Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 5 Sayı: 4, 161 - 167, 20.12.2021
https://doi.org/10.26701/ems.773106

Öz

Kaynakça

  • Navier, C.-L.-M.-H. (1827) . Mémoire sur le lois de l’équilibre et du mouvement des corps solides élastiques (1821), Mémoires de l’Academie des Sciences de l’Institut de France, s. II, 7: 375–393.
  • Cauchy, A.-L. (1828) . Sur l’équilibre et le mouvement d’un système de points matériels sollicités par des forces d’attraction ou de répulsion mutuelle, Exercices de Mathématiques, 3, 188–213, 1822, 1827; Oeuvres, 2(8): 227–252 .
  • Poisson, S.D. (1829). Mémoire sur l’équilibre et le mouvement des corps élastiques 1828. Mémoires de l’Académie des Sciences de l’Institut de France, s. II, 8: 357–380.
  • Trovalusci, P., Capecchi, D., Ruta, G. (2009). Genesis of the multiscale approach for materials with microstructure. Archive of Applied Mechanics 79: 981-997.
  • Mindlin, R. D. (1964). Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16(1): 51–78,.
  • Kunin, I. A. (1968). The theory of elastic media with microstructure and the theory of dislocation. Kröner, E. (Eds.), Mechanics of Generalized Continua, Springer, Berlin Heidelberg, p. 321.
  • Capriz, G. (1989). Continua with Microstructure. Springer Tracts in Natural Philosophy. Springer-Verlag.
  • Maugin, G.A. (1993). Material Inhomogeneities in Elasticity. Applied Mathematics. Taylor & Francis.
  • Eringen, A. C. (1999). Microcontinuum Field Theory. Springer.
  • Eringen, A. C. (2002). Nonlocal Continuum Field Theories. Springer-Verlag.
  • Rapaport, D.C. (1995). The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge.
  • Baggio, C., Trovalusci, P. (1998). Limit analysis for no-tension and friction three dimensional discrete systems. Mechanics of Structures and Mach., 26:287 – 304,.
  • Trovalusci, P. (2014). Molecular approaches for multifield continua: origins and current developments. Tomasz Sadowski and Patrizia Trovalusci (Eds.), Multiscale Modeling of Complex Materials: Phenomenological, Theoretical and Computational Aspects. Springer Vienna, p. 211–278.
  • Kunin, I. A. (1984). On foundations of the theory of elastic media with microstructure. International Journal of Engineering Sciences, 22(8):969 – 978.
  • Tuna, M., Leonetti, L., Trovalusci, P., Kirca, M. (2020). ‘Explicit’ and ‘implicit’ non-local continuous descriptions for a plate with circular inclusion in tension. Meccanica 55: 927–944.
  • Tuna, M., Trovalusci, P. (2020). Scale dependent continuum approaches for discontinuous assemblies: ’explicit’ and ’implicit’ non-local models. Mech. Res. Commun., 103:103461, 6 pages.
  • Abdollahi, R., Boroomand, B. (2013) Benchmarks in nonlocal elasticity defined by Eringen’s integral model. International Journal of Solids and Structures 50(18): 2758-2771.
  • Benvenuti, E., Simone, A. (2013). One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect. Mechanics Research Communications, 48: 46-51.
  • Zaera R., Serrano, Ó., Fernández-Sáez, J. (2019). On the consistency of the nonlocal strain gradient elasticity. International Journal of Engineering Sciences 138:65-81.
  • Eroglu, U. (2020). Perturbation approach to Eringen’s local/non-local constitutive equation with applications to 1-D structures. Meccanica, 55: 1119-1134.
  • Romano, G., Barretta, R., Diaco, M., de Sciarra, F.M. (2017). Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams. International Journal of Mechanical Sciences 121:151-156.
  • Polyanin, P., Manzhirov, A. (2008). Handbook of integral equations. Chapman and Hall/CRC, London.

Some New Approximate Solutions in Closed-Form to Problems of Nanobars

Yıl 2021, Cilt: 5 Sayı: 4, 161 - 167, 20.12.2021
https://doi.org/10.26701/ems.773106

Öz

Following recent technological advancements, a great attention has been paid to mechanical behaviour of structural elements of nanosize. In this study, some solutions to mechanical problems of bars of nanosize is examined using Eringen’s two-phase nonlocal elasticity. Assuming the fraction coefficient of nonlocal part of the material is small, a perturbation expansion with respect to it is performed. With this procedure, the original nonlocal problem is broken into a set of local elasticity problems. Solutions to some example problems of nanobars are provided in closed-form for the first time, and commented on. The new solutions provided herein may well serve for benchmark studies, as well as identification of material parameters of nano-sized structural elements, such as carbon nanotubes.

Kaynakça

  • Navier, C.-L.-M.-H. (1827) . Mémoire sur le lois de l’équilibre et du mouvement des corps solides élastiques (1821), Mémoires de l’Academie des Sciences de l’Institut de France, s. II, 7: 375–393.
  • Cauchy, A.-L. (1828) . Sur l’équilibre et le mouvement d’un système de points matériels sollicités par des forces d’attraction ou de répulsion mutuelle, Exercices de Mathématiques, 3, 188–213, 1822, 1827; Oeuvres, 2(8): 227–252 .
  • Poisson, S.D. (1829). Mémoire sur l’équilibre et le mouvement des corps élastiques 1828. Mémoires de l’Académie des Sciences de l’Institut de France, s. II, 8: 357–380.
  • Trovalusci, P., Capecchi, D., Ruta, G. (2009). Genesis of the multiscale approach for materials with microstructure. Archive of Applied Mechanics 79: 981-997.
  • Mindlin, R. D. (1964). Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16(1): 51–78,.
  • Kunin, I. A. (1968). The theory of elastic media with microstructure and the theory of dislocation. Kröner, E. (Eds.), Mechanics of Generalized Continua, Springer, Berlin Heidelberg, p. 321.
  • Capriz, G. (1989). Continua with Microstructure. Springer Tracts in Natural Philosophy. Springer-Verlag.
  • Maugin, G.A. (1993). Material Inhomogeneities in Elasticity. Applied Mathematics. Taylor & Francis.
  • Eringen, A. C. (1999). Microcontinuum Field Theory. Springer.
  • Eringen, A. C. (2002). Nonlocal Continuum Field Theories. Springer-Verlag.
  • Rapaport, D.C. (1995). The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge.
  • Baggio, C., Trovalusci, P. (1998). Limit analysis for no-tension and friction three dimensional discrete systems. Mechanics of Structures and Mach., 26:287 – 304,.
  • Trovalusci, P. (2014). Molecular approaches for multifield continua: origins and current developments. Tomasz Sadowski and Patrizia Trovalusci (Eds.), Multiscale Modeling of Complex Materials: Phenomenological, Theoretical and Computational Aspects. Springer Vienna, p. 211–278.
  • Kunin, I. A. (1984). On foundations of the theory of elastic media with microstructure. International Journal of Engineering Sciences, 22(8):969 – 978.
  • Tuna, M., Leonetti, L., Trovalusci, P., Kirca, M. (2020). ‘Explicit’ and ‘implicit’ non-local continuous descriptions for a plate with circular inclusion in tension. Meccanica 55: 927–944.
  • Tuna, M., Trovalusci, P. (2020). Scale dependent continuum approaches for discontinuous assemblies: ’explicit’ and ’implicit’ non-local models. Mech. Res. Commun., 103:103461, 6 pages.
  • Abdollahi, R., Boroomand, B. (2013) Benchmarks in nonlocal elasticity defined by Eringen’s integral model. International Journal of Solids and Structures 50(18): 2758-2771.
  • Benvenuti, E., Simone, A. (2013). One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect. Mechanics Research Communications, 48: 46-51.
  • Zaera R., Serrano, Ó., Fernández-Sáez, J. (2019). On the consistency of the nonlocal strain gradient elasticity. International Journal of Engineering Sciences 138:65-81.
  • Eroglu, U. (2020). Perturbation approach to Eringen’s local/non-local constitutive equation with applications to 1-D structures. Meccanica, 55: 1119-1134.
  • Romano, G., Barretta, R., Diaco, M., de Sciarra, F.M. (2017). Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams. International Journal of Mechanical Sciences 121:151-156.
  • Polyanin, P., Manzhirov, A. (2008). Handbook of integral equations. Chapman and Hall/CRC, London.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliği
Bölüm Research Article
Yazarlar

Uğurcan Eroğlu 0000-0002-2446-0947

Yayımlanma Tarihi 20 Aralık 2021
Kabul Tarihi 26 Temmuz 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 5 Sayı: 4

Kaynak Göster

APA Eroğlu, U. (2021). Some New Approximate Solutions in Closed-Form to Problems of Nanobars. European Mechanical Science, 5(4), 161-167. https://doi.org/10.26701/ems.773106
AMA Eroğlu U. Some New Approximate Solutions in Closed-Form to Problems of Nanobars. EMS. Aralık 2021;5(4):161-167. doi:10.26701/ems.773106
Chicago Eroğlu, Uğurcan. “Some New Approximate Solutions in Closed-Form to Problems of Nanobars”. European Mechanical Science 5, sy. 4 (Aralık 2021): 161-67. https://doi.org/10.26701/ems.773106.
EndNote Eroğlu U (01 Aralık 2021) Some New Approximate Solutions in Closed-Form to Problems of Nanobars. European Mechanical Science 5 4 161–167.
IEEE U. Eroğlu, “Some New Approximate Solutions in Closed-Form to Problems of Nanobars”, EMS, c. 5, sy. 4, ss. 161–167, 2021, doi: 10.26701/ems.773106.
ISNAD Eroğlu, Uğurcan. “Some New Approximate Solutions in Closed-Form to Problems of Nanobars”. European Mechanical Science 5/4 (Aralık 2021), 161-167. https://doi.org/10.26701/ems.773106.
JAMA Eroğlu U. Some New Approximate Solutions in Closed-Form to Problems of Nanobars. EMS. 2021;5:161–167.
MLA Eroğlu, Uğurcan. “Some New Approximate Solutions in Closed-Form to Problems of Nanobars”. European Mechanical Science, c. 5, sy. 4, 2021, ss. 161-7, doi:10.26701/ems.773106.
Vancouver Eroğlu U. Some New Approximate Solutions in Closed-Form to Problems of Nanobars. EMS. 2021;5(4):161-7.

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