1532-153.   DOI
9 Ekinci, K.L. (2005), "Electromechanical transducers at the nanoscale: Actuation and sensing of motion in nanoelectromechanical systems (NEMS)", Small, 1(8-9), 786-797.   DOI
10 Eringen, A.C. (1983), "Linear theory of nonlocal elasticity and dispersion of plane waves", J. Appl. Phys., 54, 4703-4710.   DOI
11 Fisher, F.T., Bradshaw, R.D. and Brinson, L.C. (2003), "Fiber waviness in nanotube-reinforced polymer composites-I: Modulus predictions using effective nanotube properties", Compos. Sci. Technol., 63(11), 1689-1703.   DOI
12 Guo, R., Barisci, J.N., Innis, P.C., Too, C.O., Wallace, G.G. and Zhou, D. (2000), "Electrohydrodynamic polymerization of 2-methoxyaniline-5-sulfonic acid", Synthetic Met., 114(3), 267-272.   DOI
13 Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solid. Struct., 48(18), 2496-2510.   DOI
14 Hu, Y.G., Liew, K.M. and Wang, Q. (2009), "Nonlocal elastic beam models for flexural wave propagation in double-walled carbon nanotubes", J. Appl. Phys., 106(4):044301.   DOI
15 Huang, C., Ye, C., Wang, S., Stakenborg, T. and Lagae, L. (2012), "Gold nanoring as a sensitive plasmonic biosensor for on-chip DNA detection", Appl. Phys. Lett., 100, 173114.   DOI
16 Joshi, A.Y., Sharma, S.C. and Harsha, S.P. (2010) "Dynamic analysis of a clamped wavy single walled carbon nanotube based nanomechanical sensors", J. Nanotechnol. Eng. Med., 1, 031007-7.   DOI
17 Kong, J., Franklin, N.R., Zhou, C.W., Chapline, M.G., Peng, S., Cho, K. and Dai, H.J. (2000), "Nanotube molecular wires as chemical sensors", Science, 287, 622-625.   DOI
18 Li, C. (2014), "A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries", Compos. Struct., 118, 607-621.   DOI
19 Kong, X.Y., Ding, Y., Yang, R. and Wang, Z.L. (2004), "Single-crystal nanorings formed by epitaxial self-coiling of polar nanobelts", Science, 303, 1348-1351.   DOI
20 Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48(3), 415-434.   DOI
21 Li, C. and Chou, T.W. (2003), "Single-walled carbon nanotubes as ultra-high frequency nanomechanical resonators", Phys. Rev. B, 68(7), 073405.   DOI
22 Li, C., Li, S., Yao, L.Q. and Zhu, Z.K. (2015a),"Nonlocal theoretical approaches and atomistic simulations for longitudinal free vibration of nanorods/nanotubes and verification of different nonlocal models", Appl. Math. Model., 39, 4570-4585.   DOI
23 Li, C., Yao, L.Q., Chen, W.Q and Li, S. (2015b), "Comments on nonlocal effects in nano-cantilever beams", Int. J. Eng. Sci., 87, 47-57.   DOI
24 Liu, Y.P. and Reddy, J.N. (2011), "A nonlocal curved beam model based on a modified couple stress theory", Int. J. Struct. Stab. Dyn., 11(3), 495-512.
25 Mayoof, F.N. and Hawwa, M.A. (2009), "Chaotic behavior of a curved carbon nanotube under harmonic excitation", Chaos Solit. Fract., 42(3), 1860-1867.   DOI
26 McFarland, A.W. and Colton, J.S. (2005), "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng., 15, 1060-1067.   DOI
27 Povstenko, Y.Z. (1995), "Straight disclinations in nonlocal elasticity", Int. J. Eng. Sci., 33(4), 575-582.   DOI
28 Paola, M.D., Failla, G. and Zingales, M. (2013), "Non-local stiffness and damping models for shear-deformable beams", Eur. J. Mech. A-Solid., 40, 69-83.   DOI
29 Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Solid. Struct., 41, 305-312.
30 Polizzotto, C., Fuschi, P. and Pisano, A.A. (2006), "A nonhomogeneous nonlocal elasticity model", Eur. J. Mech. A-Solid., 25(2), 308-333.   DOI
31 Pradhan, S.C. and Sarkar, A. (2009), "Analyses of tapered fgm beams with nonlocal theory", Struct. Eng. Mech., 32(6), 811-833.   DOI
32 Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307.   DOI
33 Roukes, M. (2001), "Nanoelectromechanical systems face the future", Phys. World, 14, 25-31
34 Sudak, L.J. (2003), "Column buckling of multi-walled carbon nanotubes using nonlocal elasticity", J. Appl. Phys., 94, 7281.   DOI
35 Taghizadeh, M., Ovesy, H.R. and Ghannadpour, S.A.M. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., 54(4) 755-769.   DOI
36 Treacy, M.M.J., Ebbesen, T.W. and Gibson, J.W. (1996), "Exceptionally high Young's modulus observed for individual carbon nanotubes", Nature, 381(6584), 678-680.   DOI
37 Tufekci, E. (2001), "Exact solution of free in-plane vibration of shallow circular arches", Int. J. Struct. Stab. Dyn., 1, 409-428.   DOI
38 Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 89, 124301.
39 Tufekci, E. and Arpaci, A. (2006), "Analytical solutions of in-plane static problems for non-uniform curved beams including axial and shear deformations", Struct. Eng. Mech., 22(2), 131-150.   DOI
40 Wang, L.F. and Hu, H.Y. (2005), "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B, 71(19) 195412.   DOI
41 Wang, Q. and Shindo, Y. (2006), "Nonlocal continuum models for carbon nanotubes subjected to static loading", J. Mech. Mater. Struct., 1(4), 663-680.   DOI
42 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710.   DOI
43 Zhang, Z., Wang C.M. and Challamel, N. (2015), "Eringen's length-scale coefficients for vibration and buckling of nonlocal rectangular plates with simply supported edges", J. Eng. Mech., 141(2), 04014117.   DOI
44 Zhao, Q., Gan, Z.H. and Zhuang, O.K. (2002), "Electrochemical sensors based on carbon nanotubes", Electroanal., 14(23), 1609-13.   DOI