بررسی تاثیر تنش سطحی بر پایداری کمانشی نانوتیوب با استفاده از نظریه الاستیسیته غیرمحلی اصلاح شده

نوع مقاله: مقاله علمی پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، واحد پرند، دانشگاه آزاد اسلامی، پرند، ایران

2 دانشیار، گروه مهندسی مکانیک، واحد پرند، دانشگاه آزاد اسلامی، پرند، ایران

3 گروه مهندسی مکانیک، واحدپرند، دانشگاه آزاد اسلامی، پرند، ایران

چکیده

در این مقاله، تحلیل کمانش نانوتیوب اویلر- برنولی با استفاده از نظریه الاستیسیته غیرمحلی اصلاح شده با در نظر گرفتن اثر الاستیسیته سطح، تنش سطحی و پارامتر غیرمحلی مورد بررسی قرار گرفته‌است. با بهره‌گیری از اصل همیلتون و نظریه الاستیسیته غیرمحلی اصلاح شده و با در نظر گرفتن اثر تنش سطحی، معادلات حاکم بر دینامیک نانوتیر استخراج شده‌است. حل تحلیلی معادلات الاستیسیته غیرمحلی اصلاح شده برای استخراج رابطه نیروی بحرانی کمانش نانوتیوب با در نظر گرفتن تنش سطحی با استفاده از روش ناویر ارائه شده‌‌است. تأثیر تغییر پارامترهایی مانند ضریب مود کمانش، طول و قطر نانوتیوب، مقدار تنش سطحی و پارامتر غیرمحلی در مقدار نیروی بحرانی کمانش نانوتیوب با استفاده از نظریه الاستیسیته غیرمحلی اصلاح شده بررسی شده‌‌است.

کلیدواژه‌ها

موضوعات


[1] Eringen, A.C., “Nonlocal Polar Elastic Continua”, International Journal of Engineering Science”, Vol. 10, No. 1, pp. 1-16, (1972).

 

[2] Eringen, A.C., and Edelen, D.G.B., “On Nonlocal Elasticity”, International Journal of Engineering Science, Vol. 10, No. 3, pp. 233-248, (1972).

 

[3] Eringen, A.C., “On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves”, Journal of Applied Physics, Vol. 54, No. 9, pp. 4703-4710, (1983).

 

[4] Govindjee, S., and Sackman, J.L., “On the use of Continuum Mechanics to Estimate the Properties of Nanotubes”, Solid State Communications, Vol. 110, No. 4, pp. 227-230, (1999).

 

[5] Eringen, A.C., “Nonlocal Continuum Field Theories”, Springer Science & Business Media, (2002).

 

[6] Peddieson, J., Buchanan, G. R., and McNitt, R.P., “Application of Nonlocal Continuum Models to Nanotechnology”, International Journal of Engineering Science, Vol. 41, No. 3, pp. 305-312, (2003).

 

[7] Lim, C.W., and Wang, C.M., “Exact Variational Nonlocal Stress Modeling with Asymptotic Higher-order Strain Gradients for Nanobeams”, Journal of Applied Physics, Vol. 101, No. 5, pp. 054312, (2007).

 

[8] Kumar, D., Heinrich, C., and Waas, A.M., “Buckling Analysis of Carbon Nanotubes Modeled using Nonlocal Continuum Theories”, Journal of Applied Physics, Vol. 103, No. 7, pp. 073521, (2008).

 

[9] He, J., and Lilley, C.M., “Surface Effect on the Elastic Behavior of Static Bending Nanowires”, Nano Letters, Vol. 8, No. 7, pp. 1798-1802, (2008).

 

[10] Challamel, N., and Wang, C.M., “The Small Length Scale Effect for a Non-local Cantilever Beam: a Paradox Solved”, Nanotechnology, Vol. 19, No. 34, pp. 345703, (2008).

 

[11] Wang, G.F., and Feng, X.Q., “Surface Effects on Buckling of Nanowires under Uniaxial Compression”, Applied Physics Letters, Vol. 94, No. 14, pp. 141913, (2009).

 

[12] Wang, G.F., and Feng, X.Q., “Timoshenko Beam Model for Buckling and Vibration of Nanowires with Surface Effects”, Journal of Physics D: Applied Physics, Vol. 42, No. 15, pp. 155411, (2009).

 

[13] Lim, C.W., “On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium, Governing Equation and Static Deflection”, Applied Mathematics and Mechanics, Vol. 31, No. 1, pp. 37-54, (2010).

 

[14] On, B.B., Altus, E., and Tadmor, E.B., “Surface Effects in Non-uniform Nanobeams: Continuum vs. Atomistic Modeling”, International Journal of Solids and Structures, Vol. 47, No. 9, pp. 1243-1252, (2010).

 

[15] Lee, H.L., and Chang, W.J., “Surface Effects on Frequency Analysis of Nanotubes using Nonlocal Timoshenko Beam Theory”, Journal of Applied Physics, Vol. 108, No. 9, pp. 093503, (2010).

 

[16] Demir, C., Civalek, O., and Akgoz, B., “Free Vibration Analysis of Carbon Nanotubes Based on Shear Deformable Beam Theory by Discrete Singular Convolution Technique”, Mathematical and Computational Applications, Vol. 15, No. 1, pp. 57-65, (2010).

 

[17] Amara, K., Tounsi, A., and Mechab, I., “Nonlocal Elasticity Effect on Column Buckling of Multiwalled Carbon Nanotubes under Temperature Field”, Applied Mathematical Modelling, Vol. 34, No. 12, pp. 3933-3942, ( 2010).

 

[18] Liu, C., Rajapakse, R.K N.D., and Phani, A. S., “Finite Element Modeling of Beams with Surface Energy Effects”, Journal of Applied Mechanics, Vol. 78, No. 3, 031014, pp. 1-10, (2011).

 

[19] Wang, D.H., and Wang, G.F., “Surface Effects on the Vibration and Buckling of Double-Nanobeam-systems”, Journal of Nanomaterials, Vol. 2011, Article ID 518706, pp. 1-7, (2011).

 

[20] Wang, L., “A Modified Nonlocal Beam Model for Vibration and Stability of Nanotubes Conveying Fluid”, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 1, pp. 25-28, (2011).

 

[21] Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E., and Meletis, E.I., “Static Analysis of Nanobeams Including Surface Effects by Nonlocal Finite Element”, Journal of Mechanical Science and Technology, Vol. 26, No. 11, pp. 3555-3563, (2012).

 

[22] Sun, Y.G., Yao, X.H., Liang, Y.J., and Han, Q., “Nonlocal Beam Model for Axial Buckling of Carbon Nanotubes with Surface Effect”, EPL (Europhysics Letters), Vol. 99, No. 5, 56007, (2012).

 

[23] Lim, C.W., Yang, Q., and Zhang, J. B., “Thermal Buckling of Nanorod Based on Non-local Elasticity Theory”, International Journal of Non-Linear Mechanics, Vol. 47, No. 5, pp. 496-505, (2012).

 

[24] Yang, Q., and Lim, C.W., “Thermal Effects on Buckling of Shear Deformable Nanocolumns with von Karman Nonlinearity Based on Nonlocal Stress Theory”, Nonlinear Analysis: Real World Applications, Vol. 13, No. 2, pp. 905-922, (2012).

 

[25] Hosseini-Ara, R., Mirdamadi, H. R., Khademyzadeh, H., and Mostolizadeh, R., “Stability Analysis of Carbon Nanotubes Based on a Novel Beam Model and its Comparison with Sanders Shell Model and Molecular Dynamics Simulations”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 34, No. 2, pp. 126-134, (2012).

 

[26] Jam, J.E., and Samaei, A.T., “Buckling of Nanotubes under Compression Considering Surface Effects”, International Journal of Nano Dimension, Vol. 4, No. 2, pp. 131-134, (2013).

 

[27] Ansari, R., and Sahmani, S., “Prediction of Biaxial Buckling Behavior of Single-layered Graphene Sheets Based on Nonlocal Plate Models and Molecular Dynamics Simulations”, Applied Mathematical Modelling, Vol. 37, No. 12, pp. 7338-7351, (2013).

 

[28] Ghannadpour, S.A.M., Mohammadi, B., and Fazilati, J., “Bending, Buckling and Vibration Problems of Nonlocal Euler Beams using Ritz Method”, Composite Structures, Vol. 96, pp. 584-589, (2013).

 

[29] Shakouri, A., Ng, T. Y., and Lin, R.M., “A Study of the Scale Effects on the Flexural Vibration of Graphene Sheets using REBO Potential Based Atomistic Structural and Nonlocal Couple Stress Thin Plate Models”, Physica E: Low-dimensional Systems and Nanostructures, Vol. 50, pp. 22-28, (2013).

 

[30] Liang, X., Hu, S., and Shen, S., “A New Bernoulli–Euler Beam Model Based on a Simplified Strain Gradient Elasticity Theory and its Applications”, Composite Structures, Vol. 111, pp. 317-323, (2014).

 [31] Ashoori, A., and Mahmoodi, M.J., “The Modified Version of Strain Gradient and Couple Stress Theories in General Curvilinear Coordinates”, European Journal of Mechanics-A/Solids, Vol. 49, pp. 441-454, (2015).

 

[32] Mousavi, Z., Shahidi, S.A., and Boroomand, B., “A New Method for Bending and Buckling Analysis of Rectangular Nano Plate: Full Modified Nonlocal Theory”, Meccanica, Vol. 52, No. 11-12, pp. 2751-2768, (2017).