Stress-driven nonlocal integral model with discontinuity for size-dependent buckling and bending of cracked nanobeams using Laplace transform

Due to the frequent occurrence of cracks as structures age, examining the size-dependent responses of cracked micro/nanobeams is critical for safely designing and optimizing high-tech devices such as those used in MEMS/NEMS. With this understanding, we present the size-dependent bending and buckling studies of cracked nanobeams with different boundary edges adopting the well-posed stress-driven nonlocal integral model with discontinuity. Since the presence of a crack, the beam is divided into two segments connected by a rotary spring and a linear spring, whose elastic coefficients can be determined through compliance calibration methods. We propose an efficient method to solve the original integral model directly by converting the integral form of the nonlocal constitutive equation into a general equation through the Laplace transform technique, equipped with three extra constraint conditions. Subsequently, the governing equations of two beam segments are solved by considering the standard boundary and compatibility conditions as well as the extra constraint conditions, while the bending deformation and buckling loads of various bounded nanobeams are presented analytically in the presence of a crack. After verifying the derived formulation, the influence of crack length and location as well as nonlocality on the beam deflections and buckling loads of the first several modes are investigated in detail. Communicated by Rossana Dimitri.