Abstract
A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be useful for the design and optimization of small-scale devices exhibiting flexural behaviour.
Highlights
Some devices designed at small scales [1,2,3,4], such as nano- and micro-sensors, actuators, piezoelectric systems, and AFM indenters can be modeled as beams but require specific stress–strain relations to predict their mechanical behaviour
This issue is taken into account and it is overcome with the aid of a nonlocal formulation
Bending behaviour modeling is a crucial issue in the design of several structures at small scales
Summary
Some devices designed at small scales [1,2,3,4], such as nano- and micro-sensors, actuators, piezoelectric systems, and AFM indenters can be modeled as beams but require specific stress–strain relations to predict their mechanical behaviour. That consistent approach [31,32], useful to detect some analytical solutions of mechanical problems of applicative interest [33], is adopted in this paper to formulate a proper nonlocal stress–strain relation In this way the strain at a point becomes a function of the stress field introducing a space dependence that makes the nonlocal constitutive law different from the local elastic one. This article shows a useful approach to finding analytical solutions of the viscoelastic nonlocal Timoshenko bending problem In this way, a mechanical model and a parametric study—useful for mechanical design of advanced structural devices at small scales—are provided, and some useful tools for predicting the time-dependent behaviour of nano-systems are shown in detail
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