Steel and Composite Structures

  • 제27권3호
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  • Pages.371-388
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  • 2018
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory

  • Rahmani, Omid (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Deyhim, Soroush (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Hosseini, S. Amir Hossein (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan)
  • 투고 : 2017.01.07
  • 심사 : 2018.03.27
  • 발행 : 2018.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a new model based on nonlocal high order theory is proposed to study the size effect on the bending of nano-sandwich beams with a compliance core. In this model, in contrast to most of the available sandwich theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core are obtained through an elasticity solution. Equations of motion and boundary conditions for nano-sandwich beam are derived by using Hamilton's principle and an analytical solution is presented for simply supported nano-sandwich beam. The results are validated with previous studies in the literature. These results can be utilized in the study of nano-sensors and nano-actuators. The effect of nonlocal parameter, Young's modulus of the core and aspect ratio on the deflection of the nano-sandwich beam is investigated. It is concluded that by including the small-scale effects, the deflection of the skins is increased and by increasing the nonlocal parameter, the influence of small-scale effects on the deflections is increased.

키워드

참고문헌

  1. Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  3. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  4. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  5. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  6. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  7. Eichenfield, M., Camacho, R., Chan, J., Vahala, K.J. and Painter, O. (2009), "A picogram-and nanometre-scale photonic-crystal optomechanical cavity", Nature, 459(7246), 550-555. https://doi.org/10.1038/nature08061
  8. Emam, S.A. (2013), "A general nonlocal nonlinear model for buckling of nanobeams", Appl. Math. Model., 37(10), 6929-6939. https://doi.org/10.1016/j.apm.2013.01.043
  9. Frostig, Y. (2014), "Non-linear behavior of a face-sheet debonded sandwich panel-Thermal effects", Int. J. Non-Linear Mech., 64, 1-25. https://doi.org/10.1016/j.ijnonlinmec.2014.03.001
  10. Frostig, Y., Baruch, M., Vilnay, O. and Sheinman, I. (1992), "High-order theory for sandwich-beam behavior with transversely flexible core", J. Eng. Mech., 118(5), 1026-1043. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:5(1026)
  11. Frostig, Y., Phan, C.N. and Kardomateas, G.A. (2013), "Free vibration of unidirectional sandwich panels, Part I: Compressible core", J. Sandw. Struct. Mater., 45(4), 377-411.
  12. Ghavanloo, E. and Fazelzadeh, S.A. (2013), "Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics", Nanotechnology, 24(7), 075702. https://doi.org/10.1088/0957-4484/24/7/075702
  13. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  14. Hayati, H., Hosseini, S.A. and Rahmani, O. (2016), "Coupled twist-bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory", Microsyst. Technol., 23(7), 2393-2401.
  15. Hosseini, S. and Rahmani, O. (2016), "Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model", Int. J. Struct. Stabil. Dyn., 16(10), 1550077. https://doi.org/10.1142/S0219455415500777
  16. Jandaghian, A.A. and Rahmani, O. (2015), "On the buckling behavior of piezoelectric nanobeams: An exact solution", J. Mech. Sci. Technol., 29(8), 3175-3182. https://doi.org/10.1007/s12206-015-0716-7
  17. Khalili, S.M.R., Rahmani, O., Malekzadeh Fard, K. and Thomsen, O.T. (2014), "High-order modeling of circular cylindrical composite sandwich shells with a transversely compliant core subjected to low velocity impact", Mech. Adv. Mater. Struct., 21(8), 680-695. https://doi.org/10.1080/15376494.2012.707297
  18. Lashkari, M.J. and Rahmani, O. (2016), "Bending behavior of sandwich structures with flexible functionally graded core based on high-order sandwich panel theory", Meccanica, 51(5), 1093-1112. https://doi.org/10.1007/s11012-015-0263-4
  19. Miandoab, E.M., Yousefi-Koma, A. and Pishkenari, H.N. (2015), "Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams", Microsyst. Technol., 21(2), 457-464. https://doi.org/10.1007/s00542-014-2110-2
  20. Murmu, T. and Adhikari, S. (2010), "Nonlocal transverse vibration of double-nanobeam-systems", J. Appl. Phys., 108(8), 083514. https://doi.org/10.1063/1.3496627
  21. Murmu, T. and Adhikari, S. (2011a), "Axial instability of doublenanobeam-systems", Phys. Lett. A, 375(3), 601-608. https://doi.org/10.1016/j.physleta.2010.11.007
  22. Murmu, T. and Adhikari, S. (2011b), "Nonlocal vibration of bonded double-nanoplate-systems", Compos. Part B: Eng., 42(7), 1901-1911. https://doi.org/10.1016/j.compositesb.2011.06.009
  23. Murmu, T., Sienz, J., Adhikari, S. and Arnold, C. (2011), "Nonlocal buckling behavior of bonded double-nanoplatesystems", J. Appl. Phys., 110(8), 084316. https://doi.org/10.1063/1.3644908
  24. Najafi, F., Shojaeefard, M.H. and Googarchin, H.S. (2016), "Nonlinear low-velocity impact response of functionally graded plate with nonlinear three-parameter elastic foundation in thermal field", Compos. Part B: Eng., 107, 123-140. https://doi.org/10.1016/j.compositesb.2016.09.070
  25. Najafi, F., Shojaeefard, M.H. and Googarchin, H.S. (2017), "Nonlinear dynamic response of FGM beams with Winkler-Pasternak foundation subject to noncentral low velocity impact in thermal field", Compos. Struct., 167, 132-143. https://doi.org/10.1016/j.compstruct.2017.01.063
  26. Nguyen, N.T., Kim, N.I. and Lee, J. (2014), "Analytical solutions for bending of transversely or axially FG nonlocal beams", Steel Compos. Struct., Int. J., 17(5), 641-665. https://doi.org/10.12989/scs.2014.17.5.641
  27. Patti, A., Barretta, R., de Sciarra, F.M., Mensitieri, G., Menna, C. and Russo, P. (2015), "Flexural properties of multi-wall carbon nanotube/polypropylene composites: Experimental investigation and nonlocal modeling", Compos. Struct., 131, 282-289. https://doi.org/10.1016/j.compstruct.2015.05.002
  28. Phan, C.N., Frostig, Y. and Kardomateas, G.A. (2012a), "Analysis of sandwich beams with a compliant core and with in-plane rigidity-extended high-order sandwich panel theory versus elasticity", J. Appl. Mech., 79(4), 041001. https://doi.org/10.1115/1.4005550
  29. Phan, C.N., Kardomateas, G.A. and Frostig, Y. (2012b), "Global buckling of sandwich beams based on the extended high-order theory", AIAA Journal, 50(8), 1707-1716. https://doi.org/10.2514/1.J051454
  30. Pourseifi, M., Rahmani, O. and Hoseini, S.A.H. (2015), "Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories", Meccanica, 50(5), 1351-1369. https://doi.org/10.1007/s11012-014-0096-6
  31. Rahmani, O. (2014), "On the flexural vibration of pre-stressed nanobeams based on a nonlocal theory", Acta Phys. Pol. A, 125(2), 532. https://doi.org/10.12693/APhysPolA.125.532
  32. Rahmani, O., Khalili, S.M.R. and Thomsen, O.T. (2012), "A highorder theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads", Composite Structures, 94(7), 2129-2142. https://doi.org/10.1016/j.compstruct.2012.02.002
  33. Rahmani, O., Hosseini, S.A.H. and Hayati, H. (2016), "Frequency analysis of curved nano-sandwich structure based on a nonlocal model", Modern Physics Letters B, 30(10), 1650136.
  34. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  35. Shojaeefard, M.H., Googarchin, H.S., Ghadiri, M. and Mahinzare, M. (2017), "Micro temperature-dependent FG porous plate: free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT", Appl. Math. Model., 50, 633-655. https://doi.org/10.1016/j.apm.2017.06.022
  36. Shojaeefard, M.H., Googarchin, H.S., Mahinzare, M. and Ghadiri, M. (2018), "Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate", Microsystem Technologies, 24(3), 1525-1543. https://doi.org/10.1007/s00542-017-3557-8
  37. Simsek, M. (2011), "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Compos. Struct., Int. J., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059
  38. Wang, Q. and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15(2), 659. https://doi.org/10.1088/0964-1726/15/2/050
  39. Yuan, Z., Kardomateas, G.A. and Frostig, Y. (2015), "Finite element formulation based on the extended high-order sandwich panel theory", AIAA Journal, 53(10), 3006-3015. https://doi.org/10.2514/1.J053736
  40. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693

피인용 문헌

  1. Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory vol.26, pp.11, 2018, https://doi.org/10.1177/1077546319890170