نوع مقاله : علمی پژوهشی

نویسنده

گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه جیرفت، جیرفت، ایران

چکیده

در مطالعه حاضر خیز بزرگ نانوتیرها همراه با اثرات سطح بررسی شده‌است. اثرات سطح در این مطالعه با استفاده از معادله یانگ لاپلاس عمومی اعمال شده‌است. همچنین روش اجزاء محدود برای تحقیق در مورد رفتار مکانیکی نانوتیرهای با خیز بزرگ مورد استفاده قرارگرفته که امکان حل مسئله با کمترین فرضیات و با شرایط مرزی و هندسه دلخواه را فراهم می‌کند. به کمک مدل ارائه شده می‌توان نانوتیرها با خیز کوچک تا بزرگ با شرایط بارگذاری و تکیه‌گاهی مختلف را تحلیل کرد. در این پژوهش تاثیر پارامترهای مختلف همچون نسبت لاغری، مدول الاستیک سطح و تنش مانده سطح بر روی خیز بزرگ نانوتیر‌ یکسرگیردار با سطح مقطع دایره‌ای تحت بار گسترده سینوسی، بررسی شده‌است. نتایج بدست‌آمده اهمیت در نظر گرفتن اثرات سطح در بررسی خیز بزرگ نانوتیرها را نشان می‌دهد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of Large Deflection of Nanobeams with Circular Cross Section under Distributed Load Taking into Surface Effects

نویسنده [English]

  • Ehsan Raeisi Estabragh

Department of Mechanical Engineering, Faculty of Engineering, University of Jiroft, Jiroft, Iran

چکیده [English]

In the present study, the large deflection of nanobeams with surface effects has been investigated. The surface effects are modeled by using the generalized Young–Laplace equation. The finite element method has been used to investigate the mechanical behavior of nanobeams. This method provides the possibility of solving the problem with the least assumptions and with the arbitrary boundary conditions and geometry. With the use of the proposed model, nanobeams small to large deflection with different loading and support conditions can be analyzed. In this study, the large deflection of circular cross-sectional nanobeams under sinusoidal distributed load with surface effects has been investigated. The effect of various parameters such as aspect ratio, surface elastic modulus and residual surface stress on the large deflection of nanobeams has been investigated. The result obtained show the importance of considering the surface effects in the study of large deflection of nanobeams.

کلیدواژه‌ها [English]

  • Finite element method
  • Surface effects
  • Large deflection
  • Timoshenko beam theory
  • Nanobeam
[1]           F. Braakman and M. Poggio, "Force sensing with nanowire cantilevers," Nanotechnology, vol. 30, no. 33, p. 332001, 2019.
[2]           M. Ray, "Analysis of smart nanobeams integrated with a flexoelectric nano actuator layer," Smart Materials and Structures, vol. 25, no. 5, p. 055011, 2016.
[3]           D. Liu et al., "Toward a further understanding of size effects in the torsion of thin metal wires: an experimental and theoretical assessment," International Journal of Plasticity, vol. 41, pp. 30-52, 2013.
[4]           Z. Li, Y. He, J. Lei, S. Guo, D. Liu, and L. Wang, "A standard experimental method for determining the material length scale based on modified couple stress theory," International Journal of Mechanical Sciences, vol. 141, pp. 198-205, 2018.
[5]           J.-G. Guo and Y.-P. Zhao, "The size-dependent bending elastic properties of nanobeams with surface effects," Nanotechnology, vol. 18, no. 29, p. 295701, 2007.
[6]           J. He and C. M. Lilley, "Surface effect on the elastic behavior of static bending nanowires," Nano letters, vol. 8, no. 7, pp. 1798-1802, 2008.
[7]           L. Jiang and Z. Yan, "Timoshenko beam model for static bending of nanowires with surface effects," Physica E: Low-dimensional systems and Nanostructures, vol. 42, no. 9, pp. 2274-2279, 2010.
[8]           P. Kasirajan, R. Amirtham, and J. N. Reddy, "Surface and non-local effects for non-linear analysis of Timoshenko beams," International Journal of Non-Linear Mechanics, vol. 76, pp. 100-111, 2015.
[9]           D.-M. Zhao and J.-L. Liu, "New insights on the deflection and internal forces of a bending nanobeam," Chinese Physics Letters, vol. 34, no. 9, p. 096201, 2017.
[10]         Y. Yao and S. Chen, "Surface effect in the bending of nanowires," Mechanics of Materials, vol. 100, pp. 12-21, 2016.
[11]         J. He and Z. Yan, "Surface Effect and nonlocal effect on nanowires bent by a point force at an arbitrary axial position," IEEE Transactions on Nanotechnology, vol. 16, no. 4, pp. 527-533, 2016.
[12]         J. Zou and X.-F. Li, "Effect of the Casimir force on buckling of a double-nanowire system with surface effects," International Journal of Structural Stability and Dynamics, vol. 18, no. 10, p. 1850118, 2018.
[13]         Y. Taghipour and G. H. Baradaran, "A finite element modeling for large deflection analysis of uniform and tapered nanowires with good interpretation of experimental results," International Journal of Mechanical Sciences, vol. 114, pp. 111-119, 2016.
[14]         Y. Taghipour and G. H. Baradaran, "Large deflection analysis of nanowires based on nonlocal theory using total Lagrangian finite element method," Acta Mechanica, vol. 228, pp. 2429-2442, 2017.
[15]         E. R. Estabragh and G. H. Baradaran, "Large amplitude free vibration analysis of nanobeams based on modified couple stress theory," International Journal of Structural Stability and Dynamics, vol. 21, no. 09, p. 2150129, 2021.
[16]         E. Raeisi Estabragh and G. H. Baradaran, "Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method," Archive of Applied Mechanics, vol. 91, no. 12, pp. 4717-4734, 2021.
[17]         M. Mojahedi, M. M. Zand, and M. Ahmadian, "Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method," Applied Mathematical Modelling, vol. 34, no. 4, pp. 1032-1041, 2010.
[18]         P. A. Hassanpour, E. Esmailzadeh, W. L. Cleghorn, and J. K. Mills, "Nonlinear vibration of micromachined asymmetric resonators," Journal of sound and vibration, vol. 329, no. 13, pp. 2547-2564, 2010.
[19]         D. Zeng and Q. Zheng, "Large deflection theory of nanobeams," Acta Mechanica Solida Sinica, vol. 23, no. 5, pp. 394-399, 2010.
[20]         J. He and C. M. Lilley, "The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation," Computational Mechanics, vol. 44, pp. 395-403, 2009.
[21]         J. Liu, Y. Mei, R. Xia, and W. Zhu, "Large displacement of a static bending nanowire with surface effects," Physica E: Low-dimensional systems and Nanostructures, vol. 44, no. 10, pp. 2050-2055, 2012.
[22]         Y. Sapsathiarn and R. Rajapakse, "A model for large deflections of nanobeams and experimental comparison," IEEE transactions on nanotechnology, vol. 11, no. 2, pp. 247-254, 2011.
[23]         J. Su, Y. Xiang, L.-L. Ke, and Y.-S. Wang, "Surface effect on static bending of functionally graded porous nanobeams based on Reddy’s beam theory," International Journal of Structural Stability and Dynamics, vol. 19, no. 06, p. 1950062, 2019.
[24]         F. Lin, L. Tong, H.-S. Shen, C. Lim, and Y. Xiang, "Assessment of first and third order shear deformation beam theories for the buckling and vibration analysis of nanobeams incorporating surface stress effects," International Journal of Mechanical Sciences, vol. 186, p. 105873, 2020.
[25]         W. M. Lai, D. Rubin, and E. Krempl, Introduction to continuum mechanics. Butterworth-Heinemann, 2009.
[26]         C. A. Felippa, "Nonlinear finite element methods," Aerospace Engineering Sciences Department of the University of Colorado. Boulder, 2001.
[27]         C. A. Felippa, "Nonlinear finite element methods," University of Colorado, Boulder, Colorado, USA, 2001.
[28]         C. Liu and R. Rajapakse, "Continuum models incorporating surface energy for static and dynamic response of nanoscale beams," IEEE Transactions on Nanotechnology, vol. 9, no. 4, pp. 422-431, 2010.
[29]         R. C. Cammarata, "Surface and interface stress effects in thin films," Progress in surface science, vol. 46, no. 1, pp. 1-38, 1994.