A stress-driven local-nonlocal mixture model for Timoshenko nano-beams

TL;DR

This paper introduces a well-posed stress-driven mixture model for Timoshenko nano-beams that combines local and nonlocal effects, providing analytical solutions and revealing scale-dependent stiffening behavior.

Contribution

It proposes a novel stress-driven mixture model that overcomes ill-posedness in existing nonlocal beam theories and offers analytical solutions for nano-beam problems.

Findings

The model is well-posed and convex, avoiding issues of previous strain-driven formulations.

Analytical solutions for specific boundary conditions are derived.

Numerical results show stiffening behavior with increasing scale parameter.

Abstract

A well-posed stress-driven mixture is proposed for Timoshenko nano-beams. The model is a convex combination of local and nonlocal phases and circumvents some problems of ill-posedness emerged in strain-driven Eringen-like formulations for structures of nanotechnological interest. The nonlocal part of the mixture is the integral convolution between stress field and a bi-exponential averaging kernel function characterized by a scale parameter. The stress-driven mixture is equivalent to a differential problem equipped with constitutive boundary conditions involving bending and shear fields. Closed-form solutions of Timoshenko nano-beams for selected boundary and loading conditions are established by an effective analytical strategy. The numerical results exhibit a stiffening behavior in terms of scale parameter.