Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory

ABSTRACT

Many experimental observations have shown that most nanostructures, such as carbon nanotubes, are often characterized by a certain degree of waviness along their axial direction. This geometrical imperfection has profound effects on the mechanical behavior of carbon nanotubes. In the present work, stability of a slightly curved carbon nanotube under lateral loading is investigated based on Eringen's nonlocal elasticity theory. Euler Bernoulli and Timoshenko beam theories are employed to obtain equilibrium equations. Winkler-Pasternak elastic foundation is used to approximate the effect of matrix. Effects of initial curvature, nonlocal parameter, beam length, and elastic foundation parameters on initiation of critical conditions are investigated.

KEYWORDS:

• Carbon nanotube
• snap-through
• nonlocal elasticity theory
• stability analysis
• Timoshenko beam theory
• waviness