In this paper, the buckling analysis of laminated composite plates reinforced by single-walled carbon nanotubes (SWCNTs) is carried out using an analytical approach as well as the finite element method. The developed model is based on the classical laminated plate theory (CLPT) and the third-order shear deformation theory for moderately thick laminated plates. The critical buckling loads for the symmetrical layup are determined for different support edges. The Mori-Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight nanotubes. The effect of the agglomeration of the randomly oriented straight nanotubes on the critical buckling load is also analyzed. The results of analytical solution are compared and verified with the FEM calculations The critical buckling loads obtained by the finite element and the analytical methods for different layup and boundary conditions are in good agreement with each other. In this article, the effects of the carbon nanotubes (CNTs) orientation angle, the edge conditions, and the aspect ratio on the critical buckling load are also demonstrated using both the analytical and finite element methods.
In this article, the buckling and vibration analysis of a double-bonded nanocomposite piezoelectric plate reinforced by a boron nitride nanotube based on the Eshelby-Mori-Tanaka approach is developed using modified couple stress theory under electro-thermo-mechanical loadings surrounded by an elastic foundation. Using Hamilton's principle, the governing equations of motion are obtained by applying a modified couple stress theory and the Eshelby-Mori-Tanaka approach for piezoelectric material and Kirchhoff plate. These equations are coupled for the double-layer plate using the Pasternak foundation and solved using Navier’s type solution. Then the dimensionless frequencies and critical buckling load for simply-supported boundary conditions are obtained. The effects of material length scale parameter, elastic foundation coefficients, aspect ratio ( a/b), length to thickness ratio ( a/h), transverse and longitudinal wave numbers on the dimensionless natural are investigated. The dimensionless frequency of a double-bonded nanocomposite piezoelectric plate increases with increasing length to thickness ratio and decreases with increasing aspect ratio. In addition, the effect of the elastic foundation on the dimensionless frequency of double-bonded nanocomposite piezoelectric plates is more considerable for higher elastic medium parameters. The critical buckling load also decreases with an increase in the dimensionless material length scale parameter.
The small-scale effect on the torsional buckling of a double-walled carbon nanotube (DWCNT) embedded on Winkler and Pasternak foundations is investigated in this study using the theory of nonlocal elasticity. The effects of the surrounding elastic medium, such as the spring constant of the Winkler type and the shear constant of the Pasternak type, as well as the van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. Finally, based on the theory of nonlocal elasticity and by employing the continuum models, an elastic double-shell model is presented for the nonlocal torsional buckling load of a DWCNT. It is seen from the results that the shear constant of the Pasternak type increases the nonlocal critical torsional buckling load, while the difference between the presence and the absence of the shear constant of the Pasternak type becomes large. It is shown that the nonlocal critical buckling load is lower than the local critical buckling load. Moreover, a simplified analysis is carried out to estimate the nonlocal critical torque for the torsional buckling of a DWCNT.
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