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

Levent Turan; Bekir Akgöz

doi:10.24107/ijeas.1641966

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

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

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.

Details

Primary Language

English

Subjects

Solid Mechanics

Journal Section

Research Article

Authors

Levent Turan
0000-0002-2414-5242
Türkiye

Bekir Akgöz ^*
0000-0003-2097-2555
Türkiye

Publication Date

September 5, 2025

Submission Date

February 19, 2025

Acceptance Date

May 17, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

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

IZ

https://izlik.org/JA35XX86DD

Cite

RIS / Bibtex

APA

Turan, L., & Akgöz, B. (2025). Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences, 17(2), 94-105. https://doi.org/10.24107/ijeas.1641966

AMA

1.Turan L, Akgöz B. Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory. IJEAS. 2025;17(2):94-105. doi:10.24107/ijeas.1641966

Chicago

Turan, Levent, and Bekir Akgöz. 2025. “Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences 17 (2): 94-105. https://doi.org/10.24107/ijeas.1641966.

EndNote

Turan L, Akgöz B (September 1, 2025) Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences 17 2 94–105.

IEEE

[1]L. Turan and B. Akgöz, “Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory”, IJEAS, vol. 17, no. 2, pp. 94–105, Sept. 2025, doi: 10.24107/ijeas.1641966.

ISNAD

Turan, Levent - Akgöz, Bekir. “Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences 17/2 (September 1, 2025): 94-105. https://doi.org/10.24107/ijeas.1641966.

JAMA

1.Turan L, Akgöz B. Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory. IJEAS. 2025;17:94–105.

MLA

Turan, Levent, and Bekir Akgöz. “Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences, vol. 17, no. 2, Sept. 2025, pp. 94-105, doi:10.24107/ijeas.1641966.

Vancouver

1.Levent Turan, Bekir Akgöz. Bending Analysis of a Boron Nitride Nanotube Cantilever Beam Based on Modified Couple Stress Theory. IJEAS. 2025 Sep. 1;17(2):94-105. doi:10.24107/ijeas.1641966