On nonlocal mechanics of curved elastic beams

TL;DR

This paper develops a nonlocal continuum mechanics model for curved nano-beams, capturing size effects and predicting stiffening behaviors crucial for nanotechnological device design.

Contribution

It generalizes nonlocal modeling from straight to curved structures, providing a mathematically well-posed framework for nano-beam analysis.

Findings

Size-dependent stiffening behavior predicted

Analytical responses for nano-sensors and nano-actuators established

Model applicable to a wide range of nanotechnological devices

Abstract

Curved beams are basic structural components of Nano-Electro-Mechanical-Sistems (NEMS) whose design requires appropriate modelling of scale effects. In the present paper, the size-dependent static behaviour of curved elastic nano-beams is investigated by stress-driven nonlocal continuum mechanics. Axial strain and flexural curvature fields are integral convolutions between equilibrated axial force and bending moment fields and an averaging kernel. The nonlocal integral methodology formulated here is the generalization to curved structures of the treatment in [Int. J. Eng. Science 115 (2017) 14-27] confined to straight beams. The corresponding nonlocal differential problem, supplemented with non-standard boundary conditions, is highlighted and shown to lead to mathematically well-posed problems of nano-engineering. The theoretical predictions, exhibiting stiffening nonlocal behaviours, are therefore appropriate to significantly model a wide range of small-scale devices of nanotechnological interest. The nonlocal approach is exploited by analytically establishing size-dependent responses of curved elastic nano-sensors and nano-actuators that are driven by the small-scale characteristic parameter.