Functionally graded nanobeams subjected to large deflection by considering surface effects

Abstract

In the current study, structurally graded nanobeams with distributed load are subjected to a large deflection analysis that takes surface effects into account. The nanobeams Young's elasticity modulus changes with thickness under a power-law function. The displacement elements are presented, generalization of the Young-Laplace formula is employed to account for the surface effects, and the total Lagrangian finite element formulation is utilized to get the outcomes by cracking the system of nonlinear differential equations founded on the Timoshenko beams theory. The reliability and correctness of the findings are confirmed by comparison with previously published publications. The investigation is done into how various characteristics, including length-to-thickness ratio, material gradient index, boundary conditions, and surface effects, affect the outcomes. The findings demonstrate that, in the presence of surface effects, residual surface tension plays a significant influence on the deflection of nanobeams. Additionally, a comparison of the power-law and exponential kinds of FG distribution is conducted in this study, and it is discovered that the FG materials with the power-law distribution are more applicable since they are less susceptible to surface effects than the exponential type.