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Comparison of small scale effect theories for buckling analysis of nanobeams

Year 2017, Volume: 9 Issue: 3, 87 - 97, 31.10.2017
https://doi.org/10.24107/ijeas.340958

Abstract

Theories which
consider small scale effect have a great importance on analysis in micro and
nano scale. In present paper, three kind of nanotubes (Carbon Nanotube (CNT),
Boron Nitride Nanotube (BNNT), and Silicon Carbide Nanotube (SiCNT)) are analyzed
in case of buckling on two parameters elastic foundation. Three different small
scale theories (Nonlocal Elasticity Theory (NET), Surface Elasticity Theory
(SET), and Nonlocal Surface Elasticity Theory (NET&SET)) are applied to
calculate the buckling loads. Also Classical Euler-Bernoulli Beam Theory (CT)
is used to see the effect of small scale effective theories. Comparative results
are given for simply supported nanotubes in figures.  

References

  • [1] Iijima, S., Helical Microtubules of Graphitic Carbon. Nature, 354(6348), 56-58, 1991.
  • [2] Sudak, L., Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. Journal of Applied Physics, 94(11), 7281-7287, 2003.
  • [3] Civalek, Ö., Demir, Ç., Akgöz, B., Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory. International Journal of Engineering and Applied Sciences, 2(1), 47-56, 2009.
  • [4] Akgoz, B., Civalek, O., Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories. Journal of Computational and Theoretical Nanoscience, 8(9), 1821-1827, 2011.
  • [5] Elishakoff, I., Carbon Nanotubes and Nanosensors: Vibration, Buckling and Balistic Impact2013; John Wiley & Sons,2013.
  • [6] Shokuhfar, A., Ebrahimi-Nejad, S., Effects of structural defects on the compressive buckling of boron nitride nanotubes. Physica E: Low-dimensional Systems and Nanostructures, 48, 53-60, 2013.
  • [7] Arani, A.G., Roudbari, M., Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle. Thin Solid Films, 542, 232-241, 2013.
  • [8] Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Composite Structures, 143, 300-309, 2016.
  • [9] Mercan, K., Civalek, Ö., Demir, Ç., Akgöz, B. Buckling of boron nitride nanotubes surrounded by an elastic matrix.International Conference on Mechanics of Composites, Year.
  • [10] Mercan, K., A Comparative Buckling Analysis of Silicon Carbide Nanotube and Boron Nitride Nanotube. International Journal of Engineering & Applied Sciences (IJEAS), 8(4), 99-107, 2016.
  • [11] Baei, M.T., Kaveh, F., Torabi, P., Sayyad-Alangi, S.Z., Adsorption Properties of Oxygen on H-Capped (5,5) Boron Nitride Nanotube (BNNT)- A Density Functional Theory. E-Journal of Chemistry, 8(2), 609-614, 2011.
  • [12] Arani, A.G., Jamali, S.A., Amir, S., Maboudi, M.J., Electro-thermo--mechanical nonlinear buckling of Pasternak coupled DWBNNTs based on nonlocal piezoelasticity theory. Turkish Journal of Engineering and Environmental Sciences, 37(3), 231-246, 2014.
  • [13] Schulz, M., Shanov, V., Yin, Z., Nanotube Superfiber Materials: Changing Engineering Design2013; William Andrew,2013.
  • [14] Panchal, M.B., Upadhyay, S., Cantilevered single walled boron nitride nanotube based nanomechanical resonators of zigzag and armchair forms. Physica E: Low-dimensional Systems and Nanostructures, 50, 73-82, 2013.
  • [15] Zhou, M., Lu, Y.-H., Cai, Y.-Q., Zhang, C., Feng, Y.-P., Adsorption of gas molecules on transition metal embedded graphene: a search forhigh-performance graphene-based catalysts and gas sensors. Nanotechnology, 22(38), 385502, 2011.
  • [16] Akgoz, B., Civalek, O., Investigation of Size Effects on Static Response of Single-Walled Carbon Nanotubes Based on Strain Gradient Elasticity. International Journal of Computational Methods, 9(2), 2012.
  • [17] Civalek, O., Akgoz, B., Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix. Computational Materials Science, 77, 295-303, 2013.
  • [18] Mercan, K., Demir, Ç., Civalek, Ö., Coordinate Transformation for Sector and Annular Sector Shaped Graphene Sheets on Silicone Matrix. International Journal of Engineering & Applied Sciences (IJEAS), 7(2), 56-73, 2015.
  • [19] Akgoz, B., Civalek, O., Static and dynamic response of sector-shaped graphene sheets. Mechanics of Advanced Materials and Structures, 23(4), 432-442, 2016.
  • [20] Mercan, K., Civalek, Ö., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Composites Part B: Engineering, 114, 34-45, 2017.
  • [21] Mercan, K., Numanoglu, H., Akgöz, B., Demir, C., Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 1-18, 2017.
  • [22] [cited 2017 24.09.2017]; Available from: https://www.nasa.gov/.
  • [23] Civalek, Ö., Finite Element analysis of plates and shells. Elazığ: Fırat University, 1998.
  • [24] Akgoz, B., Civalek, O., Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Composite Structures, 134, 294-301, 2015.
  • [25] Civalek, O., Analysis of Thick Rectangular Plates with Symmetric Cross-ply Laminates Based on First-order Shear Deformation Theory. Journal of Composite Materials, 42(26), 2853-2867, 2008.
  • [26] Gürses, M., Civalek, Ö., Korkmaz, A.K., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first‐order shear deformation theory. International journal for numerical methods in engineering, 79(3), 290-313, 2009.
  • [27] Fantuzzi, N., Tornabene, F., Bacciocchi, M., Dimitri, R., Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates. Composites Part B-Engineering, 115, 384-408, 2017.
  • [28] Tornabene, F., Fantuzzi, N., Bacciocchi, M., A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis. Composite Structures, 171, 429-461, 2017.
  • [29] Tornabene, F., Fantuzzi, N., Bacciocchi, M., Linear Static Behavior of Damaged Laminated Composite Plates and Shells. Materials, 10(7), 2017.
  • [30] Tornabene, F., Fantuzzi, N., Bacciocchi, M., Finite Elements Based on Strong and Weak Formulations for Structural Mechanics: Stability, Accuracy and Reliability. International Journal of Engineering & Applied Sciences (IJEAS), 9(2), 1-21, 2017.
  • [31] Demir, C., Mercan, K., Numanoglu, H.M., Civalek, O., Bending Response of Nanobeams Resting on Elastic Foundation. Journal of Applied and Computational Mechanics, -, 2017.
  • [32] Akgoz, B., Civalek, O., Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory. Acta Astronautica, 119, 1-12, 2016.
  • [33] Akgoz, B., Civalek, O., Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity. Structural Engineering and Mechanics, 48(2), 195-205, 2013.
  • [34] Gurses, M., Akgoz, B., Civalek, O., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Applied Mathematics and Computation, 219(6), 3226-3240, 2012.
  • [35] Reddy, J., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2), 288-307, 2007.
  • [36] Mercan, K., Numanoglu, H.M., Akgöz, B., Demir, C., Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 2017.
  • [37] Wang, G.-F., Feng, X.-Q., Timoshenko beam model for buckling and vibration of nanowires with surface effects. Journal of physics D: applied physics, 42(15), 155411, 2009.
  • [38] Rahmani, O., Asemani, S.S., Hosseini, S.A., Study the Surface Effect on the Buckling of Nanowires Embedded in Winkler–Pasternak Elastic Medium Based on a Nonlocal Theory. Journal of Nanostructures, 6(1), 90-95, 2016.
  • [39] Demir, Ç., Civalek, Ö., Nonlocal finite element formulation for vibration. International Journal of Engineering and Applied Sciences, 8(2), 109-117, 2016.
  • [40] Demir, Ç., Civalek, Ö., On the analysis of microbeams. International Journal of Engineering Science, 121(Supplement C), 14-33, 2017.
  • [41] Demir, Ç., Civalek, Ö., Nonlocal deflection of microtubules under point load. International Journal of Engineering and Applied Sciences, 7(3), 33-39, 2015.
Year 2017, Volume: 9 Issue: 3, 87 - 97, 31.10.2017
https://doi.org/10.24107/ijeas.340958

Abstract

References

  • [1] Iijima, S., Helical Microtubules of Graphitic Carbon. Nature, 354(6348), 56-58, 1991.
  • [2] Sudak, L., Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. Journal of Applied Physics, 94(11), 7281-7287, 2003.
  • [3] Civalek, Ö., Demir, Ç., Akgöz, B., Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory. International Journal of Engineering and Applied Sciences, 2(1), 47-56, 2009.
  • [4] Akgoz, B., Civalek, O., Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories. Journal of Computational and Theoretical Nanoscience, 8(9), 1821-1827, 2011.
  • [5] Elishakoff, I., Carbon Nanotubes and Nanosensors: Vibration, Buckling and Balistic Impact2013; John Wiley & Sons,2013.
  • [6] Shokuhfar, A., Ebrahimi-Nejad, S., Effects of structural defects on the compressive buckling of boron nitride nanotubes. Physica E: Low-dimensional Systems and Nanostructures, 48, 53-60, 2013.
  • [7] Arani, A.G., Roudbari, M., Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle. Thin Solid Films, 542, 232-241, 2013.
  • [8] Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Composite Structures, 143, 300-309, 2016.
  • [9] Mercan, K., Civalek, Ö., Demir, Ç., Akgöz, B. Buckling of boron nitride nanotubes surrounded by an elastic matrix.International Conference on Mechanics of Composites, Year.
  • [10] Mercan, K., A Comparative Buckling Analysis of Silicon Carbide Nanotube and Boron Nitride Nanotube. International Journal of Engineering & Applied Sciences (IJEAS), 8(4), 99-107, 2016.
  • [11] Baei, M.T., Kaveh, F., Torabi, P., Sayyad-Alangi, S.Z., Adsorption Properties of Oxygen on H-Capped (5,5) Boron Nitride Nanotube (BNNT)- A Density Functional Theory. E-Journal of Chemistry, 8(2), 609-614, 2011.
  • [12] Arani, A.G., Jamali, S.A., Amir, S., Maboudi, M.J., Electro-thermo--mechanical nonlinear buckling of Pasternak coupled DWBNNTs based on nonlocal piezoelasticity theory. Turkish Journal of Engineering and Environmental Sciences, 37(3), 231-246, 2014.
  • [13] Schulz, M., Shanov, V., Yin, Z., Nanotube Superfiber Materials: Changing Engineering Design2013; William Andrew,2013.
  • [14] Panchal, M.B., Upadhyay, S., Cantilevered single walled boron nitride nanotube based nanomechanical resonators of zigzag and armchair forms. Physica E: Low-dimensional Systems and Nanostructures, 50, 73-82, 2013.
  • [15] Zhou, M., Lu, Y.-H., Cai, Y.-Q., Zhang, C., Feng, Y.-P., Adsorption of gas molecules on transition metal embedded graphene: a search forhigh-performance graphene-based catalysts and gas sensors. Nanotechnology, 22(38), 385502, 2011.
  • [16] Akgoz, B., Civalek, O., Investigation of Size Effects on Static Response of Single-Walled Carbon Nanotubes Based on Strain Gradient Elasticity. International Journal of Computational Methods, 9(2), 2012.
  • [17] Civalek, O., Akgoz, B., Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix. Computational Materials Science, 77, 295-303, 2013.
  • [18] Mercan, K., Demir, Ç., Civalek, Ö., Coordinate Transformation for Sector and Annular Sector Shaped Graphene Sheets on Silicone Matrix. International Journal of Engineering & Applied Sciences (IJEAS), 7(2), 56-73, 2015.
  • [19] Akgoz, B., Civalek, O., Static and dynamic response of sector-shaped graphene sheets. Mechanics of Advanced Materials and Structures, 23(4), 432-442, 2016.
  • [20] Mercan, K., Civalek, Ö., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Composites Part B: Engineering, 114, 34-45, 2017.
  • [21] Mercan, K., Numanoglu, H., Akgöz, B., Demir, C., Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 1-18, 2017.
  • [22] [cited 2017 24.09.2017]; Available from: https://www.nasa.gov/.
  • [23] Civalek, Ö., Finite Element analysis of plates and shells. Elazığ: Fırat University, 1998.
  • [24] Akgoz, B., Civalek, O., Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Composite Structures, 134, 294-301, 2015.
  • [25] Civalek, O., Analysis of Thick Rectangular Plates with Symmetric Cross-ply Laminates Based on First-order Shear Deformation Theory. Journal of Composite Materials, 42(26), 2853-2867, 2008.
  • [26] Gürses, M., Civalek, Ö., Korkmaz, A.K., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first‐order shear deformation theory. International journal for numerical methods in engineering, 79(3), 290-313, 2009.
  • [27] Fantuzzi, N., Tornabene, F., Bacciocchi, M., Dimitri, R., Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates. Composites Part B-Engineering, 115, 384-408, 2017.
  • [28] Tornabene, F., Fantuzzi, N., Bacciocchi, M., A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis. Composite Structures, 171, 429-461, 2017.
  • [29] Tornabene, F., Fantuzzi, N., Bacciocchi, M., Linear Static Behavior of Damaged Laminated Composite Plates and Shells. Materials, 10(7), 2017.
  • [30] Tornabene, F., Fantuzzi, N., Bacciocchi, M., Finite Elements Based on Strong and Weak Formulations for Structural Mechanics: Stability, Accuracy and Reliability. International Journal of Engineering & Applied Sciences (IJEAS), 9(2), 1-21, 2017.
  • [31] Demir, C., Mercan, K., Numanoglu, H.M., Civalek, O., Bending Response of Nanobeams Resting on Elastic Foundation. Journal of Applied and Computational Mechanics, -, 2017.
  • [32] Akgoz, B., Civalek, O., Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory. Acta Astronautica, 119, 1-12, 2016.
  • [33] Akgoz, B., Civalek, O., Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity. Structural Engineering and Mechanics, 48(2), 195-205, 2013.
  • [34] Gurses, M., Akgoz, B., Civalek, O., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Applied Mathematics and Computation, 219(6), 3226-3240, 2012.
  • [35] Reddy, J., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2), 288-307, 2007.
  • [36] Mercan, K., Numanoglu, H.M., Akgöz, B., Demir, C., Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 2017.
  • [37] Wang, G.-F., Feng, X.-Q., Timoshenko beam model for buckling and vibration of nanowires with surface effects. Journal of physics D: applied physics, 42(15), 155411, 2009.
  • [38] Rahmani, O., Asemani, S.S., Hosseini, S.A., Study the Surface Effect on the Buckling of Nanowires Embedded in Winkler–Pasternak Elastic Medium Based on a Nonlocal Theory. Journal of Nanostructures, 6(1), 90-95, 2016.
  • [39] Demir, Ç., Civalek, Ö., Nonlocal finite element formulation for vibration. International Journal of Engineering and Applied Sciences, 8(2), 109-117, 2016.
  • [40] Demir, Ç., Civalek, Ö., On the analysis of microbeams. International Journal of Engineering Science, 121(Supplement C), 14-33, 2017.
  • [41] Demir, Ç., Civalek, Ö., Nonlocal deflection of microtubules under point load. International Journal of Engineering and Applied Sciences, 7(3), 33-39, 2015.
There are 41 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Kadir Mercan 0000-0003-3657-6274

Ömer Civalek 0000-0003-1907-9479

Publication Date October 31, 2017
Acceptance Date October 31, 2017
Published in Issue Year 2017 Volume: 9 Issue: 3

Cite

APA Mercan, K., & Civalek, Ö. (2017). Comparison of small scale effect theories for buckling analysis of nanobeams. International Journal of Engineering and Applied Sciences, 9(3), 87-97. https://doi.org/10.24107/ijeas.340958
AMA Mercan K, Civalek Ö. Comparison of small scale effect theories for buckling analysis of nanobeams. IJEAS. October 2017;9(3):87-97. doi:10.24107/ijeas.340958
Chicago Mercan, Kadir, and Ömer Civalek. “Comparison of Small Scale Effect Theories for Buckling Analysis of Nanobeams”. International Journal of Engineering and Applied Sciences 9, no. 3 (October 2017): 87-97. https://doi.org/10.24107/ijeas.340958.
EndNote Mercan K, Civalek Ö (October 1, 2017) Comparison of small scale effect theories for buckling analysis of nanobeams. International Journal of Engineering and Applied Sciences 9 3 87–97.
IEEE K. Mercan and Ö. Civalek, “Comparison of small scale effect theories for buckling analysis of nanobeams”, IJEAS, vol. 9, no. 3, pp. 87–97, 2017, doi: 10.24107/ijeas.340958.
ISNAD Mercan, Kadir - Civalek, Ömer. “Comparison of Small Scale Effect Theories for Buckling Analysis of Nanobeams”. International Journal of Engineering and Applied Sciences 9/3 (October 2017), 87-97. https://doi.org/10.24107/ijeas.340958.
JAMA Mercan K, Civalek Ö. Comparison of small scale effect theories for buckling analysis of nanobeams. IJEAS. 2017;9:87–97.
MLA Mercan, Kadir and Ömer Civalek. “Comparison of Small Scale Effect Theories for Buckling Analysis of Nanobeams”. International Journal of Engineering and Applied Sciences, vol. 9, no. 3, 2017, pp. 87-97, doi:10.24107/ijeas.340958.
Vancouver Mercan K, Civalek Ö. Comparison of small scale effect theories for buckling analysis of nanobeams. IJEAS. 2017;9(3):87-9.

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