Bending Responses of Bi-Directional Advanced Composite Nanobeams Using Higher Order Nonlocal Strain Gradient Theory

Abstract

The bending response of two-dimensional (2D) functionally graded (FG) nonlocal strain gradient nanobeams is explored analytically in this work. The longitudinal and transverse orientations vary in material gradation and material characteristics. Kinematic relations of nanobeams are proposed according to hybrid hyperbolic-parabolic functions. The virtual work principle obtains the equilibrium equations, which are then solved using Navier's method. The accuracy and dependability of the suggested analytical model are demonstrated by comparing the results to predictions made in the literature. A thorough parametric study also determines how sensitive the material distribution, the nonlocal length-scale parameter, the strain gradient microstructure-scale parameter, and the geometry are to how the bending response and stresses of 2D FG nanobeams. The results obtained provide benchmark results, which can be used in the design of composite structures.