404
Views
32
CrossRef citations to date
0
Altmetric
Original Articles

Timoshenko nonlocal strain gradient nanobeams: Variational consistency, exact solutions and carbon nanotube Young moduli

ORCID Icon, ORCID Icon, &
Pages 1523-1536 | Received 05 Aug 2019, Accepted 18 Oct 2019, Published online: 14 Nov 2019

References

  • T. Fan, Nano porous piezoelectric energy harvester by surface effect model, Mech. Adv. Mater. Struct., 2019. DOI: 10.1080/15376494.2018.1495791.
  • S. Namilae, J. Li, and S. Chava, Improved piezoresistivity and damage detection application of hybrid carbon nanotube sheet-graphite platelet nanocomposites, Mech. Adv. Mater. Struct., vol. 26, no. 15, pp. 1333–1341, 2019. DOI: 10.1080/15376494.2018.1432812.
  • F. Zhu, C. Park, and G.J. Yun, An extended Mori-Tanaka micromechanics model for wavy CNT nanocomposites with interface damage, Mech. Adv. Mater. Struct, pp. 1, 2019. DOI: 10.1080/15376494.2018.1562135.
  • P. Udatha, A.S. Sekhar, and R. Velmurugan, The effect of CNT to enhance the dynamic properties of hybrid composite tube shafts, Mech. Adv. Mater. Struct., vol. 26, no. 1, pp. 88–92, 2019. DOI: 10.1080/15376494.2018.1534172.
  • J.R. Pothnis, S. Gururaja, and D. Kalyanasundaram, Development and characterization of electric field directed preferentially aligned CNT nanocomposites, Mech. Adv. Mater. Struct., vol. 26, no. 1, pp. 35–41, 2019. DOI: 10.1080/15376494.2018.1534165.
  • R. Barretta, M. Brčić, M. Čanađija, R. Luciano, and F. Marotti de Sciarra, Application of gradient elasticity to armchair carbon nanotubes: Size effects and constitutive parameters assessment, Eur. J. Mech. A. Solids, vol. 65, pp. 1–13, 2017. DOI: 10.1016/j.euromechsol.2017.03.002.
  • V. Borjalilou, and M. Asghari, Size-dependent analysis of thermoelastic damping in electrically actuated microbeams, Mech. Adv. Mater. Struct., pp. 1, 2019. DOI: 10.1080/15376494.2019.1614700.
  • M.H. Ghayesh, and A. Farajpour, Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects, Mech. Adv. Mater. Struct., 2019. DOI: 10.1080/15376494.2018.1473537.
  • B. Babu, and B.P. Patel, On the finite element formulation for second-order strain gradient nonlocal beam theories, Mech. Adv. Mater. Struct., vol. 26, no. 15, pp. 1316–1332, 2019. DOI: 10.1080/15376494.2018.1432807.
  • A. Khurana, and S.K. Tomar, Waves at interface of dissimilar nonlocal micropolar elastic half-spaces, Mech. Adv. Mater. Struct., vol. 26, no. 10, pp. 825–833, 2019. DOI: 10.1080/15376494.2018.1430261.
  • B. Umesh, A. Rajagopal, and J.N. Reddy, One dimensional nonlocal integro-differential model & gradient elasticity model: Approximate solutions and size effects, Mech. Adv. Mater. Struct., vol. 26, pp. 260–273, 2019. DOI: 10.1080/15376494.2017.1373313.
  • R. Barretta, and F. Marotti de Sciarra, Variational nonlocal gradient elasticity for nano-beams, Int. J. Eng. Sci., vol. 143, pp. 73–91, 2019. DOI: 10.1016/j.ijengsci.2019.06.016.
  • R. Barretta, S.A. Faghidian, and F. Marotti de Sciarra, Aifantis versus Lam strain gradient models of Bishop elastic rods, Acta Mech., vol. 230, no. 8, pp. 2799–2812, 2019. DOI: 10.1007/s00707-019-02431-w.
  • H.M. Ouakad, and H.M. Sedighi, Static response and free vibration of MEMS arches assuming out-of-plane actuation pattern, Int. J. Non. Linear Mech., vol. 110, pp. 44–57, 2019. DOI: 10.1016/j.ijnonlinmec.2018.12.011.
  • G.-L. She, Y.-R. Ren, and F.-G. Yuan, Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems, Steel Compos. Struct., vol. 31, pp. 641–653, 2019.
  • R. Kumar, R. Rani, and A. Miglani, Nonlocal elasticity theory for microstretch circular plate with mechanical source, Mech. Adv. Mater. Struct., vol. 25, no. 13, pp. 1133–1139, 2018. DOI: 10.1080/15376494.2017.1341580.
  • M. Shishesaz, M.M. Shirbani, H.M. Sedighi, and A. Hajnayeb, Design and analytical modeling of magneto-electro-mechanical characteristics of a novel magneto-electro-elastic vibration-based energy harvesting system, J. Sound Vibr., vol. 425, pp. 149–169, 2018. DOI: 10.1016/j.jsv.2018.03.030.
  • G.-L. She, Y.-R. Ren, F.-G. Yuan, and W.-S. Xiao, On vibrations of porous nanotubes, Int. J. Eng. Sci., vol. 125, pp. 23–35, 2018. DOI: 10.1016/j.ijengsci.2017.12.009.
  • G.-L. She, F.-G. Yuan, and Y.-R. Ren, On wave propagation of porous nanotubes, Int. J. Eng. Sci., vol. 130, pp. 62–74, 2018. DOI: 10.1016/j.ijengsci.2018.05.002.
  • G.-L. She, K.-M. Yan, Y.-L. Zhang, H.-B. Liu, and Y.-R. Ren, Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory, Eur. Phys. J. Plus., vol. 133, pp. 368, 2018. DOI: 10.1140/epjp/i2018-12196-5
  • M.M. Shirbani, H.M. Sedighi, H.M. Ouakad, and F. Najar, Experimental and mathematical analysis of a piezoelectrically actuated multilayered imperfect microbeam subjected to applied electric potential, Compos. Struct., vol. 184, pp. 950–960, 2018. DOI: 10.1016/j.compstruct.2017.10.062.
  • M.M. Shirbani, M. Shishesaz, H.M. Sedighi, and A. Hajnayeb, Parametric modeling of a novel longitudinal vibration-based energy harvester using magneto-electro-elastic materials, Microsyst. Technol., vol. 23, no. 12, pp. 5989–6004, 2017. DOI: 10.1007/s00542-017-3402-0.
  • A. Farajpour, M.H. Ghayesh, and H. Farokhi, A review on the mechanics of nanostructures, Int. J. Eng. Sci., vol. 133, pp. 231–263, 2018. DOI: 10.1016/j.ijengsci.2018.09.006.
  • M.H. Ghayesh, and A. Farajpour, A review on the mechanics of functionally graded nanoscale and microscale structures, Int. J. Eng. Sci., vol. 137, pp. 8–36, 2019. DOI: 10.1016/j.ijengsci.2018.12.001.
  • A. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
  • G. Romano, R. Luciano, R. Barretta, and M. Diaco, Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours, Continuum Mech. Thermodyn., vol. 30, no. 3, pp. 641–655, 2018. DOI: 10.1007/s00161-018-0631-0.
  • G. Romano, and R. Barretta, Nonlocal elasticity in nanobeams: The stress-driven integral model, Int. J. Eng. Sci., vol. 115, pp. 14–27, 2017. DOI: 10.1016/j.ijengsci.2017.03.002.
  • R. Barretta, R. Luciano, F. Marotti de Sciarra, and G. Ruta, Stress-driven nonlocal integral model for Timoshenko elastic nano-beams, Eur. J. Mech. A Solids, vol. 72, pp. 275–286, 2018. DOI: 10.1016/j.euromechsol.2018.04.012.
  • R. Barretta, S.A. Faghidian, and F. Marotti de Sciarra, Stress-driven nonlocal integral elasticity for axisymmetric nano-plates, Int. J. Eng. Sci., vol. 136, pp. 38–52, 2019. DOI: 10.1016/j.ijengsci.2019.01.003.
  • R. Barretta, F. Fabbrocino, R. Luciano, F. Marotti de Sciarra, and G. Ruta, Buckling loads of nano-beams in stress-driven nonlocal elasticity, Mech. Adv. Mater. Struct, pp. 1, 2019. DOI: 10.1080/15376494.2018.1501523.
  • R. Barretta, M. Čanađija, R. Luciano, and F. Marotti de Sciarra, Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams, Int. J. Eng. Sci., vol. 126, pp. 53–67, 2018. DOI: 10.1016/j.ijengsci.2018.02.012.
  • R. Barretta, M. Čanađija, and F. Marotti de Sciarra, Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams, Compos. Struct., vol. 225, pp. 111104, 2019. DOI: 10.1016/j.compstruct.2019.111104.
  • R. Barretta, S.A. Faghidian, R. Luciano, C.M. Medaglia, and R. Penna, Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress driven nonlocal models, Compos. Part B, vol. 154, pp. 20–32, 2018. DOI: 10.1016/j.compositesb.2018.07.036.
  • R. Barretta, S.A. Faghidian, and R. Luciano, Longitudinal vibrations of nano-rods by stress-driven integral elasticity, Mech. Adv. Mater. Struct., vol. 26, no. 15, pp. 1307–1315, 2019. DOI: 10.1080/15376494.2018.1432806.
  • E.C. Aifantis, On the gradient approach–relation to Eringen’s nonlocal theory, Int. J. Eng. Sci., vol. 49, no. 12, pp. 1367–1377, 2011. DOI: 10.1016/j.ijengsci.2011.03.016.
  • C.W. Lim, G. Zhang, and J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, vol. 78, pp. 298–313, 2015. DOI: 10.1016/j.jmps.2015.02.001.
  • S.A. Faghidian, On non-linear flexure of beams based on non-local elasticity theory, Int. J. Eng. Sci., vol. 124, pp. 49–63, 2018. DOI: 10.1016/j.ijengsci.2017.12.002.
  • S.A. Faghidian, Integro-differential nonlocal theory of elasticity, Int. J. Eng. Sci., vol. 129, pp. 96–110, 2018. DOI: 10.1016/j.ijengsci.2018.04.007.
  • R. Zaera, Ó. Serrano, and J. Fernández-Sáez, On the consistency of the nonlocal strain gradient elasticity, Int. J. Eng. Sci., vol. 138, pp. 65–81, 2019. DOI: 10.1016/j.ijengsci.2019.02.004.
  • R. Barretta, and F. Marotti de Sciarra, Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams, Int. J. Eng. Sci., vol. 130, pp. 187–198, 2018. DOI: 10.1016/j.ijengsci.2018.05.009.
  • A. Apuzzo, R. Barretta, S.A. Faghidian, R. Luciano, and F. Marotti de Sciarra, Free vibrations of elastic beams by modified nonlocal strain gradient theory, Int. J. Eng. Sci., vol. 133, pp. 99–108, 2018. DOI: 10.1016/j.ijengsci.2018.09.002.
  • A. Apuzzo, R. Barretta, S.A. Faghidian, R. Luciano, and F. Marotti de Sciarra, Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams, Compos. Part B., vol. 164, pp. 667–674, 2019. DOI: 10.1016/j.compositesb.2018.12.112.
  • R. Barretta, M. Čanadija, and F. Marotti de Sciarra, Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes, Appl. Sci., vol. 9, no. 3, pp. 514, 2019. DOI: 10.3390/app9030514.
  • G. Romano, A. Barretta, and R. Barretta, On torsion and shear of Saint-Venant beams, Eur. J. Mech. Solid, vol. 35, pp. 47–60, 2012. DOI: 10.1016/j.euromechsol.2012.01.007.
  • S.A. Faghidian, Unified formulation of the stress field of saint-Venant’s flexure problem for symmetric cross-sections, Int. J. Mech. Sci., vol. 111–112, pp. 65–72, 2016. DOI: 10.1016/j.ijmecsci.2016.04.003.
  • S.A. Faghidian, Unified formulations of the shear coefficients in Timoshenko beam theory, J. Eng. Mech., vol. 143, pp. 06017013, 2017. DOI: 10.1061/(ASCE)EM.1943-7889.0001297
  • F. Marotti de Sciarra, and R. Barretta, A gradient model for Timoshenko nanobeams, Physica E, vol. 62, pp. 1–9, 2014. DOI: 10.1016/j.physe.2014.04.005.
  • L. Lu, X. Guo, and J. Zhao, A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms, Int. J. Eng. Sci., vol. 119, pp. 265–277, 2017. DOI: 10.1016/j.ijengsci.2017.06.024.
  • K. Duan, L. Li, Y. Hu, and X. Wang, Enhanced interfacial strength of carbon nanotube/copper nanocomposites via Ni-coating: Molecular-dynamics insights, Physica E, vol. 88, pp. 259–264, 2017. DOI: 10.1016/j.physe.2017.01.015.
  • X. Zhu, and L. Li, Closed form solution for a nonlocal strain gradient rod in tension, Int. J. Eng. Sci., vol. 119, pp. 16–28, 2017. DOI: 10.1016/j.ijengsci.2017.06.019.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.