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In this paper, based on the density functional theory (DFT) and finite element method (FEM), the elastic, buckling and vibrational behaviors of the monolayer bismuthene are studied.

The computed elastic properties based on DFT are used to develop a finite element (FE) model for the monolayer bismuthene in which the Bi-Bi bonds are simulated by beam elements. Furthermore, mass elements are used to model the Bi atoms. The developed FE model is used to compute Young's modulus of monolayer bismuthene. The model is then used to evaluate the buckling force and fundamental natural frequency of the monolayer bismuthene with different geometrical parameters.

Comparing the results of the FEM and DFT, it is shown that the proposed model can predict Young's modulus of the monolayer bismuthene with an acceptable accuracy. It is also shown that the influence of the vertical side length on the fundamental natural frequency of the monolayer bismuthene is not significant. However, vibrational characteristics of the bismuthene are significantly affected by the horizontal side length.

DFT and FEM are used to study the elastic, vibrational and buckling properties of the monolayer bismuthene. The developed model can be used to predict Young's modulus of the monolayer bismuthene accurately. Effect of the vertical side length on the fundamental natural frequency is negligible. However, vibrational characteristics are significantly affected by the horizontal side length.

Based on the molecular mechanics approach, the purpose of this paper is to analytically investigate the torsional buckling behavior of single-walled silicon carbide nanotubes (SiCNTs) with different values of diameter and chiral angles.

To this end, the mechanical properties and atomic structure of a silicon carbide (SiC) sheet are evaluated based on the density functional theory (DFT) within the framework of the generalized gradient approximation. After that force constants of the total potential energy are theoretically obtained through establishing a linkage between the viewpoints of the quantum mechanics and molecular mechanics. Explicit expressions are presented to obtain the critical buckling shear strain corresponding to different types of chirality. The present model is capable to calculate the torsional buckling behavior of SiCNTs related to various chiral angles. The critical buckling shear strain is obtained for various types of chirality and compared with each other.

It is concluded that for all diameters, zigzag nanotubes are more stable than armchair ones. Besides it is found that the minimum critical buckling shear strain is for nanotubes with (n, n/2) chiral vector.

Investigating the torsional buckling behavior of single-walled SiCNTs with different values of diameter and chiral angle. Obtaining the mechanical properties and atomic structure of the SiC sheet based on the DFT calculations. Establishing a linkage between the molecular mechanics and quantum mechanics and obtaining the force constants of the molecular mechanics. Presenting the closed-form expression to calculate the critical buckling shear strain of single-walled SiCNTs corresponding to various types of chirality.