Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Archive of Applied Mechanics
Erschienen in: Archive of Applied Mechanics 12/2021

07.09.2021 | Original

Buckling analysis of nanobeams with deformable boundaries via doublet mechanics

verfasst von: Ömer Civalek, Busra Uzun, Mustafa Özgür Yayli

Erschienen in: Archive of Applied Mechanics | Ausgabe 12/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Buckling analysis of nanobeams with deformable boundary conditions is researched within the framework of doublet mechanics. This theory is an alternative nanomechanics theory for continuum modeling of the granular micromaterials. Doublet mechanics theory takes into consideration the small size parameter due to dealing with also granular nanosized structures. In many studies, rigid supporting conditions are explored in the nanomechanical analysis of beams. Even though the supporting conditions are accepted as undeformable, it is not possible to provide the desired rigidity in practice. A few studies have been conducted to explore the effects of deformable boundaries. In the present work, Fourier sine series as well as Stokes’ transformation are utilized to attain the eigenvalue formulation and eigenvector characteristics of the problem. The combination of these two methods is a new approach in applied mechanics; at the same time, it is planned to create a bridge between rigid and deformable boundary conditions. By solving various examples, the accuracy of the proposed method has been tested and an excellent agreement has been achieved with the literature. In addition, the effect of the springs in the boundaries on the critical buckling load has been examined and given in a series of graphs.
Vorheriger Artikel Analysis of nominal halo orbits in the Sun–Earth system
Nächster Artikel The static and stress analyses of axially functionally graded exact super-elliptical beams via mixed FEM

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Ansari, R., Gholami, R., Sahmani, S.: Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory. Arch. Appl. Mech. 83, 1439–1449 (2013)MATHCrossRef
2.
Jalaei, M., Civalek, O.: A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects. Compos. Struct. 220, 209–220 (2019)CrossRef
3.
Kounadis, A.N., Mallis, J., Sbarounis, A.: Postbuckling analysis of columns resting on an elastic foundation. Arch. Appl. Mech. 75, 395–404 (2006)MATHCrossRef
4.
Jalaei, M., Civalek, O.: On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Int. J. Eng. Sci. 143, 14–32 (2019)MathSciNetMATHCrossRef
5.
Liu, J.J., Li, C., Fan, X.L., Tong, L.H.: Transverse free vibration and stability of axially moving nanoplates based on nonlocal elasticity theory. Appl. Math. Comput. 45, 65–84 (2017)MathSciNetMATH
6.
Demir, Ç., Civalek, Ö.: Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models. Appl. Math. Modell. 37(22), 9355–9367 (2013)CrossRef
7.
Li, C., Liu, J.J., Cheng, M., Fan, X.L.: Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces. Compos. Part B Eng. 116, 153–169 (2017)CrossRef
8.
Li, C., Yao, L.Q., Chen, W.Q., Li, S.: Comments on nonlocal effects in nano-cantilever beams. Int. J. Eng. Sci. 87, 47–57 (2015)CrossRef
9.
Li, C.: A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries. Compos. Struct. 118, 607–621 (2014)CrossRef
10.
Civalek, Ö., Uzun, B., Yaylı, M.O.: Stability analysis of nanobeams placed in electromagnetic field using a finite element method. Arab. J. Geosci. 13(21), 1–9 (2020)CrossRef
11.
Uzun, B., Yaylı, M.O.: Nonlocal vibration analysis of Ti–6Al–4V/\(\text{ ZrO}_2\) functionally graded nanobeam on elastic matrix. Arab. J. Geosci. 13(21), 1–10 (2020)
12.
Uzun, B., Civalek, Ö., Yaylı, M.Ö.: Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mech. Based Des. Struct. Mach. 1–20 (2020)
13.
Arda, M.: Axial dynamics of functionally graded Rayleigh-Bishop nanorods. Microsyst. Technol. 27(1), 269–282 (2021)CrossRef
14.
Karamanli A.: ‘Structural behaviours of zigzag and armchair nanobeams using finite element doublet mechanics’, European Journal of Mechanics-A/Solids, (2021), 104287
15.
Karamanli, A., Vo, T.P.: Bending, vibration, buckling analysis of bi-directional FG porous microbeams with a variable material length scale parameter. Appl. Math. Modell. 91, 723–748 (2021)MathSciNetCrossRef
16.
Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M.: Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory. Comput. Concrete 26(5), 439–450 (2020)
17.
Bendenia, N., Zidour, M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Adda Bedia, E.A., Mahmoud, S.R., Tounsi, A.: Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation. Comput. Concrete 26(3), 213–226 (2020)
18.
Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S.R., Adda Bedia, E.A., Tounsi, A.: A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells. Comput. Concrete 26(2), 185–201 (2020)
19.
Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M., Mahmoud, S.R.: Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method. Comput. Concrete 27(1), 73–83 (2021)
20.
She, G.L., Liu, H.B., Karami, B.: Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets. Thin-Walled Struct. 160, 107407 (2021)CrossRef
21.
Sahmani, S., Aghdam, M.M., Rabczuk, T.: Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs. Compos. Struct. 198, 51–62 (2018)CrossRef
22.
Arefi, M., Bidgoli, E.M.R., Dimitri, R., Tornabene, F.: Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets. Aerosp. Sci. Technol. 81, 108–117 (2018)CrossRef
23.
Nguyen, N.V., Nguyen, L.B., Nguyen-Xuan, H., Lee, J.: Analysis and active control of geometrically nonlinear responses of smart FG porous plates with graphene nanoplatelets reinforcement based on Bezier extraction of NURBS. Int. J. Mech. Sci. 180, 105692 (2020)CrossRef
24.
Beni, Y.T.: Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling. Mech. Res. Commun. 75, 67–80 (2016)CrossRef
25.
Kim, J., Żur, K.K., Reddy, J.N.: Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos. Struct. 209, 879–888 (2019)CrossRef
26.
Żur, K.K., Arefi, M., Kim, J., Reddy, J.N.: Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Compos. Part B Eng. 182, 107601 (2020)CrossRef
27.
Barretta, R., Faghidian, S.A., De Sciarra, F.M.: Stress-driven nonlocal integral elasticity for axisymmetric nano-plates. Int. J. Eng. Sci. 136, 38–52 (2019)MathSciNetMATHCrossRef
28.
Zenkour, A.M.: Nonlocal elasticity and shear deformation effects on thermal buckling of a CNT embedded in a viscoelastic medium. Eur. Phys. J. Plus 133, 1–14 (2018)CrossRef
29.
Arefi, M., Zenkour, A.M.: Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam. Acta Mech. 228(10), 3657–3674 (2017)MathSciNetMATHCrossRef
30.
Arefi, M., Zenkour, A.M.: Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory. J. Sandwich Struct. Mater. 28(1), 2751–2778 (2019)CrossRef
31.
Arefi, M., Zenkour, A.M.: Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory. Alexandria Eng. J. 57(3), 2177–2185 (2018)CrossRef
32.
Arefi, M., Zenkour, A.M.: Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory. J. Intell. Mater. Syst. Struct. 29(7), 1394–1406 (2018)CrossRef
33.
Arefi, M., Zenkour, A.M.: Transient analysis of a three-layer microbeam subjected to electric potential. Int. J. Smart Nano Mater. 8(1), 20–40 (2017)CrossRef
34.
Arefi, M., Zenkour, A.M.: Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenkos sandwich piezoelectric microbeam. J. Sandwich Struct. Mater. 21(4), 1243–1270 (2019)CrossRef
35.
Arefi, M., Bidgoli, E.M.R., Dimitri, R., Tornabene, F., Reddy, J.N.: Size-dependent free vibrations of FG polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on Pasternak foundations. Appl. Sci. 9(8), 1580 (2019)CrossRef
36.
Reddy, J.N., Pang, S.D.: Nonlocal continuum theories of beam for the analysis of carbon nanotubes. J. Appl. Phys. 103, 1–16 (2008)CrossRef
37.
Wang, Q., Liew, K.M.: Application of nonlocal continuum mechanics to static analysis of micro and nano-structures. Phys. Lett. A 363, 236–242 (2007)CrossRef
38.
Yayli, M.O.: Buckling analysis of a microbeam embedded in an elastic medium with deformable boundary conditions. IET Micro Nano Lett. 11, 741–745 (2016)CrossRef
39.
Yayli, M.O.: Buckling analysis of a cantilever single-walled carbon nanotube embedded in an elastic medium with an attached spring. IET Micro Nano Lett. 12, 255–259 (2017)CrossRef
40.
Yayli, M.O., Yanik, F., Kandemir, S.Y.: Longitudinal vibration of nanorods embedded in an elastic medium with elastic restraints at both ends. IET Micro Nano Lett. 10, 641–644 (2015)CrossRef
41.
Yayli, M.O.: On the axial vibration of carbon nanotubes with different boundary conditions. IET Micro Nano Lett. 9, 807–811 (2014)CrossRef
42.
Yayli, M.O.: A compact analytical method for vibration analysis of single-walled carbon nanotubes with restrained boundary conditions. J. Vib. Control 22, 2542–2555 (2016)MathSciNetCrossRef
43.
Simsek, M.: Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory. Phys.-E Low-dimensional Syst. Nanostruct. 43, 182–191 (2010)CrossRef
44.
Ece, M.C., Aydogdu, M.: Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes. Acta Mech. 190, 185–195 (2007)MATHCrossRef
45.
Aydogdu, M.: Axial vibration of the nanorods with the nonlocal continuum rod model. Phys.-E Low-dimensional Syst. Nanostruct. 41, 861–864 (2009)CrossRef
46.
Yoon, J., Ru, C.Q., Mioduchowski, A.: Vibration of an embedded multiwall carbon nanotube. Compos. Sci. Technol. 63, 1533–1542 (2003)CrossRef
47.
Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. 11, 415–448 (1962)MathSciNetMATHCrossRef
48.
Koiter, W.T.: Couple stresses in the theory of elasticity I and II. Proc. K Ned. Akad Wet (B) 67, 17–44 (1964)MathSciNetMATH
49.
Toupin, R.A.: Theory of elasticity with couple stresses. Arch. Ration. Mech. Anal. 17, 85–112 (1964)MATHCrossRef
50.
Fleck, N.A., Hutchinson, J.W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825–1857 (1993)MathSciNetMATHCrossRef
51.
Fleck, N.A., Hutchinson, J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245–2271 (2001)MATHCrossRef
52.
Eringen, A.C.: Theory of micropolar plates. Z. Angew. Math. Phys. 18, 12–30 (1967)CrossRef
53.
Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface-waves. J. Appl. Phys. 1983(54), 4703–4710 (1983)CrossRef
54.
55.
Numanoglu, H.M., Akgoz, B., Civalek, O.: On dynamic analysis of nanorods. Int. J. Eng. Sci. 130, 33–50 (2018)CrossRef
56.
Gul, U., Aydogdu, M.: Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics. Compos. Part B Eng. 137, 60–73 (2018)CrossRef
57.
58.
59.
Zhang, B., He, Y., Liu, D., Gan, Z., Shen, L.: Non-classical Timoshenko beam element based on the strain gradient elasticity theory. Finite Elements Anal. Des. 79, 22–39 (2014)MathSciNetCrossRef
60.
61.
Yayli, M.O.: Torsion of nonlocal bars with equilateral triangle cross sections. J. Comput. Theore. Nanosci. 10, 376–379 (2013)CrossRef
62.
Yayli, M.O.: Weak formulation of finite element method for nonlocal beams using additional boundary conditions. J. Comput. Theore. Nanosci. 8, 2173–2180 (2011)CrossRef
63.
Barretta, R., Canadija, M., de Sciarra, F.M.: A higher-order Eringen model for Bernoulli-Euler nanobeams. Arch. Appl. Mech. 87(11), 483–495 (2016)MATHCrossRef
64.
Jalaei, M., Civalek, O.: On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Arch. Appl. Mech. 143, 14–32 (2019)MathSciNetMATH
65.
Arefi, M., Saeed, F., Bidgoli, E.M.R., Civalek, O.: Analysis of porous micro -plates reinforced with FG-GNPs based on Reddy plate theory. Compos. Struct. 247, 112391 (2020)CrossRef
66.
Rahmani, O., Refaeinejad, V., Hosseini, S.A.H.: Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams. Steel Compos. Struct. 23(3), 339–350 (2017)CrossRef
67.
Ebrahimi, F., Barati, M.R., Civalek, O.: Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Eng. Comput. 36, 953–964 (2020)CrossRef
68.
Arefi, M., Zenkour, A.M.: Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model. J. Intell. Mater. Syst. Struct. 28(17), 2403–2413 (2017)CrossRef
69.
Zenkour, A.M.: A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods. J. Brazilian Soc. Mech. Sci. Eng. 42, 1–10 (2020)CrossRef
70.
Zenkour, A.M., Sobhy, M.: ’Axial magnetic field effect on wave propagation in bi-layer FG graphene platelet-reinforced nanobeams.’, Eng. Comput. (2021), pp. 1–17
71.
Zenkour, A.M., Radwan, A.F.: A nonlocal strain gradient theory for porous functionally graded curved nanobeams under different boundary conditions. Phys. Mesomech. 323, 601–615 (2020)CrossRef
72.
Zenkour, A.M., Radwan, A.F.: A compressive study for porous FG curved nanobeam under various boundary conditions via a nonlocal strain gradient theory. Eur. Phys. J. Plus 136(2), 1–16 (2021)CrossRef
73.
Sobhy, M., Zenkour, A.M.: The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations. Mech. Adv. Mater. Struct. 27(7), 525–538 (2020)CrossRef
74.
Barati, M.R., Faleh, N.M., Zenkour, A.M.: Dynamic response of nanobeams subjected to moving nanoparticles and hygro-thermal environments based on nonlocal strain gradient theory. Mech. Adv. Mater. Struct. 26(19), 1661–1669 (2019)CrossRef
75.
Fatahi-Vajari, A., Imam, A.: Axial vibration of single-walled carbon nanotubes using doublet mechanics. Indian J. Phys. 90(4), 447–455 (2016)MATHCrossRef
76.
Yayli, M.O.: A compact analytical method for vibration of micro-sized beams with different boundary conditions. Mech. Adv. Mater. Struct. 24, 496–508 (2016)CrossRef
77.
Yayli, M.O.: Free vibration behavior of a gradient elastic beam with varying cross section. Shock Vib. 801696,(2014)
78.
Gul, U., Aydogdu, M.: Structural modelling of nanorods and nanobeams using doublet mechanics theory. Int. J. Mech. Mater. Des. 14, 195–212 (2018)CrossRef
Metadaten
Titel
Buckling analysis of nanobeams with deformable boundaries via doublet mechanics
verfasst von
Ömer Civalek
Busra Uzun
Mustafa Özgür Yayli
Publikationsdatum
07.09.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 12/2021
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-021-02032-x

Weitere Artikel der Ausgabe 12/2021

Archive of Applied Mechanics 12/2021 Zur Ausgabe

Original

A receding contact problem between a graded piezoelectric layer and a piezoelectric substrate

Original

Analysis of nominal halo orbits in the Sun–Earth system

Review

On the appearance of horseshoe chaos in a nonlinear hysteretic systems with negative stiffness

Original

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

Technical notes

Miniaturized but efficient cantilever beam vibration energy harvesters for wireless bridge health monitoring applications

Original

Elastoplastic nonlinear analysis of functionally graded beams utilizing the symplectic method

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise