Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics

This paper proposes a novel variable-length beam element that takes into account the effect of beam spinning. This is the first such beam element of variable length based on the absolute nodal coordinate formulation. In addition to the position and slope vectors, the angles of rotation around the element axis of cross sections that contain two nodes are introduced into the element coordinates to describe the spinning of an assumed Euler-Bernoulli beam with circular cross section. The material coordinates of the two nodes are also included in the arbitrary Lagrangian-Eulerian description used for previous element to describe the varying element length caused by mass transportation at the boundaries. The proposed element facilitates convenient and effective numerical modeling of the dynamics of a circular-cross-section beam with transportation boundaries and that is spinning. Numerical examples demonstrate that the proposed element can describe the dynamic behavior of a circular-cross-section beam effectively. In the field of engineering, this novel element could be used in the dynamic analysis of drill stems, the slender workpiece of a cylindrical shaft during the turning process, and the lead screw in a ball screw mechanism.

Section: Introductionmentioning

confidence: 99%

A Variable-Length Beam Element Incorporating the Effect of Spinning

Shao‐Horn

Deng

Sun

et al. 2017

“…modified continuum mechanics approaches) is required as they are relatively simple to be applied with less time-consuming without compromising the accuracy of the results. Eringen (1983) proposed the nonlocal elasticity theory which has been widely used for continuum mechanics modeling of CNTs (Wang et al, 2008;Murmu and Pradhan, 2010;Wang et al, 2010;Murmu and Adhikari, 2011;Narendar and Gopalakrishnan, 2012;Thai, 2012;Thai and Vo, 2012;Şimşek and Yurtcu, 2013;Tounsi et al, 2013, Asemi et al, 2014. In this theory, the effects of small scaling parameter on the mechanical analysis of nanostructures are taken into account.…”

Section: Introductionmentioning

confidence: 99%

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

Setoodeh

Derahaki

Bavi

2015

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

“…Nanoplates are used in several nanotechnology applications and often subjected to in-plane loads which can lead to failure by buckling, especially considering their extremely small thickness (Asemi et al, 2014a(Asemi et al, , 2014b. Buckling behavior and sensitivity of nonlocal orthotropic nanoplates with material uncertainty have been investigated by Radebe and Adali (2014) neglecting the surface effect.…”

Section: Introductionmentioning

confidence: 99%

Effect of Surface Stress on the Buckling of Nonlocal Nanoplates Subject to Material Uncertainty

Radebe

Adali

2015

At the nano scale, the effect of surface stress becomes prominent as well as the so-called small scale effect. Furthermore due to difficulties in making accurate measurements at nano-scale as well as due to due to molecular defects and manufacturing tolerances, there exists a certain degree of uncertainty in the determination of the material properties of nano structures This, in turn, introduces some degree of uncertainty in the computation of the mechanical response of the nano-scale components. In the present study a convex model is employed to take surface tension, small scale parameter and the elastic constants as uncertain-butbounded quantities in the buckling analysis of rectangular nanoplates. The objective is to determine the lowest buckling load for a given level of uncertainty to obtain a conservative estimate by taking the worst-case variations of material properties. Moreover the sensitivity of the buckling load to material uncertainties is also investigated.