Large deflection of a nonlocal gradient cantilever beam

Analysing scale phenomena in nanostructures is crucial for modelling and optimizing modern nanotechnological devices. Notably, soft nanostructures can be effectively designed as basic components of smart electro-mechanical systems that require geometrically nonlinear analyses as their structural parts undergo large deflection. Adoption of non-conventional approaches for accurate assessment of size effects is thus needed. The paper investigates the elastostatic behaviour of small-scale beams experiencing large displacements exploiting a consistent model of integral gradient elasticity. An iterative analytical solution procedure is proposed to address the geometrically nonlinear problem of soft nanobeams. The presented nonlocal stress gradient methodology is able to capture both stiffening and softening size-dependent nonlinear responses, thus generalizing the outcomes contributed by Vaccaro (2022). Effectiveness of the proposed approach for modelling and designing next-generation smart devices is finally shown by solving applicative nanomechanical problems. The presented methodology can be further extended to nonlinear analyses of three-dimensional nanocontinua to capture size effects of arbitrarily shaped structures undergoing large configuration changes.