Nonlocal nonlinear first-order shear deformable beam model for post-buckling analysis of magneto-electro-Thermo-elastic nanobeams

In this study, the size-dependent post-buckling behavior of Magneto-Electro-Thermo-Elastic (METE) nanobeams with different edge supports is investigated. Based on the nonlocal first-order shear deformation beam theory and considering the von Karman hypothesis, a size-dependent nonlinear METE nanobeam model is developed, in which the effects of small-scale parameter and thermo-electro-magnetic-mechanical loadings are incorporated. A numerical solution procedure based on the Generalized Differential Quadrature (GDQ) and pseudo arc-length continuation methods is utilized to describe the size-dependent post-buckling behavior of METE nanobeams under various boundary conditions. The effects of different parameters such as nonlocal parameter, external electric voltage, external magnetic potential, and temperature rise on the post-buckling path of METE nanobeams are explored. The results indicate that increasing the nondimensional nonlocal parameter, imposed positive voltage, negative magnetic potential, and temperature rise decreases the critical buckling load and post-buckling load-carrying capacity of METE nanobeams, while an increase in the negative voltage and positive magnetic potential leads to a considerable increase of critical buckling load as well as post-buckling strength of the METE nanobeams.