A challenging task in nonlocal continuum mechanics consists in formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted to overcome issues inherent applicability of Eringen’s pure nonlocal theory to nanostructures, such as local/nonlocal mixtures of elasticity and integral models involving modified averaging kernels. These strategies can be applied to the ill-posed problem of flexure of a beam on Wieghardt nonlocal foundation without considering any fictitious boundary forces of constitutive type. A consistent formulation of nonlocal elastic foundation underlying a Bernoulli–Euler beam is thus conceived in the present paper by requiring that transverse displacements are convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem, equipped with nonlocal boundary conditions, which can be effectively exploited to solve nonlocal problems of beams resting on mixture reaction-driven continuous foundation. Effectiveness of the developed nonlocal approach is illustrated by analytically solving simple elasto-static problems of structural mechanics.

Elasticity problems of beams on reaction-driven nonlocal foundation / Pinnola, Francesco Paolo; Vaccaro, Marzia Sara; Barretta, Raffaele; Marotti de Sciarra, Francesco; Ruta, Giuseppe. - In: ARCHIVE OF APPLIED MECHANICS. - ISSN 0939-1533. - (2022), pp. 1-31. [10.1007/s00419-022-02161-x]

Elasticity problems of beams on reaction-driven nonlocal foundation

Ruta, Giuseppe
Membro del Collaboration Group
2022

Abstract

A challenging task in nonlocal continuum mechanics consists in formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted to overcome issues inherent applicability of Eringen’s pure nonlocal theory to nanostructures, such as local/nonlocal mixtures of elasticity and integral models involving modified averaging kernels. These strategies can be applied to the ill-posed problem of flexure of a beam on Wieghardt nonlocal foundation without considering any fictitious boundary forces of constitutive type. A consistent formulation of nonlocal elastic foundation underlying a Bernoulli–Euler beam is thus conceived in the present paper by requiring that transverse displacements are convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem, equipped with nonlocal boundary conditions, which can be effectively exploited to solve nonlocal problems of beams resting on mixture reaction-driven continuous foundation. Effectiveness of the developed nonlocal approach is illustrated by analytically solving simple elasto-static problems of structural mechanics.
2022
Wieghardt foundation; Mixture nonlocal model; Soil-structure interaction; Nonlocal effects; Eringen’s nonlocal elasticity
01 Pubblicazione su rivista::01a Articolo in rivista
Elasticity problems of beams on reaction-driven nonlocal foundation / Pinnola, Francesco Paolo; Vaccaro, Marzia Sara; Barretta, Raffaele; Marotti de Sciarra, Francesco; Ruta, Giuseppe. - In: ARCHIVE OF APPLIED MECHANICS. - ISSN 0939-1533. - (2022), pp. 1-31. [10.1007/s00419-022-02161-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1635023
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