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3271
Torsional Statics of Circular Nanostructures: Numerical Approach
Abstract:
Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which governs the nonlocal material behavior. The new NL-FEM is adopted in such a way that the postulated nonlocal elastic behavior of material is captured by a finite element endowed with a set of (cross-stiffness) element itself by the other elements in mesh. An example with their analytical solutions and the relevant numerical findings for various load and boundary conditions are presented and discussed in details. It is observed from the numerical solutions that the torsional deformation angle decreases with increasing nonlocal nanoscale parameter. It is also noted that the analytical solution fails to capture the nonlocal effect in some cases where numerical solutions handle those situation effectively which prove the reliability and effectiveness of numerical techniques.
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References:

[1] H. Gleiter, "Nanocristalline materials," Progress in Materials Science, vol. 33, pp. 223-315, 1989.
[2] M. E. Gurtin, A. Murdoch, "A continuum theory of elastic material surfaces," Archive for Rational Mechanics Analysis, vol. 57 (4), pp. 291-323, 1975.
[3] C. W. Lim, Z. R. Li, L. H. He, "Size dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress," International Journal of Solids and Structures, vol. 43 (17), pp. 5055- 5065, 2006.
[4] E. Kröner, "Elasticity theory of materials with long range cohesive forces," International Journal of Solids and Structures, vol. 3, pp. 731- 742, 1967.
[5] I. A. Kunin, "The theory of elastic media with microstructures and the theory of dislocaltion," In: Kröner E. ed. Mechanices of Geeneralized Continua, Proceedings of IUTAM Symposium 1967. New York: Springer, 1968.
[6] J. A. Krumhansl, "Some considerations on the relations between solid state physics and generalized continuum mechanics," In: Kröner E. ed. Mechanices of Geeneralized Continua. Berlin: Springer-Verlag, 1968, pp. 298-331.
[7] D. G. B. Edelen, "Protoelastic bodies with large deformations," Archive for Rational Mechanics Analysis, vol. 34 pp. 283-300, 1969.
[8] D. G. B. Edelen, N. Laws, "On the thermodynamics of systems with nonlocality," Archive for Rationale Mechanics and Analysis, vil. 43, pp. 24-35, 1971.
[9] D. G. B. Edelen, A. E. Green, N. Laws, "Nonlocal continuum mechanics," Archive for Rationale Mechanics and Analysis, vol. 43, pp. 36-44, 1971.
[10] A. C. Eringen, "Nonlocal polar elastic continua," International Journal of Engineering Science, vol. 10, pp. 1-16, 1972.
[11] A.C. Eringen, "Linear theory of nonlocal elasticity and dispersion of plane waves," International Journal of Engineering Science, vol. 10, pp. 425-435, 1972.
[12] A. C. Eringen, "Nonlocal Continuum Field Theories," New York, Springer, 2002.
[13] A. C. Eringen, D. B. G. Edelen, "On nonlocal elasticity," International Journal of Engineering Science. Vol. 10, pp. 233-248, 1972.
[14] A. C. Eringen, "On differential equations of nonlocal elasticity and solution of screw dislocaltion and surface waves," Journal of Applied Physics, vol. 54, pp.4703-4710, 1983.
[15] J. Peddieson, G.R. Buchanan, R. P. McNitt, "Application of nonlocal continuum models to nanotechnology," International Journal of Engineering Science, vol. 41, pp. 305-312, 2003.
[16] L. J. Sudak, "Column buckling of multi-walled carbon nanotubes using nonlocal continuum mechanics," Journal of Applied Physics, vol. 94 (11), pp. 7281-7287, 2003.
[17] C. M. Wang, Y.Y. Zhang, S. S. Ramesh, S. Kitipornchai, "Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory," Journal of Physics D: Applied Physics, vol. 39 (17), pp. 3904-3909, 2006.
[18] Y.Y. Zhang, C.M. Wang, W.H. Duan, Y. Xiang, Z. Zong, "Assessment of continuum mechanics models in predicting buckling of single-walled carbon nanotubes," Nanotechnology, vol. 20 (39), pp. 395707(8pp), 2009.
[19] T. H. Thai, "A nonlocal beam theory for bending buckling, and vibration of nanobeams," International Journal of Engineering Science, vol. 52, pp. 56-64, 2012.
[20] C. Polizzotto, "Nonlocal elasticity and related variational principles," International Journal of Solids and Structures, vol. 38, pp. 7359-7380, 2001.
[21] A. C. Eringen, B. S. Kim, "Stress concentration at the tip of a crack," Mechanics Research Communications, vol. 1, pp. 233-237, 1974.
[22] A. C. Eringen, C. G. Speziale, B.S. Kim, "Crack-tip problem in nonlocal elasticity," Journal of Mechanics, Physics and Silods, vol. 25, pp. 339- 355, 1977.
[23] A. C. Eringen, "Theory of nonlocal elasticity and some applications," Res Mechaica, vol. 21, pp. 313-342, 1987.
[24] S. B. Altan, "Existance in nonlocal elasticity," Archive Mechanics, vol. 41, pp. 25-36, 1989.
[25] A. A. Pasano, A. Sofi, P. Fuschi, "Nonlocal integral elasticity: 2D finite element based solutions," International Journal of Solids and Structures, vol. 46, pp. 3836-3849, 2009.
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