Buckling of nanobeams and nanorods with cracks

Abstract

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

Buckling analysis of cantilever nanobeams with defects

“…The slope v ′ of the displacement has finite jumps passing through the cross sections with stable cracks. According to the papers by Lellep and Sakkov (2006), Arif and Lellep (2019), Lellep and Lenbaum (2018), Lellep and Lenbaum (2019), the jump conditions for the spring model can be presented as In ( 17) the square brackets denote the finite jumps of the corresponding quantities at the given point. The value of the bending moment M at the step location a k can be derived from (6).…”

“…A new theory for the investigation of nanomaterials which does not ignore the internal length scale and accounts for the forces acting between atoms was developed by Eringen (2002Eringen ( , 1983. The nonlocal theory developed in (Eringen 1983) was successfully applied for determination of eigenvalues in problems of natural vibrations of nanobeams and nanorods shown by Lu et al (2006), Li et al (2011), Xia et al (2010), Arif and Lellep (2019), Roostai and Haghpanahi (2014), also by Lellep and Lenbaum (2018), Lellep and Lenbaum (2019) and Bagdatli (2015), Thai (2012). Polizzotto (2001) employed variational principles for derivation of main equations of nonlocal theory of elasticity.…”

Stability of nanobeams and nanoplates with defects

“…The critical buckling loads for simply supported and cantilever nanobeams can be determined by following the papers by Arif and Lellep [5,6]. The boundary conditions for simply supported and cantilever nanobeams are presented by ( 17)-(20).…”