Abstract
In this work, the thermal buckling properties of carbon nanotube with small scale effect are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equation is derived and the critical buckling temperature is presented. The influences of the scale coefficients, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia are discussed. It can be observed that the small scale effects are significant and should be (...)
Highlights
In this work, the thermal buckling properties of carbon nanotube with small scale effect are studied
The influences of the ratio of the length to the diameter (L/d) on the critical buckling temperature are shown in fig
The scale effects on the nondimensional critical buckling temperature will diminish with the ratio (i.e. L/d) increasing. It implies that the scale effects on the thermal buckling properties are not obvious for slender carbon nanotube but should be taken into account for short nanotube
Summary
Where W is the transverse displacement and ψ the rotation caused by bending. For the Timoshenko beam model with the thermal stress, the following relation can be derived:. Where S is the shear force, M the resultant bending moment and NT the thermal force which can be expressed as: NT. Where α is the thermal expansion coefficient, T the temperature change, Ac the cross area and υ the Poisson’s ratio. The bending moment and the shear force can be defined by. Where I = Ac z2dAc is the moment of inertia and K the shear correction factor which is used to compensate for the error due to the constant shear stress assumption
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