DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory

Abstract

To investigate the thermal buckling of curved carbon nanotubes (CCNTs) embedded in an elastic medium, nonlocal elasticity theory is employed in combination with the theory of thin curved beams. Differential quadrature (DQ) method is implemented to discretize the resulted governing equations. Solving these equations enables us to estimate the critical temperature and the critical axial buckling load for CCNTs surrounded by an elastic medium and under the effect of a uniform temperature change. The elastic interaction between the nanotube and its surrounding medium is modeled as a Winkler-Pasternak elastic foundation. The fast convergence of the DQ method is demonstrated and also its accuracy is verified by comparing the results with available solutions in the literature. The effects of various parameters such as different boundary conditions, nonlocal parameter, Winkler and Pasternak elastic modulus, temperature and nanotube curvature on the critical buckling temperature and load are successfully studied. The results reveal that the critical buckling load depends significantly on the curvature of the CCNT. KeywordsCurved carbon nanotubes; thermal buckling; nonlocal elasticity theory; differential quadrature method.DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory 1 INTRODUCTION Nano-electro-mechanical systems (NEMS) are among fast growing technologies which deal with the production of nano-scale machines. These devices are being extensively used in many advanced industries such as aerospace, automotive, biotechnology, and audiometric equipment (Dai et al., 1996). Among the nanostructures, carbon nanotubes (CNTs) are one of the most important structures

Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

“…The relation between length of circular curved beam ( ) and the angle of curvature of beam ( ) can be written as [32] = .…”

“…where is the density of the circular curved nanobeam. The work done corresponding to temperature changes and elastic foundations can be written in the following form [32]:…”

“…In this research the problem was formulated on the framework of nonlocal elasticity theory. Furthermore, DQ thermal buckling analysis of embedded curved carbon nanotubes via nonlocal elasticity model has been presented by Setoodeh et al [32]. Nevertheless, explicit solution has been shown for size-and geometry-dependent free vibration of curved nanobeams including surface effects by Assadi and Farshi [33].…”