TY - JOUR
T1 - Buckling analysis of embedded nanotubes using gradient continuum theory
AU - Wang, B. L.
AU - Hoffman, M.
AU - Yu, A. B.
PY - 2012
Y1 - 2012
N2 - The buckling of nanotubes embedded in an elastic matrix is modeled within the framework of Timoshenko beams. Both a stress gradient and a strain gradient approach are considered. The energy variational approach is adopted to obtain the critical buckling loads. The dependences of the buckling load on the nonlocal parameter, the stiffness of the surrounding elastic matrix, and the transverse shear stiffness of the nanotubes are obtained. The results show a significant dependence of critical buckling load on the nonlocal parameter and the stiffness of the surround matrix. The Euler beam model, which neglects the shear stiffness of the nanotubes, over-predicts the critical buckling load. It is also found that the strain gradient model provides the lower bound and the stress gradient model provides the upper bound for the critical buckling load of nanotubes. In addition to mechanical buckling, thermally induced buckling of the nanotubes embedded in an elastic matrix is also studied. All results are expressed in closed-form and therefore are easy to use by materials scientists and engineers for the design of nanotubes and their composites.
AB - The buckling of nanotubes embedded in an elastic matrix is modeled within the framework of Timoshenko beams. Both a stress gradient and a strain gradient approach are considered. The energy variational approach is adopted to obtain the critical buckling loads. The dependences of the buckling load on the nonlocal parameter, the stiffness of the surrounding elastic matrix, and the transverse shear stiffness of the nanotubes are obtained. The results show a significant dependence of critical buckling load on the nonlocal parameter and the stiffness of the surround matrix. The Euler beam model, which neglects the shear stiffness of the nanotubes, over-predicts the critical buckling load. It is also found that the strain gradient model provides the lower bound and the stress gradient model provides the upper bound for the critical buckling load of nanotubes. In addition to mechanical buckling, thermally induced buckling of the nanotubes embedded in an elastic matrix is also studied. All results are expressed in closed-form and therefore are easy to use by materials scientists and engineers for the design of nanotubes and their composites.
UR - http://handle.uws.edu.au:8081/1959.7/548504
U2 - 10.1016/j.mechmat.2011.10.003
DO - 10.1016/j.mechmat.2011.10.003
M3 - Article
SN - 0167-6636
VL - 45
SP - 52
EP - 60
JO - Mechanics of Materials
JF - Mechanics of Materials
ER -