203
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Size dependent buckling analysis of nano sandwich beams by two schemes

&
Pages 975-990 | Received 26 Mar 2018, Accepted 19 Jul 2018, Published online: 11 Jan 2019

References

  • H.-T. Thai, A nonlocal beam theory for bending, buckling, and vibration of nanobeams, Int. J. Eng. Sci., vol. 52, pp. 56–64, 2012.
  • Y. Y. Zhang, C. M. Wang, W. H. Duan, Y. Xiang, and Z. Zong, Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes, Nanotechnology, vol. 20, no. 39, pp. 395707, 2009.
  • M. Şimşek, and H. H. Yurtcu, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Compos. Struct., vol. 97, pp. 378–386, 2013.
  • A. C. M. Chong, F. Yang, D. C. C. Lam, and P. Tong, Torsion and bending of micron-scaled structures, J. Mater. Res., vol. 16, no. 4, pp. 1052–1058, 2001.
  • Q. Ma, and D. R. Clarke, Size dependent hardness of silver single crystals, J. Mater. Res., vol. 10, no. 4, pp. 853–863, 1995.
  • M. Z. Nejad, and A. Hadi, Eringen’s non-local elasticity theory for bending analysis of bi-directional functionally graded Euler–Bernoulli nano-beams, Int. J. Eng. Sci., vol. 106, pp. 1–9, 2016.
  • A. C. 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.
  • M. Asghari, M. H. Kahrobaiyan, and M. T. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, Int. J. Eng. Sci., vol. 48, no. 12, pp. 1749–1761, 2010.
  • M. Şimşek, and J. N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. Eng. Sci., vol. 64, pp. 37–53, 2013.
  • W. D. Nix, and H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity, J. Mech. Phys. Solids, vol. 46, no. 3, pp. 411–425, 1998.
  • A. C. Eringen, Theory of micropolar plates, ZAMP, vol. 18, no. 1, pp. 12–30, 1967.
  • M. E. Gurtin, J. Weissmüller, and F. Larché, A general theory of curved deformable interfaces in solids at equilibrium, Philos. Mag. A, vol. 78, no. 5, pp. 1093–1109, 1998.
  • J. Peddieson, G. R. Buchanan, and R. P. McNitt, Application of nonlocal continuum models to nanotechnology, Int. J. Eng. Sci., vol. 41, no. 3–5, pp. 305–312, 2003.
  • A. C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci, vol. 10, no. 1, pp. 1, 1972.
  • A. C. Eringen, and D. G. B. Edelen, On nonlocal elasticity, Int. J. Eng. Sci, vol. 10, no. 3, p. 233, 1972.
  • A. C. Eringen, Nonlocal Continuum Field Theories. New York, NY: Springer, 2007.
  • T. Murmu, and S. C. Pradhan, Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model, Physica E, vol. 41, no. 8, pp. 1628–1633, 2009.
  • Ö. Civalek, and Ç. Demir, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Appl. Math. Modell., vol. 35, no. 5, pp. 2053–2067, 2011.
  • Q. Wang, and K. M. Liew, Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures, Phys. Lett. A, vol. 363, no. 3, pp. 236–242, 2007.
  • L. Li, and Y. Hu, Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory, Int. J. Eng. Sci., vol. 97, pp. 84–94, 2015.
  • M. Tuna, and M. Kirca, Bending, buckling and free vibration analysis of Euler-Bernoulli nanobeams using Eringen’s nonlocal integral model via finite element method, Compos. Struct., vol. 179, pp. 269–284, 2017.
  • X. Zhu, Y. Wang, and H.-H. Dai, Buckling analysis of Euler–Bernoulli beams using Eringen’s two-phase nonlocal model, Int. J. Eng. Sci., vol. 116, pp. 130–140, 2017.
  • A. Apuzzo, R. Barretta, R. Luciano, F. Marotti de Sciarra, and R. Penna, Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model, Compos. Part B: Eng., vol. 123, pp. 105–111, 2017.
  • C. M. Wang, Y. Y. Zhang, and X. Q. He, Vibration of nonlocal Timoshenko beams, Nanotechnology, vol. 18, no. 10, p. 105401, 2007.
  • C. M. Wang, S. Kitipornchai, C. W. Lim, and M. Eisenberger, Beam bending solutions based on nonlocal Timoshenko beam theory, J. Eng. Mech., vol. 134, no. 6, pp. 475–481, 2008.
  • M. Janghorban, and A. Zare, Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method, Physica E, vol. 43, no. 9, pp. 1602–1604, 2011.
  • M. Aydogdu, A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E, vol. 41, no. 9, pp. 1651–1655, 2009.
  • J. N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, Int. J. Eng. Sci., vol. 45, no. 2–8, pp. 288–307, 2007.
  • A. Mortensen, and S. Suresh, Functionally graded metals and metal-ceramic composites: part 1 processing, Int. Mater. Rev., vol. 40, no. 6, pp. 239–265, 1995.
  • S. Suresh, and A. Mortensen, Functionally graded metals and metal-ceramic composites: part 2 thermomechanical behaviour, Int. Mater. Rev., vol. 42, no. 3, pp. 85–116, 1997.
  • A. J. Markworth, K. S. Ramesh, and W. P. Parks, Modelling studies applied to functionally graded materials, J. Mater. Sci., vol. 30, no. 9, pp. 2183–2193, 1995.
  • D.-G. Zhang, Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Compos. Struct., vol. 100, pp. 121–126, 2013.
  • B. V. Sankar, An elasticity solution for functionally graded beams, Compos. Sci. Technol., vol. 61, no. 5, pp. 689–696, 2001.
  • A. F. Ávila, Failure mode investigation of sandwich beams with functionally graded core, Compos. Struct., vol. 81, no. 3, pp. 323–330, 2007.
  • L. A. Carlsson, and G. A. Kardomateas, Structural and Failure Mechanics of Sandwich Composites. Dordrecht and New York: Springer, 2011.
  • A. I. Osofero, T. P. Vo, T.-K. Nguyen, and J. Lee, Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories, J. Sandwich Struct. Mater., vol. 18, no. 1, pp. 3–29, 2016.
  • M. Şimşek, and M. Al-Shujairi, Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads, Compos Part B: Eng., vol. 108, pp. 18–34, 2017.
  • T. P. Vo, H.-T. Thai, T.-K. Nguyen, F. Inam, and J. Lee, A quasi-3D theory for vibration and buckling of functionally graded sandwich beams, Compos. Struct., vol. 119, pp. 1–12, 2015.
  • M. Rezaiee-Pajand, and N. Rajabzadeh-Safaei, Nonlocal static analysis of a functionally graded material curved nanobeam, Mech. Adv. Mater. Struct., vol. 25, no. 7, pp. 539–547, 2018.
  • M. Rezaiee-Pajand, M. Mokhtari, and A. R. Masoodi, Stability and free vibration analysis of tapered sandwich columns with functionally graded core and flexible connections, CEAS Aeronaut. J., pp. 1–20, 2018.
  • M. Rezaiee Pajand, A. Masoodi, and M. Mokhtari, Static analysis of functionally graded non-prismatic sandwich beams, Adv. Comput. Des., vol. 3, no. 2, pp. 165–190, 2018.
  • M. Nemat-Alla, Reduction of thermal stresses by developing two-dimensional functionally graded materials, Int. J. Solids Struct., vol. 40, no. 26, pp. 7339–7356, 2003.
  • B. Akgöz, and Ö. Civalek, Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mech., vol. 224, no. 9, pp. 2185–2201, 2013.
  • B. Akgöz, and Ö. Civalek, Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium, Int. J. Eng. Sci., vol. 85, pp. 90–104, 2014.
  • M. A. Eltaher, S. A. Emam, and F. F. Mahmoud, Static and stability analysis of nonlocal functionally graded nanobeams, Compos. Struct., vol. 96, pp. 82–88, 2013.
  • X. Li, L. Li, Y. Hu, Z. Ding, and W. Deng, Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory, Compos. Struct., vol. 165, pp. 250–265, 2017.
  • M. Z. Nejad, and A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, Int. J. Eng. Sci., vol. 105, pp. 1–11, 2016.
  • M. Z. Nejad, A. Hadi, and A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, Int. J. Eng. Sci., vol. 103, pp. 1–10, 2016.
  • R. Nazemnezhad, and S. Hosseini-Hashemi, Nonlocal nonlinear free vibration of functionally graded nanobeams, Compos. Struct., vol. 110, pp. 192–199, 2014.
  • O. Rahmani, and O. Pedram, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, Int. J. Eng. Sci., vol. 77, pp. 55–70, 2014.
  • M. Akbarzadeh Khorshidi, M. Shariati, and S. A. Emam, Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory, Int. J. Mech. Sci., vol. 110, pp. 160–169, 2016.
  • M. R. Barati, On wave propagation in nanoporous materials, Int. J. Eng. Sci., vol. 116, pp. 1–11, 2017.
  • S. S. Mirjavadi, S. Rabby, N. Shafiei, B. M. Afshari, and M. Kazemi, On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment, Appl. Phys. A, vol. 123, no. 5, p. 315, 2017.
  • S. S. Mirjavadi, A. Matin, N. Shafiei, S. Rabby, and B. Mohasel Afshari, Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam, J. Therm. Stresses, vol. 40, no. 10, pp. 1201–1214, 2017.
  • N. Shafiei, S. S. Mirjavadi, B. M. Afshari, S. Rabby, and A. M. S. Hamouda, Nonlinear thermal buckling of axially functionally graded micro and nanobeams, Compos. Struct., vol. 168, pp. 428–439, 2017.
  • S. S. Mirjavadi, B. Mohasel Afshari, M. Khezel, N. Shafiei, S. Rabby, and M. Kordnejad, Nonlinear vibration and buckling of functionally graded porous nanoscaled beams, J. Braz. Soc. Mech. Sci. Eng., vol. 40, no. 7, p. 352, 2018.
  • C. Wanji, W. Chen, and K. Y. Sze, A model of composite laminated Reddy beam based on a modified couple-stress theory, Compos. Struct., vol. 94, no. 8, pp. 2599–2609, 2012.
  • W. J. Chen, and X. P. Li, Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory, Arch. Appl. Mech., vol. 83, no. 3, pp. 431–444, 2013.
  • C. M. C. Roque, D. S. Fidalgo, A. J. M. Ferreira, and J. N. Reddy, A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Compos. Struct., vol. 96, pp. 532–537, 2013.
  • M. Mohammad Abadi, and A. R. Daneshmehr, An investigation of modified couple stress theory in buckling analysis of micro composite laminated Euler–Bernoulli and Timoshenko beams, Int. J. Eng. Sci., vol. 75, pp. 40–53, 2014.
  • A. Karamanlı, Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3D shear deformation theory, Compos. Struct., vol. 174, pp. 70–86, 2017.
  • N. Shafiei, S. S. Mirjavadi, B. MohaselAfshari, S. Rabby, and M. Kazemi, Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams, Comput. Methods Appl. Mech. Eng., vol. 322, pp. 615–632, 2017.
  • M. Azimi, S. S. Mirjavadi, N. Shafiei, A. M. S. Hamouda, and E. Davari, Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution, Mech. Adv. Mater. Struct., vol. 25, no. 6, pp. 467–480, 2018.
  • M. Azimi, S. S. Mirjavadi, N. Shafiei, and A. M. S. Hamouda, Thermo-mechanical vibration of rotating axially functionally graded nonlocal timoshenko beam, Appl. Phys. A, vol. 123, no. 1, pp. 104, 2017.
  • S. S. Mirjavadi, B. Mohasel Afshari, N. Shafiei, A. M. S. Hamouda, and M. Kazemi, Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams, Steel Compos. Struct., vol. 25, no. 4, pp. 415–426, 2017.
  • S. S. Mirjavadi, B. Mohasel Afshari, N. Shafiei, S. Rabby, and M. Kazemi, Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam, J. Vib. Control, vol. 24, no. 18, pp. 4211–4225, 2018.
  • Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, J. Appl. Phys., vol. 98, no. 12, p. 124301, 2005.
  • Q. Wang, and C. M. Wang, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology, vol. 18, no. 7, p. 075702, 2007.
  • L. B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J., vol. 82, pp. 1013–1024, 1977.
  • R. C. Batra, and G. M. Zhang, Analysis of adiabatic shear bands in elasto-thermo-viscoplastic materials by modified smoothed-particle hydrodynamics (MSPH) method, J. Comput. Phys., vol. 201, no. 1, pp. 172–190, 2004.
  • G. M. Zhang, and R. C. Batra, Modified smoothed particle hydrodynamics method and its application to transient problems, Comput. Mech., vol. 34, no. 2, pp. 137–146, 2004.
  • G. M. Zhang, and R. C. Batra, Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method, J. Comput. Phys., vol. 222, no. 1, pp. 374–390, 2007.
  • J. K. Chen, J. E. Beraun, and C. J. Jih, Completeness of corrective smoothed particle method for linear elastodynamics, Comput. Mech., vol. 24, no. 4, pp. 273–285, 1999.
  • J. K. Chen, J. E. Beraun, and C. J. Jih, An improvement for tensile instability in smoothed particle hydrodynamics, Comput. Mech., vol. 23, no. 4, pp. 279–287, 1999.
  • R. C. Batra, and G. M. Zhang, SSPH basis functions for meshless methods, and comparison of solutions with strong and weak formulations, Comput. Mech., vol. 41, no. 4, pp. 527–545, 2008.
  • G. M. Zhang, and R. C. Batra, Symmetric smoothed particle hydrodynamics (SSPH) method and its application to elastic problems, Comput. Mech., vol. 43, no. 3, pp. 321–340, 2009.
  • A. Karamanlı, Elastostatic analysis of two-directional functionally graded beams using various beam theories and symmetric smoothed particle hydrodynamics method, Compos. Struct., vol. 160, pp. 653–669, 2017.
  • S. A. Emam, A general nonlocal nonlinear model for buckling of nanobeams, Appl. Math. Modell., vol. 37, no. 10–11, pp. 6929–6939, 2013.

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.