Effects of nonlinear hygro-thermo-mechanical loading on the bending response of nanobeams using nonlocal strain gradient theory

This article analyzes the bending response of functionally graded nanobeams under hygro-thermo-mechanical loadings. The nonlocal strain gradient theory (NSGT) is implemented to consider both hardening and softening impacts on the system response. The nanobeam is constructed of functionally graded materials (FGMs), whose characteristics change smoothly across the thickness direction according to a power-law distribution function. The system is subjected to hygro-thermal environments according to the sinusoidally distributed loading. By employing Hamilton's principle, the static equations of the system are acquired. Static responses of the nanobeam are obtained with the help of the Galerkin technique. The effects of material distribution and different boundary conditions on the system deflection are examined. The impacts of several system parameters, such as the nonlocal parameter, length scale parameter, temperature gradient, and moisture variation, on the static responses of the functionally graded nanoscale beams are determined.