Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams

Adali, S.

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Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams

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Adali S.

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Warianty tytułu

Wariacyjne sformułowanie problemu wyboczenia wielościennych nanorurek węglowych modelowanych jako nielokalne belki Timoszenki

Języki publikacji

Abstrakty

Variational formulation for multi-walled carbon nanotubes subject to buckling is derived by the semi-inverse method with governing equations based on the nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. The nonlocal theory improves the range and applicability of the physical model by modelling the nano-scale phenomenon more accurately. The natural and geometric boundary conditions are derived, which lead to a set of coupled boundary conditions for multi-walled nanotubes as opposed to uncoupled boundary conditions in the case of simply supported and clamped boundaries and also in the case of a local theory. The variational principle and the corresponding Rayleigh quotient facilitate the application of approximate and numerical methods of solution.

W pracy przedyskutowano wariacyjne sformułowanie zagadnienia wyboczenia wielościennych nanorurek węglowych wyprowadzone metodą pół-odwrotną z równaniami konstytutywnymi opartymi na nielokalnej teorii belki Timoszenki uwzględniającej efekty małoskalowe i odkształcenia postaciowe. Teoria nielokalna rozszerza zakres stosowalności modelu fizycznego belki poprzez dokładniejsze odwzorowanie zjawisk nanoskalowych. Wprowadzono naturalne i geometryczne warunki brzegowe dla wielościennych nanorurek, które ostatecznie ujęto jako warunki brzegowe sprzężone, w odróżnieniu do warunków rozprzężonych w przypadku prostego podparcia lub zamurowania brzegów oraz zastosowania teorii lokalnej. Wykazano, że wykorzystane zasady wariacyjne i wynikający iloraz Rayleigha podnoszą wydajność przybliżonych metod numerycznych.

Słowa kluczowe

carbon nanotube variational formulation non-local theory

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2012

Tom

Vol. 50 nr 1

Strony

321--333

Opis fizyczny

Bibliogr. 39 poz.

Twórcy

autor

Adali S.

University of KwaZulu-Natal, School of Mechanical Engineering, Durban, South Africa, adali@ukzn.ac.za

Bibliografia

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