A generalized functions based approach for stress-driven nanobeam bending problems subjected to point loads

Abstract

The research community has widely accepted the stress-driven nonlocal integral model to study static and dynamic characteristics of nanostructures. Although closed-form solutions for stress-driven point-loaded nanobeam bending problems that find potential for applications in the design of real-world MEMS/NEMS-based sensors have been explored recently, the static bending behavior of stress-driven Bernoulli-Euler and Timoshenko nanobeams subjected to point-loading conditions in various end configurations are studied in the present work wherein, analytical solutions for the same are arrived at by expressing the input bending and shear fields in terms of generalized functions for the first time. Equipped with the Helmholtz bi-exponential kernel function to model the nonlocality, the obtained solutions have demonstrated their ability to capture size-effects consistently. An overall stiffening effect on the nanobeam is observed as a consequence of these size-effects.