Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory

Year 2025, Volume: 17 Issue: 2, 94 - 105, 05.09.2025

Levent Turan , Bekir Akgöz

https://doi.org/10.24107/ijeas.1641966

Abstract

There are difficulties in determining the properties of nano-sized materials such as bending, buckling and vibration with classical elasticity theories. For this reason, researchers have developed many theories that include the size effects of micro- and nano-sized structures.
In this study, the bending equations of a boron nitride nanotube cantilever nanobeam under different loadings are obtained according to the modified couple stress theory and Euler-Bernoulli beam theory and the results are compared.

Keywords

Modified couple stress theory , Euler-Bernoulli beam theory , Boron Nitride Nanotube , Size effect.

References

• Minoli, D., Nanotechnology Applications to Telecommunications and Networking, 1st Edition, John Wiley and Sons, 2005.
• Loos, M., Carbon Nanotube Reinforced Composites, Elsevier, 2015.
• Collins, PG., Avouris, P., Nanotubes for electronics. Scientific American, 62(283), 69, 2000.
• McFarland, A.W., Colton, J.S., Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering, 15, 1060-1067, 2005.
• Gao, Y., Lei, F-M., Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory. Biochemical and Biophysical Research Communications, 387(3), 467-471, 2009.
• Mindlin, R.D., Tiersten, H.F., Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 11, 415–448, 1962.
• Toupin, R.A., Elastic materials with couple stresses. Archive for Rational Mechanics and Analysis, 11, 385–414, 1962.
• Mindlin, R.D., Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16, 51-78, 1964.
• Koiter, W.T., Couple stresses in the theory of elasticity. I and II. Proceedings Series B, Koninklijke Nederlandse Akademie van Wetenschappen, 67, 17–44, 1964.
• Akgöz, B., Civalek, Ö., Investigation of size effects on static response of single-walled carbon nanotubes based on strain gradient elasticity. International Journal of Computational Methods, 9(02), 1240032, 2012.
• Akgöz, B., Mercan, K., Demir, Ç., Civalek, Ö., Static analysis of beams on elastic foundation by the method of discrete singular convolution. International Journal of Engineering and Applied Sciences, 8(3), 67-73, 2016.
• Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T., Eremeyev, V.A., On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. International Journal of Engineering Science, 170, 103604, 2022.
• Abouelregal, A.E., Akgöz, B., Civalek, Ö., Nonlocal thermoelastic vibration of a solid medium subjected to a pulsed heat flux via Caputo–Fabrizio fractional derivative heat conduction. Applied Physics A, 128(8), 660, 2022.
• Akbaş, Ş.D., Dastjerdi, S., Akgöz, B., Civalek, Ö., Dynamic analysis of functionally graded porous microbeams under moving load. Transport in Porous Media, 142, 209–227, 2022.
• Civalek, Ö., Akgöz, B., Size-dependent stability of embedded beams with variable cross section. International Journal of Engineering Science, 208, 104210, 2025.
• Yıldırım, A., Akgöz, B., Buckling behavior of nickel microbeams based on reformulated strain gradient theory. Applied Physics A, 130, 832, 2024.
• Wong, E.W., Sheehan, P.E. Lieber, C.M., Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes. Science, 277, 1971–1975, 1997.
• Zheng, B., Lowther, J.E., Numerical investigations into mechanical properties of hexagonal silicon carbon nanowires and nanotubes. The Royal Society of Chemistry, 2, 1733–1739, 2010.
• Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39, 2731-2743, 2002.
• Park, S.K., Gao, X-L., Bernoulli-Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16, 2355-2359, 2006.
• Akgöz, B., Yüksek mertebeden elastisite teorileriyle mikro ve nano yapıların lineer ve lineer olmayan analizleri (in Turkish). Master's thesis, Akdeniz University, Antalya, 2010.